Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem (Classic Reprint) - Hardcover

Xuejun Zhang

9780266272953: Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem (Classic Reprint)

Hardcover

ISBN 10: 0266272959 ISBN 13: 9780266272953

Publisher: Forgotten Books, 2017

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Explore advanced techniques for solving large elliptic systems with domain decomposition and multilevel methods.

This book dives into additive Schwarz and iterative substructuring methods, focusing on the biharmonic Dirichlet problem and how to achieve efficient, scalable performance on parallel computers.

The text surveys foundational theory, introduces multilevel algorithms, and presents practical algorithms using standard finite elements. It also develops new tools to prove optimal convergence and discusses numerical experiments that illustrate performance and robustness.

Understand the landscape of domain decomposition, Schwarz-type methods, and multilevel approaches.
Learn how condition numbers grow with levels and how vertex spaces improve efficiency.
See concrete algorithms for biharmonic problems discretized by bicubic, Argyris, and Bell elements.
Review numerical experiments that validate theoretical results and guide practical use.

Ideal for readers of advanced numerical analysis, scientific computing, and PDE solver design who want deeper insight into parallel-domain methods and their theoretical guarantees.

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