%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Marsha J. Berger", %%% version = "2.27", %%% date = "01 October 2024", %%% time = "09:17:13 MDT", %%% filename = "berger-marsha-j.bib", %%% address = "Courant Institute - New York University %%% 251 Mercer St. %%% New York, NY %%% USA", %%% telephone = "+1 212 998 3305", %%% FAX = "+1 212 995 4121", %%% checksum = "50965 2823 12706 126214", %%% email = "berger at cims.nyu.edu (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "Numerical Analysis", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of %%% publications of Marsha J. Berger. The %%% companion LaTeX file berger-marsha-j.ltx can %%% be used to typeset this bibliography. %%% %%% At version 2.27, the year coverage looked %%% like this: %%% %%% 1975 ( 1) 1992 ( 1) 2009 ( 1) %%% 1976 ( 0) 1993 ( 5) 2010 ( 0) %%% 1977 ( 0) 1994 ( 4) 2011 ( 1) %%% 1978 ( 1) 1995 ( 5) 2012 ( 1) %%% 1979 ( 0) 1996 ( 4) 2013 ( 1) %%% 1980 ( 0) 1997 ( 2) 2014 ( 2) %%% 1981 ( 2) 1998 ( 4) 2015 ( 1) %%% 1982 ( 1) 1999 ( 3) 2016 ( 1) %%% 1983 ( 6) 2000 ( 1) 2017 ( 2) %%% 1984 ( 2) 2001 ( 1) 2018 ( 0) %%% 1985 ( 8) 2002 ( 5) 2019 ( 0) %%% 1986 ( 1) 2003 ( 3) 2020 ( 0) %%% 1987 ( 3) 2004 ( 4) 2021 ( 1) %%% 1988 ( 1) 2005 ( 6) 2022 ( 2) %%% 1989 ( 5) 2006 ( 3) 2023 ( 1) %%% 1990 ( 3) 2007 ( 1) 2024 ( 2) %%% 1991 ( 2) 2008 ( 2) %%% %%% Article: 35 %%% Book: 2 %%% InCollection: 16 %%% InProceedings: 21 %%% Manual: 1 %%% Misc: 1 %%% PhdThesis: 1 %%% Proceedings: 16 %%% TechReport: 13 %%% %%% Total entries: 106 %%% %%% This file is available as part of the BibNet %%% Project. The master copy is available for %%% public access on ftp.math.utah.edu in the %%% directory tree /pub/bibnet/authors. It is %%% mirrored to netlib.bell-labs.com in the directory %%% tree /netlib/bibnet/authors, from which it is %%% available via anonymous ftp and the Netlib %%% service. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{"\hyphenation{Le-Veque}"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ACTA-NUMERICA= "Acta Numerica"} @String{j-AIAA= "AIAA Journal"} @String{j-APPL-NUM-MATH= "Applied Numerical Mathematics: Transactions of IMACS"} @String{j-COMM-PURE-APPL-MATH= "Communications on Pure and Applied Mathematics (New York)"} @String{j-IEEE-TRANS-COMPUT= "IEEE Transactions on Computers"} @String{j-IJHPCA= "The International Journal of High Performance Computing Applications"} @String{j-INT-J-COMPUT-FLUID-DYN= "International Journal of Computational Fluid Dynamics"} @String{j-J-COMPUT-PHYS= "Journal of computational physics"} @String{j-J-PAR-DIST-COMP= "Journal of Parallel and Distributed Computing"} @String{j-J-SCI-COMPUT= "Journal of Scientific Computing"} @String{j-MATH-COMPUT= "Mathematics of Computation"} @String{j-PHILOS-TRANS-R-SOC-LOND-SER-A= "Philosophical Transactions of the Royal Society A: Mathematical, Physical, and Engineering Sciences"} @String{j-SIAM-J-NUMER-ANAL= "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-SCI-COMP= "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP= "SIAM Journal on Scientific and Statistical Computing"}

%%% ==================================================================== %%% Publisher abbreviations:

@String{pub-ACADEMIC= "Academic Press"} @String{pub-ACADEMIC:adr= "New York, NY, USA"} @String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-AIAA= "American Institute of Aeronautics and Astronautics"} @String{pub-AIAA:adr= "Aerospace Center, 370 L'Enfant Promenade, SW, Washington, DC 20024-2518"} @String{pub-AMS= "American Mathematical Society"} @String{pub-AMS:adr= "Providence, RI, USA"} @String{pub-BIRKHAUSER= "Birkh{\"{a}}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-CRC= "CRC Press"} @String{pub-CRC:adr= "2000 N.W. Corporate Blvd., Boca Raton, FL 33431-9868, USA"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-IMACS= "IMACS"} @String{pub-IMACS:adr= "Department of Computer Science, Rutgers University, New Brunswick, NJ, USA"} @String{pub-NORTH-HOLLAND= "North-Hol{\-}land"} @String{pub-NORTH-HOLLAND:adr= "Amsterdam, The Netherlands"} @String{pub-SIAM= "Society for Industrial and Applied Mathematics"} @String{pub-SIAM:adr= "Philadelphia, PA, USA"} @String{pub-STUDENTLITTERATUR= "Studentlitteratur"} @String{pub-STUDENTLITTERATUR:adr= "Lund, Sweden"} @String{pub-SV= "Spring{\-}er-Ver{\-}lag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WILEY= "Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"} @String{pub-WORLD-SCI= "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr= "P. O. Box 128, Farrer Road, Singapore 9128"}

%%% ==================================================================== %%% Bibliography entries:

@TechReport{Allender:1975:VNC, author = "J. Allender and K. Saunders and M. Berger", title = "Verification of Numerical Circulation Models for {Lake Michigan}", number = "43", institution = "Canada Centre for Inland Waters", address = "Burlington, ON, Canada", year = "1975", bibdate = "Fri Oct 26 18:13:53 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "Scientific Series", acknowledgement = ack-nhfb, } @Manual{Berger:1978:NAP, author = "M. Berger and J. Bolstad and others", title = "Numerical Analysis Program Library User's Guide", organization = "Stanford Linear Accelerator Center Computing Services", address = "Stanford, CA, USA", year = "1978", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InCollection{Berger:1981:PCM, author = "Marsha Berger and J. Oliger and G. Rodrigue", title = "Predictor-Corrector Methods for the Solution of Time-Dependent Parabolic Problems on Parallel Processors", crossref = "Schultz:1981:EPS", pages = "197--201", year = "1981", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Lawrence Livermore Report UCRL-87522.", acknowledgement = ack-nhfb, } @PhdThesis{Berger:1982:AMR, author = "Marsha J. Berger", title = "Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations", type = "{Ph.D. dissertation}", school = "Department of Computer Science, Stanford University", address = "Stanford, CA, USA", pages = "vi + 118", month = aug, year = "1982", bibdate = "Mon Oct 22 18:06:16 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Computer Science Report No. STAN-CS-82-924.", abstract = "In many time dependent simulations, the solution on most of the domain will be fairly smooth, with discontinuities or highly oscillatory phenomena occurring over only a small fraction of the domain. In problems such as these, a mesh refinement approach can be the most efficient, and often the only practical, solution method. Refined grids with smaller and smaller mesh spacing are placed only where they are needed. Since we are solving a time dependent problem, the regions needing refinement will change, and therefore our grids must adapt with time as well. This thesis presents a method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations (pde) using explicit finite difference techniques. Based upon Richardson-type estimates of the local truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. In addition, this approach is recursive in that fine grids can themselves contain even finer subgrids. Those grids with finer mesh width in space will also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. In chapter 2 we present the full mesh refinement algorithm. This includes a discussion of the error estimation procedure, as well as the integration algorithm itself. We calculate how often the error estimation and subsequent grid generation should be performed to minimize the total cost of the algorithm. In chapter 3 we discuss the interface equations used at the boundary of the fine and coarse grids. Boundary schemes are presented for those component grids with boundaries internal to the problem domain, since in these cases boundary conditions are not supplied with the pde. We present a new stability proof for the case of interpolation interface conditions with the Lax--Wendroff difference scheme for mesh refinement in time and space. We also include in this chapter a discussion of conservation properties of the algorithm, including both the interface conditions and the regridding procedure. We develop a procedure to derive conservative interface conditions so that if the approximate solutions converge, they will converge to a weak solution of the pde. This is important in computing the correct shock location in cases where the solution is discontinuous. \ldots{}", acknowledgement = ack-nhfb, advisor = "Joe Oliger", } @InProceedings{Berger:1983:AMR, author = "Marsha Berger and G. Hedstrom and J. Oliger and G. Rodrigue", title = "Adaptive Mesh Refinement for $1$-Dimensional Gas Dynamics", crossref = "Ames:1983:MSE", pages = "43--47", year = "1983", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Also as Lawrence Livermore UCRL-87522", series = "IMACS Transactions on Scientific Computing", acknowledgement = ack-nhfb, xxauthor = "Marsha Berger and G. Hedstrom and G. Rodrigue and J. Oliger", } @InCollection{Berger:1983:DSA, author = "Marsha Berger", title = "Data Structures for Adaptive Mesh Refinement", crossref = "Babuska:1983:ACM", pages = "237--251", year = "1983", MRclass = "65M50 (65V05)", MRnumber = "792530", bibdate = "Mon Oct 22 18:39:37 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", abstract = "e examine the use of data structures in the design and implementation of an adaptive mesh refinement algorithm for solving hyperbolic partial differential equations. We also describe the algorithms and graph structures which form the core of an automatic grid generation package that is part of the mesh refinement program.", acknowledgement = ack-nhfb, classmath = "65N50 (Mesh generation and refinement (BVP of PDE)) 65N22 (Solution of discretized equations (BVP of PDE)) 35L50 (First order hyperbolic systems, boundary value problems)", keywords = "adaptive mesh refinement; automatic grid generation; data structures; graph structures", } @InCollection{Hedstrom:1983:AMR, author = "Gerald Hedstrom and Garry Rodrigue and Marsha Berger and Joseph Oliger", title = "Adaptive mesh refinement for $1$-dimensional gas dynamics", crossref = "Stepleman:1983:SCA", pages = "43--47", year = "1983", MRclass = "65M50", MRnumber = "MR751602", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Berger:1984:AMM, author = "Marsha Berger and A. Jameson", title = "An Adaptive Multigrid Method for the {Euler} Equations", crossref = "Soubbaramayer:1985:NIC", pages = "??