Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
Copyright policy )Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
The authors consider a two-dimensional parabolic equation with small diffusion coefficient (but without convection terms!) and propose an overlapping Schwarz method for its solution. Whereas for theoretical details like exponential convergence they refer to unpublished work of the first author, in this paper the algorithms and numerical results are presented: an implicit Euler method for time discretization, a Bakhvalov-type grid for spatial discretization, and the Schwarz iteration on 2 or 3 levels. For the parallelization on a distributed memory multiprocessor, the message passing interface library is used. The authors conclude that it is more effective to solve some of the subproblems on the overlapping regions on coarser grids and employing time extrapolation.
- University of Jyväskylä Finland
- Russian Academy of Sciences Russian Federation
Parallel computing, Method of lines for initial value and initial-boundary value problems involving PDEs, implicit Euler method, Iterative numerical methods for linear systems, Applied Mathematics, Parallel numerical computation, Schwarz method, numerical results, algorithms, Computational Mathematics, Multi-level Schwarz method, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, multi-level methods, Singularly perturbed parabolic problem, parabolic problem, Initial value problems for second-order parabolic equations, parallel computation, singular perturbation, Singular perturbations in context of PDEs
Parallel computing, Method of lines for initial value and initial-boundary value problems involving PDEs, implicit Euler method, Iterative numerical methods for linear systems, Applied Mathematics, Parallel numerical computation, Schwarz method, numerical results, algorithms, Computational Mathematics, Multi-level Schwarz method, Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, Finite difference methods for initial value and initial-boundary value problems involving PDEs, multi-level methods, Singularly perturbed parabolic problem, parabolic problem, Initial value problems for second-order parabolic equations, parallel computation, singular perturbation, Singular perturbations in context of PDEs
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