Adaptive Time Discretization for Retarded Potentials
Stefan A. Sauter and Alexander Veit
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Submission date: 16. Sep. 2013
published in: Numerische Mathematik, 132 (2016) 3, p. 569-595
DOI number (of the published article): 10.1007/s00211-015-0726-5
MSC-Numbers: 35L05, 65N38, 65R20
Keywords and phrases: wave equation, retarded potential integral equation, a posteriori error estimation, adaptive solution
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In this paper, we will present advanced discretization methods for solving retarded potential integral equations. We employ a C∞-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∞ 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.