MGLab3D: An interactive environment for iterative solvers
for elliptic PDEs in two and three dimensions
James Bordner and Faisal Saied*
Department of Computer Science
University of Illinois at Urbana-Champaign
MGLab3D is an enhancement of an interactive environment (MGLab) for
experimenting with iterative solvers and multigrid algorithms.
It is implemented in MATLAB.
The new version has built-in 3D elliptic pde's and several iterative
methods and preconditioners that were not available in the original
version. A sparse direct solver option has also been included. The
multigrid solvers have also been extended to 3D.
The discretization and pde domains are restricted to standard finite
differences on the unit square/cube. The power of this software
lies in the fact that no programming is needed to solve, for example, the
convection-diffusion equation in 3D with TFQMR and a customized V-cycle
preconditioner, for a variety of problem sizes and mesh Reynolds' numbers.
In addition to the graphical user interface, some sample drivers are
included to show how experiments can be composed using the underlying
suite of problems and solvers.