Efficient automatic quadrature in 3-D Galerkin BEM. (English) Zbl 0943.65139

Summary: We present cubature methods approximating the surface integrals arising by Galerkin discretization of boundary integral equations on surfaces in \(\mathbb{R}^3\). This numerical integrator does not depend on the explicit form of the kernel function, the trial and test space, or the surface parametrization. Thus, it is possible to generate the system matrix for a broad class of integral equations just by replacing the subroutine for evaluating the kernel function. We present formulae to determine the minimal order of the cubature methods for a required accuracy. Emphasis is laid on numerical experiments confirming the theoretical results.


65N38 Boundary element methods for boundary value problems involving PDEs
65D32 Numerical quadrature and cubature formulas
35J25 Boundary value problems for second-order elliptic equations
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