--??", year = "1984", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Article{Berger:1984:AMR, author = "Marsha Berger and Joseph Oliger", title = "Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations", journal = j-J-COMPUT-PHYS, volume = "53", number = "3", pages = "484--512", month = mar, year = "1984", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/0021-9991(84)90073-1", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", MRclass = "65M50", MRnumber = "739112", MRreviewer = "B. M. Herbst", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib", abstract = "An adaptive numerical method for hyperbolic partial differential equations is presented. Based upon Richardson-type estimates of the local truncation error, refined grids are created or removed during the process. The composite grid consists of a hierarchy of rotated uniform rectangular refined meshes. This makes it possible to approximate discontinuities such as moving shock fronts with arbitrary orientations. The finer grids have also smaller step sizes in time thus maintaining the ratio of space/time differencing. Various integrating schemes can be used on component grids. The interaction between grids is performed by injections and interpolations. Data structures for the composite grid are briefly but clearly described. Numerical examples in one and two space dimensions show that the adaptive method is superior to the use of a conventional uniform grid both in the terms of computational time and approximation of the solution.", acknowledgement = ack-nhfb, classmath = "65M50 (Mesh generation and refinement (IVP of PDE)) 65M15 (Error bounds (IVP of PDE)) 35L45 (First order hyperbolic systems, initial value problems)", fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", keywords = "adaptive mesh refinement; local truncation error; moving shock fronts; Numerical examples", } @Article{Berger:1985:AAG, author = "Marsha Berger and A. Jameson", title = "Automatic Adaptive Grid Refinement for the {Euler} Equations", journal = j-AIAA, volume = "23", number = "4", pages = "561--568", month = apr, year = "1985", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "MAE Report No. 1633, October 1983, Princeton University, and NYU Report No. DOE/ER/03077-202, October 1983.", acknowledgement = ack-nhfb, } @InProceedings{Berger:1985:AMM, author = "Marsha J. Berger and Antony Jameson", title = "An adaptive multigrid method for the {Euler} equations", crossref = "Soubbaramayer:1985:NIC", pages = "92--97", year = "1985", bibdate = "Mon Oct 22 18:26:59 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, classmath = "76M99 (Basic methods in fluid mechanics) 76B10 (Free-streamline theory and appl.)", keywords = "local adaptive grid refinement; local truncation error; locally uniform fine rectangles; two dimensional steady Euler equation", } @InProceedings{Berger:1985:AMR, author = "Marsha Berger", title = "Adaptive Mesh Refinement for Hyperbolic Equations", crossref = "Engquist:1985:LSC", pages = "31--40", year = "1985", MRclass = "65M50 (76-08)", MRnumber = "818760", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", abstract = "We describe a method of adaptive mesh refinement for the solution of hyperbolic partial differential equations. This algorithm uses an automatic error estimator to determine where the coarse grid accuracy is insufficient, and creates locally uniform fine grid patches in these regions. The finer grids have a smaller mesh width in time as well as space. We also discuss the stability and conservation of the numerical procedures used at an interface between a fine and coarse grid.", acknowledgement = ack-nhfb, classmath = "65M50 (Mesh generation and refinement (IVP of PDE)) 65M12 (Stability and convergence of numerical methods (IVP of PDE)) 35L45 (First order hyperbolic systems, initial value problems)", keywords = "adaptive mesh refinement; automatic error estimator; stability", } @InProceedings{Berger:1985:PSP, author = "Marsha Berger and Shahid Bokhari", title = "A Partitioning Strategy for {PDEs} across Multiprocessors", crossref = "DeGroot:1985:PIC", pages = "166--170", year = "1985", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Article{Berger:1985:SIM, author = "Marsha J. Berger", title = "Stability of Interfaces with Mesh Refinement", journal = j-MATH-COMPUT, volume = "45", number = "172", pages = "301--318", month = oct, year = "1985", CODEN = "MCMPAF", ISSN = "0025-5718 (print), 1088-6842 (electronic)", ISSN-L = "0025-5718", MRclass = "65M50 (Mesh generation and refinement (IVP of PDE)) 65M12 (Stability and convergence of numerical methods (IVP of PDE)) 35L45 (First order hyperbolic systems, initial value problems)", MRnumber = "804925", MRreviewer = "J. T. Oden", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "ICASE Report No. 83-42, August, 1983.", ZMnumber = "0647.65065", abstract = "We study the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, we derive a root condition which implies stability for the initial-boundary value problem for this type of interface. From the root condition, we prove the stability of several interface equations using the maximum principle. In some cases, the final verification step can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, we prove stability for Lax--Wendroff with all the interface conditions considered, and for leapfrog with interpolation interface conditions when the fine and coarse grids overlap.", acknowledgement = ack-nhfb, classcodes = "B0290P (Differential equations); C4170 (Differential equations)", corpsource = "Inst. for Comput. Applications in Sci. and Eng., NASA Langley Res. Center, Hampton, VA, USA", fjournal = "Mathematics of Computation", journal-URL = "http://www.ams.org/mcom/", keywords = "computer program; convergence of numerical methods; difference equations; differential equations; finite element analysis; finite-difference approximations; hyperbolic partial differential equations; initial value problems; initial-boundary value problem; interface equations; interpolation interface conditions; Lax--Wendroff method; leapfrog method; maximum principle; mesh refinement; partial; root condition; stability; unit circle", treatment = "T Theoretical or Mathematical", } @Article{Berger:1986:DSA, author = "Marsha J. Berger", title = "Data Structures for Adaptive Grid Generation", journal = j-SIAM-J-SCI-STAT-COMP, volume = "7", number = "3", pages = "904--916", month = jul, year = "1986", CODEN = "SIJCD4", ISSN = "0196-5204", bibdate = "Tue Apr 29 19:18:28 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", abstract = "This paper presents some ideas from the pattern recognition literature in designing grid generation package. Trees are used to do the grid management for this type of data structure. Automatic grid generation algorithm is used for data structure with special neighbor properties. Some numerical computations are also presented. No experiments were performed for the proposed algorithm.", acknowledgement = ack-nhfb, classification = "C1160 (Combinatorial mathematics); C4170 (Differential equations); C6120 (File organization)", corpsource = "Courant Inst. of Math. Sci., New York Univ., NY, USA", fjournal = "SIAM Journal on Scientific and Statistical Computing", journal-URL = "http://epubs.siam.org/loi/sijcd4", keywords = "adaptive grid generation; adaptive mesh refinement; automatic grid generation algorithms; data structures; difference equations; difference schemes; grid management; nearest neighbor properties; partial differential equations; Trees; trees (mathematics)", treatment = "P Practical; T Theoretical or Mathematical", } @TechReport{Berger:1987:AFD, author = "Marsha Berger", title = "Adaptive Finite Difference Methods in Fluid Dynamics", type = "NYU Report", number = "DOE/ER/03077-277", institution = "New York University", address = "New York, NY, USA", pages = "????", month = feb, year = "1987", MRclass = "76-08", MRnumber = "1024154", bibdate = "Sat Oct 24 11:11:27 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Lecture notes prepared for the short course in Computational Fluid Dynamics at the von Karman Institute for Fluid Dynamics, March 1987.", acknowledgement = ack-nhfb, } @Article{Berger:1987:CGI, author = "Marsha J. Berger", title = "On Conservation at Grid Interfaces", journal = j-SIAM-J-NUMER-ANAL, volume = "24", number = "5", pages = "967--984", month = oct, year = "1987", CODEN = "SJNAAM", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65M05 (65M10)", MRnumber = "89b:65203", MRreviewer = "O. Widlund", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; JSTOR database", note = "ICASE Report No. 84-43, September, 1984.", abstract = "A procedure is presented to derive conservative difference approximations of hyperbolic systems of conservation laws at the grid interfaces for two-dimensional grids which overlap in an arbitrary configuration. Also, interface conditions are given to guarantee that if the solution converges, it converges to a weak solution of the equations.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @Article{Berger:1987:PSN, author = "Marsha Berger and Shahid Bokhari", title = "A Partitioning Strategy for Non-Uniform Problems on Multiprocessors", journal = j-IEEE-TRANS-COMPUT, volume = "C-36", number = "5", pages = "570--580", month = may, year = "1987", CODEN = "ITCOB4", ISSN = "0018-9340 (print), 1557-9956 (electronic)", ISSN-L = "0018-9340", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "ICASE Report No. 85-55, Nov. 1985.", acknowledgement = ack-nhfb, fjournal = "IEEE Transactions on Computers", journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12", } @Article{Berger:1988:RAN, author = "Marsha Berger and Robert V. Kohn", title = "A rescaling algorithm for the numerical calculation of blowing-up solutions", journal = j-COMM-PURE-APPL-MATH, volume = "41", number = "6", pages = "841--863", year = "1988", CODEN = "CPAMAT", ISSN = "0010-3640 (print), 1097-0312 (electronic)", ISSN-L = "0010-3640", MRclass = "65P05 (35B40 35K57)", MRnumber = "MR948774 (89g:65154)", MRreviewer = "Hong Yuan Fu", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", abstract = "A method is developed for computing solutions of certain nonlinear evolution equations near a developing singularity in space-time. The main tools are rescaling and mesh refinement; in essence, the method uses a varying spatial grid and time step, linked at each point of space-time to the magnitude of the computed solution. The discussion is focused on the specific equation $ u_t - u_{xx} = u \quad p $ on an interval, with $ u = 0 $ at the endpoints. The numerical results, which remain accurate as the magnitude of $u$ grows from $ O(1)$ to $ O(10^{12})$, agree with the behavior conjectured by {\it V. A. Galaktionov} and {\it S. A. Posashkov} [Diff. Uravn. 