On numerical cubatures of nearly singular surface integrals arising in BEM collocation
Copyright policy )On numerical cubatures of nearly singular surface integrals arising in BEM collocation
The discretization of the boundary element method (BEM) in \(\mathbb{R}^ 3\) using collocation requires the numerical estimation of numerous nearly singular surface integrals. Efficient computational methods tailored to this application are developed. Local polar coordinates with a corner of the triangular surface elements as origin are used, and the radial inner integral is evaluated analytically. The second integration is performed using Gauss-Legendre quadrature of an adaptively chosen order. Numerical results illustrate the efficiency of the procedures.
- University of Zurich Switzerland
- Kiel University Germany
singular surface integrals, collocation, Multidimensional problems, cubature, Gauss-Legendre quadrature, Boundary element methods for boundary value problems involving PDEs, panel method, Numerical methods for integral equations, numerical results, Numerical quadrature and cubature formulas, numerical quadrature, Approximate quadratures, boundary element method, 1712 Software, 10123 Institute of Mathematics, 510 Mathematics, 1706 Computer Science Applications, Boundary element method, Integral equations with kernels of Cauchy type, 2614 Theoretical Computer Science, 2612 Numerical Analysis, 2605 Computational Mathematics, 1703 Computational Theory and Mathematics
singular surface integrals, collocation, Multidimensional problems, cubature, Gauss-Legendre quadrature, Boundary element methods for boundary value problems involving PDEs, panel method, Numerical methods for integral equations, numerical results, Numerical quadrature and cubature formulas, numerical quadrature, Approximate quadratures, boundary element method, 1712 Software, 10123 Institute of Mathematics, 510 Mathematics, 1706 Computer Science Applications, Boundary element method, Integral equations with kernels of Cauchy type, 2614 Theoretical Computer Science, 2612 Numerical Analysis, 2605 Computational Mathematics, 1703 Computational Theory and Mathematics
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