2014/04/08 by Stefan Sauter, Sauter, Stefan, Alexander Veit +1 · 3 citations
Engineering · Physics and Astronomy · #65N38 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · doi:10.48550/arxiv.1404.2322
openalex publication_date 2014/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 for approximation 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.