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Developments in Mathematics

Boundary Integral Equation Methods and Numerical Solutions

Thin Plates on an Elastic Foundation

Authors: Constanda, Christian, Doty, Dale, Hamill, William

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  • ​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
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eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-319-26309-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-26307-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA in USD
  • ISBN 978-3-319-79927-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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)


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-319-26309-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-26307-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA in USD
  • ISBN 978-3-319-79927-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Boundary Integral Equation Methods and Numerical Solutions
Book Subtitle
Thin Plates on an Elastic Foundation
Authors
Series Title
Developments in Mathematics
Series Volume
35
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-26309-0
DOI
10.1007/978-3-319-26309-0
Hardcover ISBN
978-3-319-26307-6
Softcover ISBN
978-3-319-79927-8
Series ISSN
1389-2177
Edition Number
1
Number of Pages
XII, 232
Number of Illustrations
55 b/w illustrations, 196 illustrations in colour
Topics