Integral Equation Methods for Evolutionary PDE - Lehel Banjai, Francisco-Javier Sayas

Integral Equation Methods for Evolutionary PDE

A Convolution Quadrature Approach
Buch | Hardcover
XIX, 268 Seiten
2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-13219-3 (ISBN)
139,09 inkl. MwSt
This book provides a comprehensive analysis of time domain boundary integral equations and their discretisation by convolution quadrature and the boundary element method.
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.

Lehel Banjai is an Associate Professor at the Maxwell Institute for Mathematics in the Sciences, Heriot-Watt University, Edinburgh. The author of over 40 journal articles, he is best known for his work on time-domain boundary integral equations. He is currently an Associate Editor of the SIAM Journal on Numerical Analysis. 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.

1 Some examples of causal convolutions.- 2 Convolution quadrature for hyperbolic symbols.- 3 Algorithms for CQ: linear multistep methods.- 4 Acoustic scattering in the time domain.- 5 Runge-Kutta CQ.- 6 Transient electromagnetism.- 7 Boundary-field formulations.- 8 Parabolic problems.- 9 Data sparse methods and other topics.

Erscheinungsdatum
Reihe/Serie Springer Series in Computational Mathematics
Zusatzinfo XIX, 268 p. 1 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 554 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte acoustics • boundary integral equations • convolution quadrature • electromagnetism • hyperbolic partial differential equations • Numerical Analysis of Partial Differential Equations • Parabolic partial differential equations • Retarded potentials • time-domain boundary integral equations • wave equation
ISBN-10 3-031-13219-X / 303113219X
ISBN-13 978-3-031-13219-3 / 9783031132193
Zustand Neuware
Haben Sie eine Frage zum Produkt?
Mehr entdecken
aus dem Bereich

von Tilo Arens; Frank Hettlich; Christian Karpfinger …

Buch (2022)
Springer Spektrum (Verlag)
79,99