Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities / Edition 1

by Zi Cai Li

Overview

In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid.
Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.

Product Details

ISBN-13:	9780792350842
Publisher:	Springer US
Publication date:	05/31/1998
Series:	Mathematics and Its Applications , #444
Edition description:	1998
Pages:	479
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

I Singularities, Treatments and Combinations.- 1 Different Numerical Methods.- 2 Singularities and Treatments.- II Combined Methods.- 3 Boundary Approximation Methods.- 4 Combinations of RGM and FEM.- 5 Combinations of Various Fems.- III Coupling Techniques.- 6 Lagrange Multipliers and Other Coupling Techniques.- 7 Penalty Techniques.- 8 Simplified Hybrid Methods.- 9 Penalty Plus Hybrid Techniques.- 10 Optimal Combinations for Various Fems.- 11 Combinations of RGM and FDM.- IV Applications and Advanced Topics.- 12 Crack-Infinity Problem.- 13 Wind Flow Over Buildings.- 14 Global Superconvergence In Combinations.- 15 Iterative Substructing Methods.- 16 Schwarz Alternating Method.- Epilogue.- Epilogue.- References.- Glossary of Symbols.

Editorial Reviews

For mathematicians and engineers, explores the questions: Which numerical methods may be combined together? and How can different numerical methods be matched together? The advantages of combined methods over single methods include high accuracy of solutions, less CPU time, less computer storage, and easy coupling with singularities as well as the complicated boundary conditions. This work provides matching rules so that optimal convergence can be achieved, and also warns of matching pitfalls to avoid. Among the topics: different numerical methods, singularities and treatments, boundary approximation methods, penalty techniques, simplified hybrid methods, crack-infinity problem, wind flow over buildings, and Schwarz alternating method. Annotation c. by Book News, Inc., Portland, Or.

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