Title / Abstract
Retarded Potential Integral EquationsIn 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
- 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.
- 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.
- M. Lopez-Fernandez and S.A. Sauter, Generalized Convolution Quadrature with Variable Time Stepping. IMA J. Numer. Anal., 33(4):1156--1175, 2013.
- C.Lubich, Convolution quadrature and discretized operational calculus I & II. Numer. Math., 52:129--145 and 413-425, 1988.
- 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