22, 1165--1173 (1986; Zbl 0632.35028)] on the basis of a formal expansion.", acknowledgement = ack-nhfb, fjournal = "Communications on Pure and Applied Mathematics", journal-URL = "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312", } @InProceedings{Berger:1989:ACM, author = "Marsha Berger and Randy LeVeque", title = "An Adaptive {Cartesian} Mesh Algorithm for the {Euler} Equations in Arbitrary Geometries", crossref = "Anonymous:1989:CFD", pages = "??", year = "1989", bibdate = "Mon Mar 6 18:16:11 MST 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Berger:1989:AMR, author = "Marsha Berger", editor = "G. Rodrigue", booktitle = "Parallel Processing for Scientific Computing, Proc. 1987 {SIAM} Conference on Parallel Processing, Los Angeles, California", title = "Adaptive Mesh Refinement for Parallel Processors", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "??", year = "1989", ISBN = "??", ISBN-13 = "??", LCCN = "??", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Ultracomputer Note 130, Dec. 1987.", acknowledgement = ack-nhfb, } @Article{Berger:1989:LAM, author = "Marsha Berger and Phillip Colella", title = "Local Adaptive Mesh Refinement for Shock Hydrodynamics", journal = j-J-COMPUT-PHYS, volume = "82", number = "1", pages = "64--84", month = may, year = "1989", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/0021-9991(89)90035-1", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib", note = "Lawrence Livermore Laboratory Report No. UCRL-97196.", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", } @InProceedings{Berger:1989:SAA, author = "Marsha Berger", editor = "J. Flaherty and others", booktitle = "Adaptive Methods for Partial Differential Equations: Proc. Workshop on Adaptive Computational Methods for Partial Differential Equations, {RPI}, Oct. 1988", title = "Some Applications of Adaptive Mesh Refinement", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "150--159", year = "1989", ISBN = "??", ISBN-13 = "??", LCCN = "??", MRclass = "65N50", MRnumber = "1107086", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", ZMnumber = "0694.65061", acknowledgement = ack-nhfb, } @InProceedings{Berger:1990:CMA, author = "Marsha Berger and Randy LeVeque", title = "{Cartesian} Meshes and Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations", crossref = "Engquist:1990:TIC", pages = "??", year = "1990", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Berger:1990:SBC, author = "Marsha Berger and Randy LeVeque", booktitle = "Proc. Symposium on Computational Technology for Flight Vehicles", title = "Stable Boundary Conditions for {Cartesian} Grid Calculations", publisher = "Pergamon Press", address = "??", pages = "??", month = nov, year = "1990", ISBN = "??", ISBN-13 = "??", LCCN = "??", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "ICASE Report No. 90-37, May, 1990.", acknowledgement = ack-nhfb, } @InCollection{Berger:1991:CMA, author = "Marsha Berger and Randall LeVeque", booktitle = "Third International Conference on Hyperbolic Problems, Vol.\ I, {II} (Uppsala, 1990)", title = "{Cartesian} meshes and adaptive refinement for hyperbolic partial differential equations", publisher = pub-STUDENTLITTERATUR, address = pub-STUDENTLITTERATUR:adr, pages = "67--73", year = "1991", MRclass = "76M20 (65N50)", MRnumber = "MR1109274", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Berger:1991:RDS, author = "Marsha Berger and Randy LeVeque", booktitle = "{AIAA 91-1602}, 10th {AIAA} Computational Fluid Dynamics Conference, Honolulu, June, 1991", title = "A Rotated Difference Scheme for {Cartesian} Grids in Complex Geometries", publisher = pub-AIAA, address = pub-AIAA:adr, pages = "??", year = "1991", ISBN = "??", ISBN-13 = "??", LCCN = "??", bibdate = "Mon Mar 6 18:16:11 MST 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Article{Berger:1992:APC, author = "Marsha Berger and Isidore Rigoutsos", title = "An Algorithm for Point Clustering and Grid Generation", journal = "IEEE Trans. Sys. Man. \& Cyber.", volume = "21", number = "5", pages = "1278--1286", month = sep # "\slash " # oct, year = "1992", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "NYU Technical Report 501, April, 1990.", acknowledgement = ack-nhfb, } @InProceedings{Berger:1993:ACG, author = "Marsha Berger and J. Melton and F. Enomoto", booktitle = "{AIAA} Paper 93-3386, 11th {AIAA} Computational Fluid Dynamics Conference, Orlando, Fla., July, 1993", title = "{3D} Automatic {Cartesian} Grid Generation for {Euler} Flows", publisher = pub-AIAA, address = pub-AIAA:adr, pages = "??", year = "1993", ISBN = "??", ISBN-13 = "??", LCCN = "??", bibdate = "Mon Mar 6 18:16:11 MST 1995", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Berger:1993:SAM, author = "Marsha Berger and J. Saltzman", title = "Structured Adaptive Mesh Refinement on the {Connection Machine}", crossref = "Sincovec:1993:PSS", pages = "??", year = "1993", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Berger:1993:UMT, author = "Marsha Berger and V. Venkatakrishnan and D. Mavriplis", title = "Unstructured Multigrid through Agglomeration", crossref = "Melson:1993:SCM", pages = "??--??", year = "1993", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, remark = "Is this the same as NASA Ames Research Laboratory report 94N21484 (3-Nov-2004)??", } @Article{Bell:1994:TDA, author = "John Bell and Marsha Berger and Jeff Saltzman and Mike Welcome", title = "Three-Dimensional Adaptive Mesh Refinement for Hyperbolic Conservation Laws", journal = j-SIAM-J-SCI-COMP, volume = "15", number = "1", pages = "127--138", month = jan, year = "1994", CODEN = "SJOCE3", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65M06 (76M20 76N10)", MRnumber = "MR1257158 (95d:65070)", MRreviewer = "Corneliu Berbente", bibdate = "Tue Apr 29 18:25:50 MDT 1997", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", abstract = "This is a descriptive account of how an adaptive mesh refinement algorithm may be used in solving systems of hyperbolic conservation laws. The method is illustrated by considering a particular case of a shock wave hitting a bubble of Freon-22. The results of the calculations are given.", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Berger:1994:AC, author = "Marsha J. Berger and Jeff S. Saltzman", title = "{AMR} on the {CM-2}", journal = j-APPL-NUM-MATH, volume = "14", number = "1--3", pages = "239--253", day = "14", month = apr, year = "1994", CODEN = "ANMAEL", ISSN = "0168-9274 (print), 1873-5460 (electronic)", ISSN-L = "0168-9274", MRclass = "65M60", MRnumber = "1 273 827", bibdate = "Wed Jul 28 14:35:41 MDT 1999", bibsource = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1994&volume=14&issue=1-3; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib", note = "Proceedings of the Third ARO Workshop on Adaptive Methods for Partial Differential Equations (Troy, NY, 1992). Also, RIACS Report No. 92-16.", URL = "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1994&volume=14&issue=1-3&aid=452", ZMnumber = "0803.76062", abstract = "We describe the development of a structured adaptive mesh algorithm (AMR) for the CM-2. We develop a data layout scheme that preserves locality even for communication between fine and coarse grids. On 8K of a 32K machine we achieve performance slightly less than one CPU of the Cray Y-MP. We apply our algorithm to an inviscid compressible flow problem.", acknowledgement = ack-nhfb, fjournal = "Applied Numerical Mathematics: Transactions of IMACS", journal-URL = "http://www.sciencedirect.com/science/journal/01689274/", keywords = "adaptive mesh algorithm (AMR); Connection Machine CM-2", } @InProceedings{Berger:1994:FVM, author = "M. J. Berger and R. J. LeVeque and L. G. Stern", title = "Finite volume methods for irregular one-dimensional grids", crossref = "Gautschi:1994:MCH", pages = "255--259", year = "1994", DOI = "https://doi.org/10.1090/psapm/048/1314852", MRclass = "65M06 (65M12 76M25)", MRnumber = "1314852", bibdate = "Thu Oct 25 14:53:00 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Aftosmis:1995:ASM, author = "M. Aftosmis and J. Melton and M. Berger", title = "Adaptation and Surface Modeling for {Cartesian} Mesh Methods", crossref = "Dolling:1995:ACF", pages = "??--??", year = "1995", bibdate = "Fri Oct 26 17:02:35 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "AIAA Paper 95-1725", acknowledgement = ack-nhfb, } @InProceedings{Aftosmis:1995:PMM, author = "Michael Aftosmis and Marsha Berger and Gedas Adomavicius", booktitle = "Proceedings of the 12th {AIAA} Computational Fluid Dynamics Conference, San Diego, {CA}, June 1995", title = "A parallel multilevel method for adaptively refined {Cartesian} grids with embedded boundaries", publisher = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", pages = "????", month = jan, year = "1995", bibdate = "Mon Oct 22 18:55:22 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "AIAA 95-1725CP", acknowledgement = ack-nhfb, } @TechReport{Berger:1995:ATC, author = "Marsha Berger and John Melton", title = "An accuracy test of a {Cartesian} grid method for steady flow in complex geometries", type = "RIACS Report", number = "95-02", institution = "????", address = "????", month = "????", year = "1995", bibdate = "Fri Oct 26 17:05:35 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Published in \cite{Berger:1996:ATC}", acknowledgement = ack-nhfb, } @TechReport{Melton:1995:ACG, author = "J. Melton and M. Berger and M. Aftosmis and M. Wong", title = "{$3$D} Applications of a {Cartesian} Grid {Euler} Method", type = "Technical Report", number = "AIAA Paper 95-0853", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", month = jan, year = "1995", bibdate = "Fri Oct 26 17:04:02 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InProceedings{Berger:1996:AAM, author = "Marsha Berger and Michael Aftosmis and John Melton", title = "Accuracy, Adaptive Methods and Complex Geometry", crossref = "Sakell:1996:PFA", pages = "??--??", year = "1996", bibdate = "Fri Oct 26 17:01:16 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InCollection{Berger:1996:ATC, author = "Marsha Berger and John Melton", editor = "J. Glimm and others", booktitle = "Hyperbolic problems: theory, numerics, applications (Stony Brook, {NY, 1994)}", title = "An accuracy test of a {Cartesian} grid method for steady flow in complex geometries", publisher = pub-WORLD-SCI, address = pub-WORLD-SCI:adr, pages = "91--100", year = "1996", ISBN = "981-02-2441-9", ISBN-13 = "978-981-02-2441-7", MRclass = "76M25 (76N10)", MRnumber = "MR1446017", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "See technical report \cite{Berger:1995:ATC}.", abstract = "We describe a method to solve the inviscid compressible Euler equations using non-body-fitted Cartesian grids. We briefly survey the geometric procedures needed for the ``grid generation'' in this approach and show some Cartesian grids for three dimensional configurations. The major source of error in these methods is at the irregular boundary cells. This has motivated us to study various improvements in the numerical scheme (a Godunov method) on a model problem with smooth flow in two space dimensions.", acknowledgement = ack-nhfb, } @InProceedings{Wang:1996:TAG, author = "Z. J. Wang and M. J. Berger", title = "Towards Automatic Grid Independent Viscous Solutions with an Adaptive {Cartesian}\slash Quad Grid Flow Solver", crossref = "Kutler:1997:FIC", pages = "??