Domain decomposition algorithm for the parabolic equation with variable coefficient. (English) Zbl 1082.65097

Sheng, Zhiqiang; Liu, Xingping; Cui, Xia

Commun. Math. Sci. 2, No. 3, 391-402 (2004).

Summary: We design a domain decomposition algorithm for the two-dimensional parabolic equation with variable coefficient by using a larger spacing at interface points and the implicit scheme at the interior points, hence get an algorithm with the relaxed stability bounds. Then we prove the stability and analyze the accuracy of the algorithm by using the idea of maximum principle. Some results of numerical experiments are also provided.

MSC:

65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K15	Initial value problems for second-order parabolic equations

Keywords:

implicit scheme; parallel computation; finite difference; stability; algorithm; maximum principle; numerical experiments