Additive Schwarz Methods for Elliptic Finite Element Problems in Three Dimensions (Classic Reprint) - Hardcover
Synopsis
Efficient strategies for solving large elliptic problems
This book presents additive Schwarz methods for three‑dimensional elliptic finite element problems, with practical algorithms and analysis designed for real‑world computations.
This work introduces a unifying framework for domain decomposition and multilevel approaches. It shows how interior substructure variables can be eliminated to focus on interface behavior, and it analyzes how different iterative schemes perform even when coefficients vary greatly. The material covers several concrete methods inspired by classic research, plus extensions to handle discontinuous coefficients.- Three main algorithms are described and analyzed within a common framework.
- Variants address problems with sharp coefficient jumps and complex substructure interfaces.
- Concrete implementations include wirebasket and vertex‑space enhancements, as well as Neumann–Neumann type methods.
- Multilevel ideas are integrated to improve scalability across mesh refinements.
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