--??", year = "1996", bibdate = "Fri Oct 26 17:00:13 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @TechReport{Aftosmis:1997:REC, author = "M. J. Aftosmis and M. J. Berger and J. E. Melton", title = "Robust and efficient {Cartesian} mesh generation for component-based geometry", type = "Technical Report", number = "AIAA 97-0196", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", month = jan, year = "1997", bibdate = "Mon Oct 22 18:55:22 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Published in \cite{Aftosmis:1998:REC}.", acknowledgement = ack-nhfb, } @InCollection{Aftosmis:1998:ACM, author = "M. J. Aftosmis and M. J. Berger and J. E. Melton", editor = "J. Thompson and B. Soni and N. Weatherill", booktitle = "Handbook of Grid Generation", title = "Adaptive {Cartesian} Mesh Generation", publisher = pub-CRC, address = pub-CRC:adr, pages = "??--??", year = "1998", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Oct 26 16:29:16 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Article{Aftosmis:1998:REC, author = "M. J. Aftosmis and M. J. Berger and J. E. Melton", title = "Robust and efficient {Cartesian} mesh generation for component-based geometry", journal = j-AIAA, volume = "36", number = "6", pages = "952--960", month = jun, year = "1998", bibdate = "Tue Sep 21 18:17:01 2010", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "See report \cite{Aftosmis:1997:REC}.", acknowledgement = ack-nhfb, } @InCollection{Berger:1998:AAR, author = "Marsha Berger and Michael Aftosmis", booktitle = "Sixteenth International Conference on Numerical Methods in Fluid Dynamics (Arcachon, 1998)", title = "Aspects (and aspect ratios) of {Cartesian} mesh methods", volume = "515", publisher = pub-SV, address = pub-SV:adr, pages = "1--12", year = "1998", DOI = "https://doi.org/10.1007/BFb0106553", ISBN = "3-540-65153-5", ISBN-13 = "978-3-540-65153-6", MRclass = "76M25 (65M70)", MRnumber = "MR1730407", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "Lecture Notes in Physics", acknowledgement = ack-nhfb, } @Article{Berger:1998:AMR, author = "Marsha J. Berger and Randall J. LeVeque", title = "Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems", journal = j-SIAM-J-NUMER-ANAL, volume = "35", number = "6", pages = "2298--2316", month = dec, year = "1998", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/S0036142997315974", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65M50 (76M20 76N15)", MRnumber = "1655847", MRreviewer = "Corneliu Berbente", bibdate = "Fri Dec 4 13:36:09 MST 1998", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SINUM/35/6; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/31597", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @TechReport{Delanaye:1999:AHC, author = "M. Delanaye and M. Aftosmis and M. J. Berger and Y. Liu and T. Pulliam", title = "Automatic Hybrid-Cartesian Grid Generation for High-{Reynolds} Number Flows around Complex Geometries", type = "Technical Report", number = "AIAA Paper 99-0777, Reno, NV", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", month = jan, year = "1999", bibdate = "Fri Oct 26 16:27:11 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InCollection{Forrer:1999:FSC, author = "Hans Forrer and Marsha Berger", booktitle = "Hyperbolic problems: theory, numerics, applications, Vol. {I} (Z{\"u}rich, 1998)", title = "Flow simulations on {Cartesian} grids involving complex moving geometries", volume = "129", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "315--324", year = "1999", ISBN = "3-7643-6080-1", ISBN-13 = "978-3-7643-6080-1", MRclass = "76M12 (Finite volume methods) 76N15 (Gas dynamics, general), 76M25", MRnumber = "MR1717201 (2000f:76096)", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "Internat. Ser. Numer. Math.", ZMnumber = "0936.76040", abstract = "We describe a method to solve the compressible time-dependent Euler equations using Cartesian grids for domains involving fixed or moving geometries. We use the concept of a mirror flow extrapolation of a given solution over a reflecting wall, which may be curved or moving at a fixed or varying speed. We apply this mirror flow to a Cartesian grid method to calculate the cells along a reflecting boundary avoiding the ``small-cell'' problem. Numerical results are presented.", acknowledgement = ack-nhfb, keywords = "Cartesian grids; compressible time-dependent Euler equations; mirror flow extrapolation; reflecting wall", } @Article{Roma:1999:AVI, author = "Alexandre M. Roma and Charles S. Peskin and Marsha J. Berger", title = "An adaptive version of the immersed boundary method", journal = j-J-COMPUT-PHYS, volume = "153", number = "2", pages = "509--534", day = "10", month = aug, year = "1999", CODEN = "JCTPAH", DOI = "https://doi.org/10.1006/jcph.1999.6293", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", MRclass = "76M25 (74F10)", MRnumber = "1705942", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib", ZMnumber = "0953.76069", abstract = "We present a computational setting for the immersed boundary method employing an adaptive mesh refinement. Enhanced accuracy for the method is attained locally by covering an immersed boundary vicinity with a sequence of nested, progressively finer rectangular grid patches which dynamically follow the immersed boundary motion. The set of equations describing the interaction between a non-stationary, viscous incompressible fluid and an immersed elastic boundary is solved by coupling a projection method, specially designed for locally refined meshes, to an implicit formulation of the immersed boundary method.\par The main contributions of this work concern the formulation and implementation of a multilevel self-adaptive version of the immersed boundary method on locally refined meshes. This approach is tested on a particular two-dimensional model problem, for which no significant difference is found between the solutions obtained on a mesh refined locally around the immersed boundary, and on the associated uniform mesh, built with the resolution of the finest level.", acknowledgement = ack-nhfb, classmath = "76M20 (Finite difference methods) 76D05 (Navier--Stokes equations (fluid dynamics)) 65M55 (Multigrid methods; domain decomposition (IVP of PDE)) 74F10 (Fluid-solid interactions)", fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", keywords = "adaptive mesh refinement; immersed boundary method; immersed elastic boundary; interface problems; multilevel self-adaptive method; projection method; viscous incompressible fluid", } @TechReport{Aftosmis:2000:PMM, author = "Michael Aftosmis and Marsha Berger and Gedas Adomavicius", title = "A parallel multilevel method for adaptively refined {Cartesian} grids with embedded boundaries", type = "Technical Report", number = "AIAA 2000-0808", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", month = jan, year = "2000", bibdate = "Mon Oct 22 18:55:22 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @InCollection{Berger:2001:PMC, author = "Marsha Berger and Michael Aftosmis and Gedas Adomavicius", booktitle = "Proceedings of the 8th International Congress on Parallel Computational Fluid Dynamics (Trondheim, Norway, June, 2000)", title = "Parallel multigrid on {Cartesian} meshes with complex geometry", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "283--290", year = "2001", ISBN = "0-444-50673-X", ISBN-13 = "978-0-444-50673-3", MRclass = "76M25", MRnumber = "MR1874028", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @TechReport{Aftosmis:2002:MEE, author = "M. J. Aftosmis and M. J. Berger", title = "Multilevel Error Estimation and Adaptive $h$-Refinement for {Cartesian} Meshes with Embedded Boundaries", type = "Technical Report", number = "AIAA 2002-0863", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", pages = "14", day = "14--17", month = jan, year = "2002", bibdate = "Mon Oct 22 18:44:59 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", URL = "http://people.nas.nasa.gov/~aftosmis/publications/aiaa2002-0863.pdf", abstract = "This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using $ \tau $ extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive $h$-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from $ 10^6$ to $ 10^7$ cells.", acknowledgement = ack-nhfb, remark = "Winner of AIAA 2002 Best Paper Award", } @InProceedings{Berger:2002:GAB, author = "Marsha J. Berger and Christiane Helzel", title = "Grid aligned $h$-box methods for conservation laws in complex geometries", crossref = "Herbin:2002:FVC", pages = "277--284", year = "2002", MRclass = "65M06 65M50 35L65", MRnumber = "2007426", bibdate = "Mon Oct 22 17:45:24 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", ZMnumber = "1059.65506", acknowledgement = ack-nhfb, xxpages = "263--270", } @Misc{Berger:2002:VNC, author = "M. Berger", title = "Triangle geometry processing for surface modeling and {Cartesian} grid generation", howpublished = "U.S. Patent \# 6445390", day = "3", month = sep, year = "2002", bibdate = "Fri Oct 26 18:15:13 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @TechReport{Murman:2002:NSR, author = "S. Murman and M. Aftosmis and M. Berger", title = "Numerical Simulation of Rolling-Airframes Using a Multi-Level {Cartesian} Method", type = "Technical Report", number = "AIAA Paper 2002-2798 (St. Louis, MO)", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", month = jun, year = "2002", bibdate = "Fri Oct 26 16:24:08 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Published in \cite{Murman:2004:NSR}.", acknowledgement = ack-nhfb, } @Article{Berger:2003:BMA, author = "Marsha J. Berger and Christiane Helzel and Randall J. LeVeque", title = "$ {H}$-Box Methods for the Approximation of Hyperbolic Conservation Laws on Irregular Grids", journal = j-SIAM-J-NUMER-ANAL, volume = "41", number = "3", pages = "893--918", month = jun, year = "2003", CODEN = "SJNAAM", DOI = "https://doi.org/10.1137/S0036142902405394", ISSN = "0036-1429 (print), 1095-7170 (electronic)", ISSN-L = "0036-1429", MRclass = "65M06 (65M12)", MRnumber = "2005187", MRreviewer = "Alexander