Multi-Patch IGA-BEM for Helmholtz Problems using B-spline Tailored Numerical Integration
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In this talk we present a collocation Isogeometric Boundary Element Method (IGA-BEM) for 3D Helmholtz problems on (non)conformal discretization spaces using suitable quadrature rules for the governing (weakly singular) integrals with B-spline trial functions. The integration rules can be described by two main features. The first one is a novel higher order isoparametric singularity extraction technique for smooth surfaces. By applying the technique, the singular part of the integral is isolated and evaluated analytically. The second one is utilized for the remaining regular part of the integral – a spline-based quasi-interpolation technique. There is no need for denser quadrature node distribution near the singular points; uniform distribution is preferable to improve the implementation efficiency. The integration scheme has high order converge rates and since it is tailored for spline integrands, it perfectly fits in the isogeometric framework. B-spline spaces with nonconformal connections across patches using a not-a-knot conditions effortlessly increase the flexibility to model problems on more challenging domains. Several numerical examples demonstrate the applications of the novel numerical integration on (non)conformal discretization spaces.
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