Numerical quadrature over triangles with weak singularities. (English) Zbl 0959.65133
Summary: The paper studies in a unified way the numerical computation of integrals over triangles with weak singularities arising from the \(\ln r\) and \(1/r\) kernels present in the boundary element method by mapping the triangle into a square and thus obtaining a regularizing effect. Three types of coordinate transformations are evaluated and their performance with respect to numerical quadrature is assessed.
MSC:
| 65N38 | Boundary element methods for boundary value problems involving PDEs |
| 65Y20 | Complexity and performance of numerical algorithms |
| 35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |
Keywords:
boundary element method; regularization; Poisson’s equation; weak singularities; coordinate transformations; performance; numerical quadratureSoftware:
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