M. Alekseenko", bibdate = "Fri Aug 15 05:57:14 MDT 2003", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/3; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/40539", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Numerical Analysis", journal-URL = "http://epubs.siam.org/sinum", } @TechReport{Murman:2003:IAM, author = "Scott Murman and Michael J. Aftosmis and Marsha J. Berger", title = "Implicit Approaches for Moving Boundaries in a {$3$-D} {Cartesian} Method", type = "Technical Report", number = "AIAA Paper 2003-1119 (Reno, NV)", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", month = jan, year = "2003", bibdate = "Fri Oct 26 16:00:28 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @TechReport{Murman:2003:SDM, author = "Scott Murman and Michael J. Aftosmis and Marsha J. Berger", title = "Simulations of {$6$-DOF} Motion with a {Cartesian} Method", type = "Technical Report", number = "AIAA Paper 2003-1246", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", month = jan, year = "2003", bibdate = "Fri Oct 26 16:16:31 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "See also \cite{Murman:2004:SDM}.", acknowledgement = ack-nhfb, } @TechReport{Aftosmis:2004:ASF, author = "M. J. Aftosmis and M. J. Berger and S. M. Murman", title = "Applications of Space-Filling Curves to {Cartesian} Methods for {CFD}", type = "Technical Report", number = "AIAA 2004-1232", institution = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", pages = "12", day = "5--8", month = jan, year = "2004", bibdate = "Mon Oct 22 18:49:53 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", URL = "http://people.nas.nasa.gov/~aftosmis/publications/aiaa2004_1232.pdf", abstract = "This paper presents a variety of novel uses of space-filling curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes both structured and unstructured. We demonstrate the use of single $ O(N \log N) $ SFC-based reordering to produce single-pass ($ O(N)$) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15\% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with $N$ unknowns to another mesh with $ O(M + N)$ operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.", acknowledgement = ack-nhfb, remark = "42nd Aerospace Sciences Meeting and Exhibit 5-8 January 2004 / Reno NV.", } @InCollection{Berger:2004:PTP, author = "Marsha Berger", booktitle = "Applied mathematics entering the 21st Century", title = "Putting together the pieces: grid generation and flow solvers for complex geometries", volume = "116", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "25--35", year = "2004", ISBN = "0-89871-559-8", ISBN-13 = "978-0-89871-559-0", MRclass = "76M25", MRnumber = "MR2296260", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "SIAM Proceedings in Applied Mathematics", acknowledgement = ack-nhfb, xxtitle = "Putting Together the Pieces: From Grid Generation to Flow Solution in Complicated Geometries", } @Article{Murman:2004:NSR, author = "S. Murman and M. Aftosmis and M. Berger", title = "Numerical Simulation of Rolling-Airframes Using a Multi-Level {Cartesian} Method", journal = "AIAA Journal of Spacecraft and Rockets", volume = "41", number = "3", pages = "??--??", month = "????", year = "2004", bibdate = "Fri Oct 26 16:23:07 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "See also technical report \cite{Murman:2002:NSR}.", acknowledgement = ack-nhfb, } @Article{Murman:2004:SDM, author = "Scott Murman and Michael J. Aftosmis and Marsha J. Berger", title = "Simulations of Store Separation from an {F/A-18} with a {Cartesian} Method", journal = "AIAA Journal of Aircraft", volume = "41", number = "4", pages = "??--??", month = "????", year = "2004", bibdate = "Fri Oct 26 16:17:40 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "See also \cite{Murman:2003:SDM}.", acknowledgement = ack-nhfb, } @TechReport{Berger:2005:ASL, author = "Marsha Berger and Michael J. Aftosmis and Scott M. Murman", title = "Analysis of Slope Limiters on Irregular Grids", type = "{AIAA} Paper", number = "2005-0490", institution = "American Institute for Aeronautics and Astronautics", address = "Reno, NV, USA", pages = "22", month = may, year = "2005", bibdate = "Fri Oct 26 15:53:40 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Also NASA TM NAS-05-007.", URL = "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.8456; http://www.nas.nasa.gov/News/Techreports/2005/PDF/nas-05-007.pdf", acknowledgement = ack-nhfb, } @Article{Berger:2005:PNC, author = "M. J. Berger and M. J. Aftosmis and D. D. Marshall and S. M. Murman", title = "Performance of a New {CFD} Flow Solver using a Hybrid Programming Paradigm", journal = j-J-PAR-DIST-COMP, volume = "65", number = "4", pages = "414--423", month = apr, year = "2005", CODEN = "JPDCER", DOI = "https://doi.org/10.1016/j.jpdc.2004.11.010", ISSN = "0743-7315 (print), 1096-0848 (electronic)", ISSN-L = "0743-7315", bibdate = "Fri Oct 26 15:56:10 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Parallel and Distributed Computing", journal-URL = "http://www.sciencedirect.com/science/journal/07437315", } @Article{Berger:2005:PSI, author = "Marsha Berger and Z. J. Wang", title = "Preface: [Special issue in celebration of {Antony Jameson}'s 70th birthday]", journal = j-INT-J-COMPUT-FLUID-DYN, volume = "19", number = "8", pages = "547", year = "2005", CODEN = "IJCFEC", DOI = "https://doi.org/10.1080/10618560500508391", ISSN = "1061-8562 (print), 1029-0257 (electronic)", ISSN-L = "1026-7417", MRclass = "01A70", MRnumber = "MR2227615", bibdate = "Fri Oct 26 18:12:56 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, fjournal = "International Journal of Computational Fluid Dynamics", } @Article{Helzel:2005:HRR, author = "Christiane Helzel and Marsha J. Berger and Randall J. LeVeque", title = "A High-Resolution Rotated Grid Method for Conservation Laws with Embedded Geometries", journal = j-SIAM-J-SCI-COMP, volume = "26", number = "3", pages = "785--809", month = may, year = "2005", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/S106482750343028X", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "35L65 (65M06 76M12)", MRnumber = "2126112", bibdate = "Sat Apr 16 12:07:23 MDT 2005", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/26/3; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", URL = "http://epubs.siam.org/sam-bin/dbq/article/43028", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @InProceedings{Mavriplis:2005:HRAa, author = "Dimitri J. Mavriplis and Michael J. Aftosmis and Marsha Berger", title = "High Resolution Aerospace Applications using the {NASA Columbia Supercomputer}", crossref = "ACM:2005:PAI", pages = "61--61", year = "2005", bibdate = "Tue Dec 27 07:58:16 MST 2005", bibsource = "http://portal.acm.org/; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", abstract = "This paper focuses on the parallel performance of two high-performance aerodynamic simulation packages on the newly installed NASA Columbia supercomputer. These packages include both a high-fidelity, unstructured, Reynolds-averaged Navier--Stokes solver, and a fully-automated inviscid flow package for cut-cell Cartesian grids. The complementary combination of these two simulation codes enables high-fidelity characterization of aerospace vehicle design performance over the entire flight envelope through extensive parametric analysis and detailed simulation of critical regions of the flight envelope. Both packages are industrial-level codes designed for complex geometry and incorporate customized multigrid solution algorithms. The performance of these codes on Columbia is examined using both MPI and OpenMP and using both the NUMAlink and InfiniBand interconnect fabrics. Numerical results demonstrate good scalability on up to 2016 cpus using the NUMAlink4 interconnect, with measured computational rates in the vicinity of 3 TFLOP/s, while InfiniBand showed some performance degradation at high CPU counts, particularly with multigrid. Nonetheless, the results are encouraging enough to indicate that larger test cases using combined MPI/OpenMP communication should scale well on even more processors.", acknowledgement = ack-nhfb, remark = "Co-winner of best paper award. Also published in \cite{Mavriplis:2007:HRAb}.", } @Article{Aftosmis:2006:ACM, author = "M. J. Aftosmis and M. J. Berger and J. J. Alonso", title = "Applications of a {Cartesian} Mesh Boundary-Layer Approach for Complex Configurations", journal = j-AIAA, pages = "??--??", month = jan, year = "2006", bibdate = "Fri Oct 26 15:47:04 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Article{Aftosmis:2006:DPC, author = "M. Aftosmis and M. Berger and R. Biswas and M. J. Djomehri and R. Hood and H. Jin and C. Kiris", title = "A Detailed Performance Characterization of {Columbia} using Aeronautics Benchmarks and Applications", journal = j-AIAA, volume = "??", pages = "??--??", month = jan, year = "2006", bibdate = "Fri Oct 26 15:52:19 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "AIAA Paper 2006-84, Reno, NV.", acknowledgement = ack-nhfb, } @Article{Krivodonova:2006:HOA, author = "Lilia Krivodonova and Marsha Berger", title = "High-order accurate implementation of solid wall boundary conditions in curved geometries", journal = j-J-COMPUT-PHYS, volume = "211", number = "2", pages = "492--512", day = "20", month = jan, year = "2006", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/j.jcp.2005.05.029", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", MRclass = "76M25 (65M50)", MRnumber = "MR2173394 (2006d:76099)", bibdate = "Mon Jan 2 22:13:16 MST 2012", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999105002846", ZMnumber = "pre02229469", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991/", } @Article{Mavriplis:2007:HRAb, author = "Dimitri J. Mavriplis and Michael J. Aftosmis and Marsha Berger", title = "High Resolution Aerospace Applications Using the {NASA Columbia Supercomputer}", journal = j-IJHPCA, volume = "21", number = "1", pages = "106--126", month = "Spring", year = "2007", CODEN = "IHPCFL", DOI = "https://doi.org/10.1177/1094342006074872", ISSN = "1094-3420 (print), 1741-2846 (electronic)", ISSN-L = "1094-3420", bibdate = "Tue Aug 31 09:59:45 MDT 2010", bibsource = "http://hpc.sagepub.com/content/21/1.toc; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", URL = "http://hpc.sagepub.com/content/21/1/106.full.pdf+html", acknowledgement = ack-nhfb, journal-URL = "http://hpc.sagepub.com/content/by/year", remark = "Also published in \cite{Mavriplis:2005:HRA}.", } @InCollection{Wissink:2008:ACM, author = "A. Wissink and B. Kosovic and M. Berger and K. Chand and F. K. Chow", title = "Adaptive {Cartesian} Methods for Modeling Airborne Dispersion", crossref = "Zomaya:2008:ACI", pages = "??