Overview
- Provides analysis and algorithms of convolution quadrature discretisation of boundary integral equations
- Includes short Matlab codes to illustrate the numerical methods
- Goes beyond basic wave scattering settings, including non-linear boundary conditions and FEM/BEM coupling
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 59)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Properties of convolution quadrature, based on both linear multistep and Runge–Kutta methods, are explained in detail, always with wave propagation problems in mind. Main algorithms for implementing the discrete schemes are described and illustrated by short Matlab codes; translation to other languages can be found on the accompanying GitHub page. The codes are used to present numerous numerical examples to give the reader a feeling for the qualitative behaviour of the discrete schemes in practice. Applications to acoustic and electromagnetic scattering are described with an emphasis on the acoustic case where the fully discrete schemes for sound-soft and sound-hard scattering are developed and analysed in detail. A strength of the book is that more advanced applications such as linear and non-linear impedance boundary conditions and FEM/BEM coupling are also covered. While the focus is on wave scattering, a chapter on parabolic problems is included which also covers the relevant fast and oblivious algorithms. Finally, a brief description of data sparse techniques and modified convolution quadrature methods completes the book.
Suitable for graduate students and above, this book is essentially self-contained, with background in mathematical analysis listed in the appendix along with other useful facts. Although not strictly necessary, some familiarity with boundary integral equations for steady state problems is desirable.
Authors and Affiliations
About the authors
Francisco-Javier Sayas was a Professor of Mathematical Sciences at the University of Delaware. He published over one hundred research articles in refereed journals and the books Retarded Potentials and Time Domain Boundary Integral Equations, Variational Techniques for Elliptic Partial Differential Equations and An Invitation to the Theory of the Hybridizable Discontinuous Galerkin Method.
Bibliographic Information
Book Title: Integral Equation Methods for Evolutionary PDE
Book Subtitle: A Convolution Quadrature Approach
Authors: Lehel Banjai, Francisco-Javier Sayas
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-031-13220-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2022
Hardcover ISBN: 978-3-031-13219-3Published: 09 November 2022
Softcover ISBN: 978-3-031-13222-3Published: 10 November 2023
eBook ISBN: 978-3-031-13220-9Published: 08 November 2022
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 1
Number of Pages: XIX, 268
Number of Illustrations: 1 b/w illustrations
Topics: Numerical Analysis, Integral Equations, Analysis