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One‐level Newton–Krylov–Schwarz algorithm for unsteady non‐linear radiation diffusion problem
Author(s) -
Ovtchinnikov Serguei,
Cai XiaoChuan
Publication year - 2004
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.386
Subject(s) - solver , scalability , mathematics , diffusion , krylov subspace , convergence (economics) , generalized minimal residual method , algorithm , computer science , computational science , mathematical optimization , iterative method , physics , database , economics , thermodynamics , economic growth
Abstract 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 diffusion problem in two‐dimensional space. A robust solver technology is required for handling the high non‐linearity and large jumps in material coefficients typically associated with simulations of radiation diffusion phenomena. We show numerically that NKS converges well even with rather large inflow flux 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 fine 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.