Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities

Erscheinungsjahr 1998
ISBN: 978-0-7923-5084-2
Verlag: Springer

Buch, Englisch, 479 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1950 g

Reihe: Mathematics and Its Applications

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.
The book is intended for both mathematicians and engineers and may be used as text for advanced students.

Zielgruppe

Research

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik

Inhaltsverzeichnis

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.