Preconditioning a mixed discontinuous finite element method for radiation diffusion

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a nite element discretization of the radiation di usion equations. In particular, these equations are solved using a mixed nite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the di usion equation will be embedded. The essence of the preconditioner is to use a continuous nite element discretization of the original, elliptic di usion equation for preconditioning the discontinuous equations. We have found that this preconditioner is very e ective and makes the iterative solution of the discontinuous di usion 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 di usion problems on unstructured, tetrahedral meshes and show numerical results that illustrate its e ectiveness. Published in 2004 by John Wiley & Sons, Ltd.