--??", year = "2008", bibdate = "Fri Oct 26 15:43:50 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Article{Berger:2009:LRF, author = "Marsha J. Berger and Donna A. Calhoun and Christiane Helzel and Randall J. LeVeque", title = "Logically rectangular finite volume methods with adaptive refinement on the sphere", journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A, volume = "367", number = "1907", pages = "4483--4496", year = "2009", CODEN = "PTRMAD, PTMSFB", DOI = "https://doi.org/10.1098/rsta.2009.0168", ISSN = "1364-503X (print), 1471-2962 (electronic)", ISSN-L = "1364-503X", MRclass = "65N08 (35Q35 86A05)", MRnumber = "2550979 (2011d:65324)", MRreviewer = "Srinivasan Natesan", bibdate = "Sat Sep 24 15:52:48 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences", journal-URL = "http://rsta.royalsocietypublishing.org/", } @Article{LeVeque:2011:TMA, author = "Randall J. LeVeque and David L. George and Marsha J. Berger", title = "Tsunami modelling with adaptively refined finite volume methods", journal = j-ACTA-NUMERICA, volume = "20", pages = "211--289", year = "2011", CODEN = "ANUMFU", DOI = "https://doi.org/10.1017/S0962492911000043", ISBN = "????", ISBN-13 = "????", ISSN = "0962-4929 (print), 1474-0508 (electronic)", ISSN-L = "0962-4929", MRclass = "86-08 (65M08 86A05)", MRnumber = "2805154", MRreviewer = "Alexander Bihlo", bibdate = "Sat Sep 24 10:23:44 MDT 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/actanumerica.bib", acknowledgement = ack-nhfb, ajournal = "Acta Numer.", fjournal = "Acta Numerica", journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=ANU", onlinedate = "28 April 2011", } @Article{Berger:2012:SBM, author = "Marsha Berger and Christiane Helzel", title = "A simplified $h$-box method for embedded boundary grids", journal = j-SIAM-J-SCI-COMP, volume = "34", number = "2", pages = "A861--A888", month = "????", year = "2012", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/110829398", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65M08 (35L65 65M12 65M20)", MRnumber = "2914307", MRreviewer = "Henryk Leszczy\AA ki", bibdate = "Tue Oct 30 14:48:54 MDT 2012", bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/34/2; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2012", } @Article{May:2013:TDS, author = "Sandra May and Marsha Berger", title = "Two-Dimensional Slope Limiters for Finite Volume Schemes on Non-Coordinate-Aligned Meshes", journal = j-SIAM-J-SCI-COMP, volume = "35", number = "5", pages = "A2163--A2187", month = "????", year = "2013", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/120875624", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", MRclass = "65M08 (65K05 90C90)", MRnumber = "3097037", MRreviewer = "Peder Aursand", bibdate = "Fri Mar 7 10:32:43 MST 2014", bibsource = "http://epubs.siam.org/toc/sjoce3/35/5; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", onlinedate = "January 2013", } @InCollection{Helzel:2014:CGE, author = "Christiane Helzel and Marsha J. Berger", booktitle = "Hyperbolic problems: theory, numerics, applications", title = "{Cartesian} grid embedded boundary methods for hyperbolic problems", volume = "8", publisher = "Am. Inst. Math. Sci. (AIMS)", address = "Springfield, MO, USA", pages = "675--683", year = "2014", ISBN = "1-60133-017-0, 1-60133-017-0", ISBN-13 = "978-1-60133-017-8, 978-1-60133-017-8", MRclass = "65M08 (35L65)", MRnumber = "3524378", bibdate = "Thu Jun 29 09:02:08 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "AIMS Ser. Appl. Math.", acknowledgement = ack-nhfb, } @InCollection{May:2014:MEI, author = "Sandra May and Marsha Berger", booktitle = "Finite volumes for complex applications {VII}. {Methods} and theoretical aspects", title = "A mixed explicit implicit time stepping scheme for {Cartesian} embedded boundary meshes", volume = "77", publisher = pub-SV, address = pub-SV:adr, pages = "393--400", year = "2014", DOI = "https://doi.org/10.1007/978-3-319-05684-5_38", ISBN = "3-319-05684-0, 3-319-05683-2", ISBN-13 = "978-3-319-05684-5, 978-3-319-05683-8", MRclass = "65M08", MRnumber = "3213370", MRreviewer = "Fausto Cavalli", bibdate = "Thu Jun 29 09:02:08 2017", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "Springer Proc. Math. Stat.", acknowledgement = ack-nhfb, } @Article{Berger:2015:NSC, author = "Marsha Berger", title = "A note on the stability of cut cells and cell merging", journal = j-APPL-NUM-MATH, volume = "96", number = "??", pages = "180--186", month = oct, year = "2015", CODEN = "ANMAEL", DOI = "https://doi.org/10.1016/j.apnum.2015.05.003", ISSN = "0168-9274 (print), 1873-5460 (electronic)", ISSN-L = "0168-9274", MRclass = "65N50", MRnumber = "3373567", bibdate = "Thu Jul 30 05:52:41 MDT 2015", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/applnummath.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0168927415000896", acknowledgement = ack-nhfb, fjournal = "Applied Numerical Mathematics: Transactions of IMACS", journal-URL = "http://www.sciencedirect.com/science/journal/01689274", } @Article{Mandli:2016:CBO, author = "Kyle T. Mandli and Aron J. Ahmadia and Marsha Berger and Donna Calhoun and David L. George and Yiannis Hadjimichael and David I. Ketcheson and Grady I. Lemoine and Randall J. LeVeque", title = "Clawpack: building an open source ecosystem for solving hyperbolic {PDEs}", journal = "PeerJ Computer Science", volume = "2", pages = "e68:1--e68:27", month = aug, year = "2016", DOI = "https://doi.org/10.7717/peerj-cs.68", ISSN = "2376-5992", bibdate = "Tue Apr 23 06:41:56 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, journal-URL = "https://peerj.com/cs/", } @InCollection{Berger:2017:CCM, author = "M. Berger", booktitle = "Handbook of numerical methods for hyperbolic problems", title = "Cut cells: meshes and solvers", volume = "18", publisher = "Elsevier\slash North-Holland", address = "Amsterdam, The Netherlands", pages = "1--22", year = "2017", ISBN = "0-444-63910-1", ISBN-13 = "978-0-444-63910-3", MRclass = "65M08 (65M50)", MRnumber = "3645386", MRreviewer = "V{\'i}t Dolej{\v{s}}{\'i}", bibdate = "Wed Aug 28 11:16:24 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "Handb. Numer. Anal.", acknowledgement = ack-nhfb, } @Article{May:2017:EIS, author = "Sandra May and Marsha Berger", title = "An Explicit Implicit Scheme for Cut Cells in Embedded Boundary Meshes", journal = j-J-SCI-COMPUT, volume = "71", number = "3", pages = "919--943", month = jun, year = "2017", CODEN = "JSCOEB", DOI = "https://doi.org/10.1007/s10915-016-0326-2", ISSN = "0885-7474 (print), 1573-7691 (electronic)", ISSN-L = "0885-7474", MRclass = "65M08 (35L65 65M12 76M12)", MRnumber = "3640668", MRreviewer = "Giuseppe Pascazio", bibdate = "Sat Jun 24 11:45:14 MDT 2017", bibsource = "http://link.springer.com/journal/10915; http://link.springer.com/journal/10915/71/3; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/jscicomput.bib", URL = "https://link.springer.com/content/pdf/10.1007/s10915-016-0326-2.pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Scientific Computing", journal-URL = "http://link.springer.com/journal/10915", } @Article{Berger:2021:SRA, author = "Marsha Berger and Andrew Giuliani", title = "A state redistribution algorithm for finite volume schemes on cut cell meshes", journal = j-J-COMPUT-PHYS, volume = "428", number = "??", pages = "Article 109820", day = "1", month = mar, year = "2021", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/j.jcp.2020.109820", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", MRclass = "65M08 (76N15)", MRnumber = "4199365", MRreviewer = "Abdallah Bradji", bibdate = "Sat Mar 13 09:06:39 MST 2021", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999120305945", acknowledgement = ack-nhfb, fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", } @InCollection{Berger:2022:AGT, author = "Marsha Berger", booktitle = "Recent advances in industrial and applied mathematics", title = "Asteroid-generated tsunamis: a review", volume = "1", publisher = "Springer", address = "Cham, Switzerland", pages = "3--17", year = "2022", DOI = "https://doi.org/10.1007/978-3-030-86236-7_1", ISBN = "3-030-86235-6; 3-030-86236-4", ISBN-13 = "978-3-030-86235-0; 978-3-030-86236-7", MRclass = "76B15", MRnumber = "4455587", bibdate = "Wed Aug 28 11:16:24 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "ICIAM 2019 SEMA SIMAI Springer Ser.", acknowledgement = ack-nhfb, } @Article{Giuliani:2022:WSR, author = "A. Giuliani and A. S. Almgren and J. B. Bell and M. J. Berger and M. T. Henry de Frahan and D. Rangarajan", title = "A weighted state redistribution algorithm for embedded boundary grids", journal = j-J-COMPUT-PHYS, volume = "464", number = "??", pages = "??--??", day = "1", month = sep, year = "2022", CODEN = "JCTPAH", DOI = "https://doi.org/10.1016/j.jcp.2022.111305", ISSN = "0021-9991 (print), 1090-2716 (electronic)", ISSN-L = "0021-9991", MRclass = "65M08 (65M50)", MRnumber = "4437693", bibdate = "Fri Jun 10 06:48:27 MDT 2022", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2020.bib", URL = "http://www.sciencedirect.com/science/article/pii/S0021999122003679", acknowledgement = ack-nhfb, articleno = "111305", fjournal = "Journal of Computational Physics", journal-URL = "http://www.sciencedirect.com/science/journal/00219991", } @InCollection{Berger:2023:TAS, author = "Marsha J. Berger and Randall J. LeVeque", booktitle = "{ICM---International Congress of Mathematicians. Vol. 7. Sections 15--20}", title = "Towards adaptive simulations of dispersive tsunami propagation from an asteroid impact", publisher = "EMS Press", address = "Berlin, Germany", pages = "5056--5071", year = "2023", ISBN = "3-9854706-5-0; 3-9854756-5-2; 3-9854705-8-8", ISBN-13 = "978-3-9854706-5-5; 978-3-9854756-5-0; 978-3-9854705-8-7", MRclass = "65M50 (65M08 76-04 76B15 86-04)", MRnumber = "4680434", bibdate = "Wed Aug 28 11:16:24 2024", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Article{Berger:2024:IAM, author = "Marsha J. Berger and Randall J. LeVeque", title = "Implicit Adaptive Mesh Refinement for Dispersive Tsunami Propagation", journal = j-SIAM-J-SCI-COMP, volume = "46", number = "4", pages = "B554--B578", month = "????", year = "2024", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/23M1585210", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Sat Aug 24 16:22:17 MDT 2024", bibsource = "http://epubs.siam.org/toc/sjoce3/46/4; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", URL = "https://epubs.siam.org/doi/10.1137/23M1585210", acknowledgement = ack-nhfb, ajournal = "SIAM J. Sci. Comput.", fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", } @Article{Berger:2024:NPS, author = "Marsha Berger and Andrew Giuliani", title = "A New Provably Stable Weighted State Redistribution Algorithm", journal = j-SIAM-J-SCI-COMP, volume = "46", number = "5", pages = "A2848--A2873", month = "????", year = "2024", CODEN = "SJOCE3", DOI = "https://doi.org/10.1137/23M1597484", ISSN = "1064-8275 (print), 1095-7197 (electronic)", ISSN-L = "1064-8275", bibdate = "Mon Sep 30 10:38:50 MDT 2024", bibsource = "http://epubs.siam.org/toc/sjoce3/46/5; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib", URL = "https://epubs.siam.org/doi/10.1137/23M1597484", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Scientific Computing", journal-URL = "http://epubs.siam.org/sisc", }

