One-level Newton-Krylov-Schwarz algorithm for unsteady non-linear radiation diffusion problem

In this paper, we present a parallel Newton–Krylov–Schwarz (NKS)-based non-linearly implicit algorithm for the numerical solution of the unsteady non-linear multimaterial radiation di usion problem in two-dimensional space. A robust solver technology is required for handling the high non-linearity and large jumps in material coe cients typically associated with simulations of radiation di usion phenomena. We show numerically that NKS converges well even with rather large in ow ux boundary conditions. We observe that the approach is non-linearly scalable, but not linearly scalable in terms of iteration numbers. However, CPU time is more important than the iteration numbers, and our numerical experiments show that the algorithm is CPU-time-scalable even without a coarse space given that the mesh is ne enough. This makes the algorithm potentially more attractive than multilevel methods, especially on unstructured grids, where course grids are often not easy to construct. Copyright ? 2004 John Wiley & Sons, Ltd.