Volume integrals for boundary element methods. (English) Zbl 0752.65016
The aim of the paper is to numerically approximate volume integrals of the form \(\int_ D f(x)dx\). By piecewise linear approximation of the volume \(D\) the integral is approximated by a finite sum of integrals which are calculated by a repeated use of the trapezoidal rule. This rule is used in an adaptive refinement procedure the algorithm of which is given. To handle singularities numerically, the singular value of the integrand is replaced by a big number a coarse choice of which is discussed. Numerical examples are given.
Reviewer: G.Hämmerlin (München)
MSC:
| 65D32 | Numerical quadrature and cubature formulas |
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 41A55 | Approximate quadratures |
| 41A63 | Multidimensional problems |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
boundary element methods; adapted quadrature methods; Poisson’s equation; volume integrals; trapezoidal rule; adaptive refinement; algorithm; singularities; Numerical examplesReferences:
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