Overview
- Presents and explains a general, efficient, and elegant method of a solution for boundary value problems for an elliptic system of partial differential equations
- Shows in detail a methodology for constructing a boundary integral equation method (BIEM), and all the attending mathematical properties are derived with full rigor
- Develops and employs a numerical scheme directly related to the BIEMs to compute approximate solutions
Part of the book series: Developments in Mathematics (DEVM, volume 35)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy.
The book is intended for graduate students and researchers in the fields of boundary integral equation methods, computational mechanics and, more generally, scientists working in the areas of applied mathematics and engineering. Given its detailed presentation of the material, the book can also be used as a text in a specialized graduate course on the applications of the boundary element method to the numerical computation of solutions in a wide variety of problems.
Reviews
“The book describes the mathematical model analytically and uses it to show how a boundary element method can be constructed and manipulated to compute a numerical solution. The book should be a good source of information for engineers, mathematicians and physicists interested in studying the boundary integral equation methods.” (Răzvan Răducanu, zbMATH 1339.74002, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Boundary Integral Equation Methods and Numerical Solutions
Book Subtitle: Thin Plates on an Elastic Foundation
Authors: Christian Constanda, Dale Doty, William Hamill
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-319-26309-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-26307-6Published: 01 April 2016
Softcover ISBN: 978-3-319-79927-8Published: 24 April 2018
eBook ISBN: 978-3-319-26309-0Published: 16 March 2016
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XII, 232
Number of Illustrations: 55 b/w illustrations, 196 illustrations in colour
Topics: Integral Equations, Partial Differential Equations, Functions of a Complex Variable