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MiS Preprint

Adaptive Time Discretization for Retarded Potentials

Stefan A. Sauter and Alexander Veit


In this paper, we will present advanced discretization methods for solving retarded potential integral equations. We employ a $C^{\infty}$-partition of unity method in time and a conventional boundary element method for the spatial discretization. One essential point for the algorithmic realization is the development of an efficient method to approximate the elements of the arising system matrix. We present here an approach which is based on quadrature for (non-analytic) $C^{\infty}$ functions in combination with certain Chebyshev expansions.

Furthermore we introduce an a posteriori error estimator for the time discretization which is employed also as an error indicator for adaptive refinement. Numerical experiments show the fast convergence of the proposed quadrature method and the efficiency of the adaptive solution process.

MSC Codes:
35L05, 65N38, 65R20
wave equation, retarded potential integral equation, a posteriori error estimation, adaptive solution

Related publications

2016 Repository Open Access
Stefan A. Sauter and Alexander Veit

Adaptive time discretization for retarded potentials

In: Numerische Mathematik, 132 (2016) 3, pp. 569-595