Please answer the following: 1. Name of conference 2. Type of Presentation Contributed: Lecture form Poster form Minisymposium: 3. Equipment for Visual Support Lecture Form/Minisymposium: Overhead Projector 2" x 2" Slide Projector (35mm) Poster Form: Easel Poster Board Other (specify) More sophisticated equipment can be provided, but you may be required to pay the rental fee. For details, indicate your requirements below: 4. If you are a speaker in a minisymposium, who is the organizer? 5. What is the minisymposium title? 6. If more than one author, who will present the paper? % This is a macro file for creating a SIAM Conference abstract in % LaTeX. % % If you have any questions regarding these macros contact: % Lillian Hunt % SIAM % 3600 University City Center Center % Philadelphia, PA 19104-2688 % USA % (215) 382-9800 % e-mail:meetings@siam.org \hsize=25.5pc \vsize=50pc \textheight 50pc \textwidth 25.5pc \parskip 0pt \parindent 0pt \pagestyle{plain} \def\title#1{\bf{#1}\vspace{6pt}} \def\abstract#1{\rm {#1}\vspace{6pt}} \def\author#1{\rm {#1}\vfill\eject} % end of style file % This is ltexconf.tex. Use this file as an example file for doing an SIAM % Conference abstract in LaTeX. \documentstyle[ltexconf]{report} \begin{document} \title{Numerical Analysis of a 1-Dimensional Immersed-Boundary\\ Method} \abstract{We present the numerical analysis of a simplified, one-dimensional version of Peskin's immersed boundary method, which has been used to solve the two- and three-dimensional Navier-Stokes equations in the presence of immersed boundaries. We consider the heat equation in a finite domain with a moving source term. We denote the solution as $u(x,t)$ and the location of the source term as $X(t)$. The source term is a moving delta function whose strength is a function of u at the location of the delta function. The p.d.e. is coupled to an ordinary differential equation whose solution gives the location of the source term. The o.d.e. is $X'(t) = u(X(t),t)$, which can be interpreted as saying the source term moves at the local velocity. The accuracy the numerical method of solution depends on how the delta function is discretized when the delta function is not at a grid point and on how the solution, u, is represented at locations between grid points. We present results showing the effect of different choices of spreading the source to the grid and of restricting the solution to the source location. The problem we analyze is also similar to the Stefan problem and the immersed-boundary method has features in common with particle-in-cell methods.} \author{\underbar{Richard P. Beyer, Jr.}\\ University of Washington, Seattle, WA\\ Randall J. LeVeque\\ University of Washington, Seattle, WA} \end{document} % end of example file. Please furnish complete addresses all co-authors. PLEASE INDICATE WHAT CONFERENCE ABSTRACT IS FOR.