Zurich Summer School 2014
Lecturer: S. Sauter18-22 August 2014

Title / Abstract

Retarded Potential Integral Equations

In my lectures I will consider the wave equation in a time-interval [0,T] and a three-dimensional domain D. I will explain how to reduce this equation to a retarded potential integral equation (RPIE) on [0,T] x S, where S is the two-dimensional surface of D.

This RPIE serves as a starting point for the numerical discretization of the wave equation. Among the most popular methods are the direct space-time Galerkin method (cf. lectures of T. Abboud) and the convolution quadrature method which will be also presented in my lectures.

Lecture Notes

Exercise Project

Readings

  1. A. Bamberger and T. Ha-Duong, Formulation variationelle espace-temps pour le calcul par potentiel retarde d'une onde acoustique. Math. Meth. Appl. Sci., 8:405--435 and 598--608, 1986.

  2. T. Ha-Duong, On Retarded Potential Boundary Integral Equations and their Discretization. In M. Ainsworth, P. Davies, D. Duncan, P. Martin, and B. Rynne, editors: Computational Methods in Wave Propagation, vol. 31, pages 301--336, Heidelberg, 2003. Springer.

  3. M. Lopez-Fernandez and S.A. Sauter, Generalized Convolution Quadrature with Variable Time Stepping. IMA J. Numer. Anal., 33(4):1156--1175, 2013.

  4. C.Lubich, Convolution quadrature and discretized operational calculus I & II. Numer. Math., 52:129--145 and 413-425, 1988.

  5. F.J. Sayas, Retarded potentials and time domain boundary integral equations: a road-map. Technical report, Dept. of Math. Sci., University of Delaware, 2014, https://www.math.udel.edu/~fjsayas/TDBIEclassnotes2012.pdf