Mathematics
and Computer Science Speaker Series
California State University, Stanislaus
Date: Friday, April 30, 2010
Time: 3:30 - 4:30 p.m
Room: P-101
Speaker: Michael Bice
Title: Multigrid Methods for Approximating Solutions of
Partial Differential Equations
Abstract: Approximating the solutions of partial differential
equations has long been a major topic of research in numerical
analysis. Methods for obtaining these approximations utilize a
discretization of the space and/or time intervals under consideration,
creating a grid of points on which the PDE's solution is
obtained. Using more points in the discretization improves the
accuracy of the approximation but increases the computational expense
of the method. In an effort to reduce this expense, multigrid
methods were developed in the 1970s and 1980s. Such methods
exploit characteristics of certain PDEs that allow their solutions to
be well-approximated on a grid with fewer points. These
approximations are then transferred to grids with more points with
little or no loss of information. I will introduce how these
methods work and discuss how multigrid methods are currently being used
on a specific class of PDEs known as hyperbolic conservation laws.