Boundary integral equations / George C. Hsiao, Wolfgang L. Wendland.

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Boundary integral equations / George C. Hsiao, Wolfgang L. Wendland.

Second edition.

9783030711276 (electronic book)
3030711277 (electronic book)
9783030711283 (print)
3030711285
9783030711290 (print)
3030711293
9783030711269
3030711269

Cham, Switzerland : Springer, [2021]

English

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

10.1007/978-3-030-71127-6 doi

QA431 .A64 2021

515.45

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.-- Provided by publisher.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed April 15, 2021).

Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 164.

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