Adaptive time discretization for retarded potentials
- Resource Type
- Authors
- Alexander Veit; Stefan A. Sauter
- Source
- Numerische Mathematik
- Subject
- Discretization
340 Law
610 Medicine & health
010103 numerical & computational mathematics
01 natural sciences
510 Mathematics
2604 Applied Mathematics
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
FOS: Mathematics
Mathematics - Numerical Analysis
0101 mathematics
Boundary element method
Mathematics
Discretization of continuous features
Numerical analysis
Applied Mathematics
Mathematical analysis
Estimator
Numerical Analysis (math.NA)
65N38
Integral equation
Quadrature (mathematics)
010101 applied mathematics
10123 Institute of Mathematics
Computational Mathematics
Nyström method
2605 Computational Mathematics
- Language
- English
In this paper, we will present advanced discretization methods for solving retarded potential integral equations. We employ a $$C^{\infty }$$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) $$C^{\infty }$$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.