Preconditioning a Mixed Discontinuous Finite Element Method for Radiation Diffusion

James S. Warsa
Transport Methods Group, Los Alamos National Laboratory, Los Alamos, NM

Michele Benzi
Department of Mathematics and Computer Science, Emory University, Atlanta, GA

Todd Wareing
Transport Methods Group, Los Alamos National Laboratory, Los Alamos, NM

Jim Morel
Transport Methods Group, Los Alamos National Laboratory, Los Alamos, NM

Abstract

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a finite element discretization of the radiation diffusion equations. In particular, these equations are solved using a mixed finite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the diffusion equation will be embedded. The essence of the preconditioner is to use a continuous discretization of the original, elliptic diffusion equation for preconditioning the discontinuous equations. We have found that this preconditioner is very effective and makes the iterative solution of the discontinuous diffusion equations practical for large problems. This approach should be applicable to discontinuous discretizations of other elliptic equations. We show how our preconditioner is developed and applied to radiation diffusion problems on unstructured, tetrahedral meshes and show numerical results that illustrate its effectiveness.


Contributed October 2, 2001.