%%% ==================================================================== %%% Cross-referenced entries must come last:

@Proceedings{Schultz:1981:EPS, editor = "Martin H. Schultz", booktitle = "{Elliptic problem solvers}", title = "{Elliptic problem solvers}", publisher = pub-ACADEMIC, address = pub-ACADEMIC:adr, pages = "xiii + 444", year = "1981", ISBN = "0-12-632620-7", ISBN-13 = "978-0-12-632620-8", LCCN = "QA377 .E53 1980", bibdate = "Fri Oct 26 19:03:26 MDT 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; z3950.loc.gov:7090/Voyager", acknowledgement = ack-nhfb, meetingname = "Elliptic Problem Solvers Conference (1980 : Santa Fe, N.M.)", remark = "Proceedings of the Elliptic Problem Solvers Conference held in Santa Fe, N.M., June 30--July 2, 1980, sponsored by the Los Alamos Scientific Laboratory.", subject = "Differential equations, Elliptic; Numerical solutions; Congresses", } @Proceedings{Ames:1983:MSE, editor = "William F. Ames", booktitle = "{Modeling and simulation in engineering: Systems simulation and scientific computation (World congress) (10th: 1982 Aug: Montreal, Canada)}", title = "{Modeling and simulation in engineering: Systems simulation and scientific computation (World congress) (10th: 1982 Aug: Montreal, Canada)}", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "????", year = "1983", ISBN = "0-444-86606-X", ISBN-13 = "978-0-444-86606-6", LCCN = "????", bibdate = "Fri Oct 26 19:07:42 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Proceedings{Babuska:1983:ACM, editor = "Ivo Babuska and Jagdish Chandra and Joseph E. Flaherty", booktitle = "{Adaptive computational methods for partial differential equations: Proceedings of the Workshop, College Park, MD, USA, 1983}", title = "{Adaptive computational methods for partial differential equations: Proceedings of the Workshop, College Park, MD, USA, 1983}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xii + 251", year = "1983", ISBN = "0-89871-191-6", ISBN-13 = "978-0-89871-191-2", LCCN = "QA377 .A29 1983", bibdate = "Tue Oct 11 12:35:12 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Proceedings{Stepleman:1983:SCA, editor = "R. S. (Robert S.) Stepleman and others", booktitle = "{Scientific computing: applications of mathematics and computing to the physical sciences}", title = "{Scientific computing: applications of mathematics and computing to the physical sciences}", volume = "1", publisher = pub-NORTH-HOLLAND, address = pub-NORTH-HOLLAND:adr, pages = "x + 363", year = "1983", ISBN = "0-444-86607-8", ISBN-13 = "978-0-444-86607-3", LCCN = "Q172 .I46 1982", bibdate = "Fri Oct 26 19:12:17 MDT 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; z3950.loc.gov:7090/Voyager", series = "IMACS transactions on scientific computation", acknowledgement = ack-nhfb, meetingname = "IMACS World Congress on Systems Simulation and Scientific Computation (10th : 1982 : Montr\'eal, Qu\'ebec)", remark = "Based on papers presented at the Tenth IMACS World Congress on System Simulation and Scientific Computation, held in Montreal, Canada, August 8--13, 1982.", subject = "Physical sciences; Mathematics; Congresses; Data processing", } @Book{Engquist:1985:LSC, editor = "Bj{\"o}rn Engquist and Stanley Osher and Richard C. J. Somerville", title = "Large-scale computations in fluid mechanics", volume = "22", publisher = pub-AMS, address = pub-AMS:adr, pages = "xv + 370 (vol. 1), x + 409 (vol. 2)", year = "1985", ISBN = "0-8218-1122-3", ISBN-13 = "978-0-8218-1122-1", LCCN = "QA901 .L37 1985", bibdate = "Fri Oct 26 19:19:28 MDT 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; z3950.loc.gov:7090/Voyager", note = "Two volumes.", series = "Lectures in applied mathematics", acknowledgement = ack-nhfb, remark = "Papers presented at the Fifteenth AMS--SIAM Summer Seminar on Applied Mathematics, held at Scripps Institution of Oceanography, La Jolla, CA, June 27--July 8, 1983.", subject = "Fluid mechanics; Congresses; Numerical analysis", } @Proceedings{Soubbaramayer:1985:NIC, editor = "Soubbaramayer and J. P. (Jean-Paul) Boujot", booktitle = "{Ninth International Conference on Numerical Methods in Fluid Dynamics: [proceedings], Gif-sur-Yvette/France 1984}", title = "{Ninth International Conference on Numerical Methods in Fluid Dynamics: [proceedings], Gif-sur-Yvette/France 1984}", volume = "218", publisher = pub-SV, address = pub-SV:adr, pages = "x + 612", year = "1985", ISBN = "0-387-13917-6", ISBN-13 = "978-0-387-13917-3", LCCN = "QA911 .I54 1984; QA911 .I58 1984; TA357 .I564 1984", bibdate = "Fri Oct 26 18:59:09 MDT 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; melvyl.cdlib.org:210/CDL90", price = "DM82.00 (West Germany)", series = "Lecture notes in physics", acknowledgement = ack-nhfb, meetingname = "International Conference on Numerical Methods in Fluid Dynamics (9th : 1984 : Centre d'\'etudes nucl\'eaires de Saclay)", remark = "English and French.", subject = "Fluid dynamics; Congresses; Numerical analysis", } @Proceedings{DeGroot:1985:PIC, editor = "Doug DeGroot", booktitle = "{Proceedings of the 1985 International Conference on Parallel Processing, August 20--23, 1985}", title = "{Proceedings of the 1985 International Conference on Parallel Processing, August 20--23, 1985}", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "xx + 868", year = "1985", ISBN = "0-8186-0637-1 (paperback), 0-8186-8637-5 (hardback), 0-8186-4637-3 (microfiche)", ISBN-13 = "978-0-8186-0637-3 (paperback), 978-0-8186-8637-5 (hardback), 978-0-8186-4637-9 (microfiche)", LCCN = "QA76.6 .I613 1985; QA76.6 .I548 1985", bibdate = "Fri Oct 26 18:27:16 MDT 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; melvyl.cdlib.org:210/CDL90", acknowledgement = ack-nhfb, meetingname = "International Conference on Parallel Processing (1985 : Pennsylvania State University)", subject = "Parallel processing (Electronic computers); Congresses", } @Proceedings{Anonymous:1989:CFD, editor = "Anonymous", booktitle = "{9th Computational Fluid Dynamics Conference, Buffalo, New York, June, 1989}", title = "{9th Computational Fluid Dynamics Conference, Buffalo, New York, June, 1989}", publisher = pub-AIAA, address = pub-AIAA:adr, pages = "????", year = "1989", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Oct 26 19:24:09 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Proceedings{Engquist:1990:TIC, editor = "Bjorn Engquist and Bertil Gustafsson", booktitle = "{Third International Conference on Hyperbolic Problems: Theory, Numerical Methods and Applications: Proceedings, Uppsala, Sweden, June 11--15, 1990}", title = "{Third International Conference on Hyperbolic Problems: Theory, Numerical Methods and Applications: Proceedings, Uppsala, Sweden, June 11--15, 1990}", publisher = "Studentlitteratur and Chartwell Bratt)", address = "Lund, Sweden and Bromley, Kent, England", pages = "various", year = "1990", ISBN = "91-44-33421-4 (Studentlitteratur), 0-86238-285-8 (Chartwell Bratt)", ISBN-13 = "978-91-44-33421-9 (Studentlitteratur), 978-0-86238-285-8 (Chartwell Bratt)", LCCN = "QA377.I563 1990", bibdate = "Tue Oct 11 12:27:07 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Two volumes.", acknowledgement = ack-nhfb, } @Proceedings{Melson:1993:SCM, editor = "N. Duane Melson and T. A. Manteuffel and S. F. McCormick", booktitle = "{Sixth Copper Mountain Conference on Multigrid Methods: proceedings of a workshop cosponsored by the National Aeronautics and Space Administration ... [et al.] and held at Copper Mountain, Colorado, April 4--9, 1993}", title = "{Sixth Copper Mountain Conference on Multigrid Methods: proceedings of a workshop cosponsored by the National Aeronautics and Space Administration ... [et al.] and held at Copper Mountain, Colorado, April 4--9, 1993}", number = "NSAS CP-3224", publisher = "National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program", address = "Washington, DC, USA", pages = "????", year = "1993", ISBN = "????", ISBN-13 = "????", ISSN = "0191-7811 ", LCCN = "????", bibdate = "Fri Oct 26 18:30:29 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Two volumes.", series = "NASA conference publication", acknowledgement = ack-nhfb, } @Proceedings{Sincovec:1993:PSS, editor = "Richard F. Sincovec and others", booktitle = "{Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, held March 22--24, 1993, in Norfolk, VA, USA}", title = "{Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, held March 22--24, 1993, in Norfolk, VA, USA}", publisher = pub-SIAM, address = pub-SIAM:adr, pages = "xix + 1041 + iv", year = "1993", ISBN = "0-89871-315-3", ISBN-13 = "978-0-89871-315-2", LCCN = "QA76.58 .S55 1993 v.1-2", bibdate = "Tue Oct 11 12:21:40 1994", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Two volumes.", acknowledgement = ack-nhfb, } @Proceedings{Gautschi:1994:MCH, editor = "Walter Gautschi", booktitle = "{Mathematics of computation, 1943--1993: a half-century of computational mathematics: Mathematics of Computation 50th Anniversary Symposium, August 9--13, 1993, Vancouver, British Columbia}", title = "{Mathematics of computation, 1943--1993: a half-century of computational mathematics: Mathematics of Computation 50th Anniversary Symposium, August 9--13, 1993, Vancouver, British Columbia}", volume = "48", publisher = pub-AMS, address = pub-AMS:adr, pages = "xix + 643", year = "1994", ISBN = "0-8218-0291-7, 0-8218-0353-0 (pt. 1), 0-8218-0354-9 (pt. 2)", ISBN-13 = "978-0-8218-0291-5, 978-0-8218-0353-0 (pt. 1), 978-0-8218-0354-7 (pt. 2)", ISSN = "0160-7634", LCCN = "QA1 .A56 v.48 1994; QA297.M385 1993", MRclass = "00B25 (11-06 65-06)", MRnumber = "95j:00014", bibdate = "Mon Oct 24 11:37:20 2011", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib; https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1940.