Boundary Integral Equations

2008
ISBN: 978-3-540-15284-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 164, 620 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1115 g

Reihe: Applied Mathematical Sciences

This book is devoted to the mathematical foundation of boundary integral equations. The combination of ?nite element analysis on the boundary with these equations has led to very e?cient computational tools, the boundary element methods (see e.g., the authors [139] and Schanz and Steinbach (eds.) [267]). Although we do not deal with the boundary element discretizations in this book, the material presented here gives the mathematical foundation of these methods. In order to avoid over generalization we have con?ned ourselves to the treatment of elliptic boundary value problems. The central idea of eliminating the ?eld equations in the domain and - ducing boundary value problems to equivalent equations only on the bou- ary requires the knowledge of corresponding fundamental solutions, and this idea has a long history dating back to the work of Green [107] and Gauss [95, 96]. Today the resulting boundary integral equations still serve as a major tool for the analysis and construction of solutions to boundary value problems.

Zielgruppe

Research

Autoren/Hrsg.

Wendland, Wolfgang L.

Hsiao, George C.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

Inhaltsverzeichnis

Boundary Integral Equations.- Representation Formulae, Local Coordinates and Direct Boundary Integral Equations.- Sobolev Spaces.- Variational Formulations.- to Pseudodifferential Operators.- Pseudodifferential Operators as Integral Operators.- Pseudodifferential and Boundary Integral Operators.- Integral Equations on ?? IR3 Recast as Pseudodifferential Equations.- Boundary Integral Equations on Curves in IR2.