Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report 461; September, 1989 (Classic Reprint) - Hardcover

Xiao-Chuan Cai

9780656193004: Some Domain Decomposition Algorithms for Nonselfadjoint Elliptic and Parabolic Partial Differential Equations: Technical Report 461; September, 1989 (Classic Reprint)

Hardcover

ISBN 10: 065619300X ISBN 13: 9780656193004

Publisher: Forgotten Books, 2018

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Accelerate solving large PDE systems with domain decomposition.

This book focuses on practical, parallel-friendly methods like the additive Schwarz method and iterative substructuring for linear systems arising from finite element discretizations of elliptic and parabolic equations.

It combines a clear abstract theory with concrete finite element implementations, and it includes analyses of convergence that are relevant for both stationary and time-dependent problems. The work emphasizes how these techniques can deliver robust performance across a range of mesh sizes and time steps, with attention to how nonselfadjoint operators behave in practice.

Learn how additive Schwarz and related substructure methods decompose a problem to solve many small systems in parallel.
Understand conditions that guarantee convergence and how these rates depend on mesh and time-step parameters.
See how GMRES and other iterative solvers fit into domain decomposition for nonselfadjoint problems.
Explore the implications of numerical experiments for symmetric and mildly nonsymmetric cases across elliptic and parabolic problems.

Ideal for readers who work with finite element PDEs and seek scalable, robust iterative strategies for large, real-world simulations.

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