Boundary Integral Equations / by George C. Hsiao, Wolfgang L. Wendland.

Format:

Book

Author/Creator:

Hsiao, G. C. (George C.), author.

Wendland, W. L. (Wolfgang L.), 1936- author.

Series:

Applied Mathematical Sciences, 2196-968X ; 164

Language:

English

Subjects (All):

Mathematics--Data processing.

Mathematics.

Numerical analysis.

Engineering mathematics.

Engineering--Data processing.

Engineering.

Mathematical analysis.

Computational Mathematics and Numerical Analysis.

Numerical Analysis.

Mathematical and Computational Engineering Applications.

Analysis.

Local Subjects:

Computational Mathematics and Numerical Analysis.

Numerical Analysis.

Mathematical and Computational Engineering Applications.

Analysis.

Physical Description:

1 online resource (xx, 783 pages) : illustrations.

Edition:

2nd ed. 2021.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2021.

Summary:

This is the second edition of the book which has two additional new chapters on Maxwell’s equations as well as a section on properties of solution spaces of Maxwell’s equations and their trace spaces. These two new chapters, which summarize the most up-to-date results in the literature for the Maxwell’s equations, are sufficient enough to serve as a self-contained introductory book on the modern mathematical theory of boundary integral equations in electromagnetics. The book now contains 12 chapters and is divided into two parts. The first six chapters present modern mathematical theory of boundary integral equations that arise in fundamental problems in continuum mechanics and electromagnetics based on the approach of variational formulations of the equations. The second six chapters present an introduction to basic classical theory of the pseudo-differential operators. The aforementioned corresponding boundary integral operators can now be recast as pseudo-differential operators. These serve as concrete examples that illustrate the basic ideas of how one may apply the theory of pseudo-differential operators and their calculus to obtain additional properties for the corresponding boundary integral operators. These two different approaches are complementary to each other. Both serve as the mathematical foundation of the boundary element methods, which have become extremely popular and efficient computational tools for boundary problems in applications. This book contains a wide spectrum of boundary integral equations arising in fundamental problems in continuum mechanics and electromagnetics. The book is a major scholarly contribution to the modern approaches of boundary integral equations, and should be accessible and useful to a large community of advanced graduate students and researchers in mathematics, physics, and engineering.

Contents:

Introduction

Boundary Integral Equations

Representation Formulae

Sobolev Spaces

Variational Formulations

Electromagnetic Fields

Introduction to Pseudodifferential Operators

Pseudodifferential Operators as Integral Operators

Pseudodifferential and Boundary Integral Operators

Integral Equations on Recast as Pseudodifferential Equations

Boundary Integral Equations on Curves in R^2. Remarks on Pseudodifferential Operators for Maxwell Equations

Appendix A: Local Coordinates

Appendix B: Vector Field Identities, Integration Formulae

References

Index.

Notes:

Includes bibliographical references and index.

ISBN:

3-030-71127-7

OCLC:

1245857973