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib", note = "See also SIAM Review, September 1995, {\bf 37}(3), p. 483.", series = "Proceedings of Symposia in Applied Mathematics", acknowledgement = ack-nhfb, author-dates = "Frank William John Olver (15 December 1924--23 April 2013)", tableofcontents = "Preface / xi \\ Mathematics of Computation: A brief history / Eugene Isaacson / xvii \\ \\ Part I. Symposium on Numerical Analysis \\ \\ Invited Papers \\ \\ On the development of multigrid methods and their analysis / James H. Bramble / 5 \\ An introduction to inverse problems / Margaret Cheney / 21 \\ Algorithms for unconstrained optimization: A review of recent developments / Donald Goldfarb / 33 \\ A survey of componentwise perturbation theory in numerical linear algebra / Nicholas J. Higham / 49 \\ Numerical evaluation of special functions / D. W. Lozier and F. W. J. Olver / 79 \\ A survey of numerical cubature over triangles / J. N. Lyness and Ronald Cools / 127 \\ New trends in the use and analysis of integral equations / J. C. Nedelec / 151 \\ Applications of multivariate splines / Larry L. Schumaker / 177 \\ Initial value problems for ordinary differential equations: Development of ideas, techniques, and implementation / Hans J. Stetter / 205 \\ Multiresolution methods for partial differential equations / Roger Temam / 225 \\ \\ Contributed Papers \\ \\ A comparison of techniques for solving ill-conditioned problems arising from the immersed boundary method / Loyce Adams and Zhiyun Yang / 243 \\ A mixed spectral-collocation and operator splitting method for the Wigner-Poisson equation / Anton Arnold / 249 \\ Finite volume methods for irregular one-dimensional grids / M. J. Berger, R. J. Leveque, and L. G. Stern / 255 \\ Linear rational interpolation of continuous functions over an interval / Jean-Paul Berrut / 261 \\ A von Neumann reflection for the 2-D Burgers equation / M. Brio and J. K. Hunter / 265 \\ Slow evolution from the boundary: A new stabilizing constraint in ill-posed continuation problems / Alfred S. Carasso / 269 \\ A finite element method for the 2D drift-diffusion semiconductor model / Zhangxin Chen / 275 \\ Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems / S. De Marchi, M. Vianello, and R. Zanovello / 281 \\ Error estimates for a quadrature rule for Cauchy principal value integrals / Kai Diethelm / 287 \\ A numerical radius approach to stable difference schemes for parabolic systems / Moshe Goldberg / 293 \\ An extension of the Olver-Sookne method for the solution of second-order linear difference equations / Takemitsu Hasegawa and Tatsuo Torii / 297 \\ The Faber polynomials for circular arcs / Matthew He / 301 \\ Finite element approximation for optimal control of electrically conducting fluid flows / L. S. Hou and S. S. Ravindran / 305 \\ ADI methods for heat equations with discontinuities along an arbitrary interface / Zhilin Li and Anita Mayo / 311 \\ Eigenvalue approximation of Fredholm integral operators / E. B. Lin / 317 \\ Spectral methods for singular perturbation problems / Wenbin Liu and Tao Tang / 323 \\ A quaternion-Jacobi method for symmetric matrices / Niloufer Mackey / 327 \\ On constructing Chebyshev series solutions of differential equations / Allan J. MacLeod / 333 \\ Multiquadric collocation methods in the numerical solution of Volterra integral and integro-differential equations / Athena Makroglou / 337 \\ Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations / Kristyn J. Maschhoff / 343 \\ Computing limiting normals to real surfaces / Donal O'Shea and Les Wilson / 349 \\ Orthogonal spline collocation solution of nonlinear Schr{\"o}dinger equations / Mark P. Robinson / 355 \\ Who invented the computer? The debate from the viewpoint of computer architecture / Ra{\'u}l Rojas / 361 \\ Locking and boundary layer effects in the finite element approximation of the Reissner--Mindlin plate model / Christoph Schwab and Manil Suri / 367 \\ Efficient spectral Galerkin methods for some elliptic problems / Jie Shen / 373 \\ Periodic solutions of higher-order difference equations in two independent variables / Qin Sheng and Ravi P. Agarwal / 377 \\ Front tracking based on high-resolution wave propagation methods / Keh-Ming Shyue / 383 \\ Time-splitting methods for nonhomogeneous conservation laws / Tao Tang and Zhen-Huan Teng / 389 \\ Numerical aspects of uniform Airy-type asymptotic expansions / N. M. Temme / 395 \\ Local dynamics and bifurcation consistencies of continuous-time dynamical systems and their numerical discretizations / Xin Wang, Edward K. Blum, and Qingnan Li / 399 \\ Computing integrals of the complex error function / J. A. C. Weideman / 403 \\ Quadratures for improper integrals and their applications in integral equations / Yuesheng Xu and Yunhe Zhao / 409 \\ Spline harmonic analysis and wavelet bases / Valery A. Zheludev / 415 \\ \\ Part II. Minisymposium on Computational Number Theory Dedicated to the memory of Derrick Henry Lehmer \\ \\ Invited Papers \\ \\ Algorithms for quadratic orders / Ingrid Biehl and Johannes Buchmann / 425 \\ Analytic computations in number theory / Andrew M. Odlyzko / 451 \\ The number field sieve / Carl Pomerance / 465 \\ Factoring integers before computers / H. C. Williams and J. O. Shallit / 481 \\ \\ Contributed Papers \\ \\ Explicit bounds for primes in residue classes / Eric Bach and Jonathan Sorenson / 535 \\ Ramanujan and Euler's constant / Richard P. Brent / 541 \\ Congruential sieves on FPGA computers / Nathan D. Bronson and Duncan A. Buell / 547 \\ Lehmer pairs of zeros and the Riemann $\xi$-function / George Csordas, Wayne Smith, and Richard S. Varga / 553 \\ A record Aliquot sequence / Andrew W. P. Guy and Richard K. Guy / 557 \\ Implications of computational mathematics for the philosophy of mathematics / Andrew J. Lazarus / 561 \\ Square roots of products of algebraic numbers / Peter L. Montgomery / 567 \\ A locally parameterized version of Lehmer's problem / Gary A. Ray / 573 \\ A new method for finding amicable pairs / H. J. J. te Riele / 577 \\ Generalized Fermat numbers / Hans Riesel and Anders Bj{\"o}rn / 583 \\ Evaluation of $\zeta_K(2)$ for some totally real algebraic number fields K of degree 9 / Kisao Takeuchi / 589 \\ The period of the Bell exponential integers modulo a prime / Samuel S. Wagstaff, Jr. / 595 \\ Computing invariant polynomials of $p$-adic reflection groups / Changsheng Xu / 599 \\ Author Index / 603 \\ Subject Index / 619", } @Proceedings{Dolling:1995:ACF, editor = "David S. Dolling and Bernard Grossman", booktitle = "{12th AIAA Computational fluid dynamics conference: a collection of technical papers: June 19--22, 1995, San Diego, CA}", title = "{12th AIAA Computational fluid dynamics conference: a collection of technical papers: June 19--22, 1995, San Diego, CA}", publisher = "American Institute of Aeronautics and Astronautics", address = "1801 Alexander Bell Drive, Suite 500, Reston, VA 20191, USA", pages = "????", year = "1995", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Oct 26 18:34:32 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", note = "Two volumes.", acknowledgement = ack-nhfb, } @Proceedings{Kutler:1997:FIC, editor = "Paul Kutler and J. (Jolen) Flores and J. J. Chattot", booktitle = "{Fifteenth International Conference on Numerical Methods in Fluid Dynamics: proceedings of the conference held in Monterey, CA, USA, 24--28 June 1996}", title = "{Fifteenth International Conference on Numerical Methods in Fluid Dynamics: proceedings of the conference held in Monterey, CA, USA, 24--28 June 1996}", volume = "490", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 655", year = "1997", ISBN = "3-540-63054-6 (Berlin)", ISBN-13 = "978-3-540-63054-8 (Berlin)", ISSN = "0075-8450 (print), 1616-6361 (electronic)", ISSN-L = "0075-8450", LCCN = "QC150 .I59 1996", bibdate = "Fri Oct 26 18:51:40 MDT 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; z3950.loc.gov:7090/Voyager", series = "Lecture notes in physics", acknowledgement = ack-nhfb, subject = "Fluid dynamics; Congresses; Industrial applications; Differential equations, Partial; Numerical solutions; Navier--Stokes equations", } @Proceedings{Sakell:1996:PFA, editor = "L. Sakell and D. Knight", booktitle = "{Proceedings of the First AFOSR Conference on Dynamic Motion CFD: New Brunswick, New Jersey, June 3--5, 1996}", title = "{Proceedings of the First AFOSR Conference on Dynamic Motion CFD: New Brunswick, New Jersey, June 3--5, 1996}", publisher = "United States Air Force Office of Scientific Research", address = "Washington, DC, USA", pages = "xiii + 453", year = "1996", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Oct 26 18:37:57 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, remark = "Organized by and hosted at Rutgers University - The State University of New Jersey", } @Proceedings{Herbin:2002:FVC, editor = "Rapha{\`e}le Herbin and Dietmar Kr{\"o}ner", booktitle = "{Finite volumes for complex applications {III}. International Symposium on Finite Volumes for Complex Applications (Third: 2002: Porquerolles Island, France)}", title = "{Finite volumes for complex applications {III}. International Symposium on Finite Volumes for Complex Applications (Third: 2002: Porquerolles Island, France)}", publisher = "Kogan Page Science", address = "London, UK", pages = "851", year = "2002", ISBN = "1-903996-34-1", ISBN-13 = "978-1-903996-34-8", LCCN = "QA911 .I56 2002", bibdate = "Mon Oct 22 17:44:08 MDT 2007", bibsource = "z3950.loc.gov:7090/Voyager; https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, meetingname = "International Symposium on Finite Volumes for Complex Applications (3rd : 2002 : Porquerolles Island, France)", subject = "Finite volume method; Congresses", } @Proceedings{ACM:2005:PAI, editor = "{ACM}", booktitle = "{Proceedings of the 2005 ACM\slash IEEE conference on Supercomputing 2005, Seattle, WA, November 12--18 2005}", title = "{Proceedings of the 2005 ACM\slash IEEE conference on Supercomputing 2005, Seattle, WA, November 12--18 2005}", publisher = pub-ACM # " and " # pub-IEEE, address = pub-ACM:adr # " and " # pub-IEEE:adr, pages = "????", year = "2005", ISBN = "1-59593-061-2", ISBN-13 = "978-1-59593-061-3", LCCN = "????", bibdate = "Tue Dec 27 08:08:01 2005", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", acknowledgement = ack-nhfb, } @Book{Zomaya:2008:ACI, editor = "A. Zomaya and M. Parashar and S. Chandra and X. Li", title = "Advanced Computational Infrastructures for Parallel and Distributed Adaptive Applications", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "????", year = "2008", ISBN = "????", ISBN-13 = "????", LCCN = "????", bibdate = "Fri Oct 26 15:44:45 2007", bibsource = "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib", series = "Wiley Book Series on Parallel and Distributed Computing", acknowledgement = ack-nhfb, }

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