Efficient Quadratures for Potential Problems in Boundary Element Method
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Attractiveness of isogeometric boundary element method relies greatly on efficient implementation of accurate numerical integration routines that exploits inter-element continuity of B-splines. In this talk we focus on quadratures for governing (weakly singular) integrals that appear in collocation boundary integral equations in 3D potential problems and discretization with tensor product B-splines. When assumed that the knot vectors of the B-splines and the collocation points are uniformly spaced, the complexity of the quadrature can be greatly reduced by storing values of simpler integrals in lookup tables. The quadratures are described by two main steps. The first one is a high order isoparametric singularity extraction technique that isolates singular contribution of the integral and evaluates it analytically. The second step is a spline-based quasi-interpolation technique, utilized on the remaining regular part of the integral. With numerical examples we demonstrate that the expected optimal orders of convergence for the approximate solutions are achieved with a small number of uniformly spaced quadrature nodes.