Sequential and parallel domain decomposition methods for a singularly perturbed parabolic convection-diffusion equation

DOI10.1134/S0081543808050180zbMath1237.65109MaRDI QIDQ764838

G. I. Shishkin, Irina V. Tselishcheva

Publication date: 14 March 2012

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergencedomain decompositionmethod of linesboundary value problemparabolic convection-diffusion equationSchwarz methodparallel copmutations

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Parallel numerical computation (65Y05) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Cites Work

• The convergence of classical Schwarz methods applied to convection--diffusion problems with regular boundary layers
• Domain Decomposition Type Iterative Techniques for Parabolic Problems on Locally Refined Grids
• Acceleration of the process of the numerical solution to singularly perturbed boundary value problems for parabolic equations on the basis of parallel computations
• High-order time-accurate parallel schemes for parabolic singularly perturbed problems with convection
• A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers
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