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A fast isogeometric BEM for the three dimensional Laplace- and Helmholtz problems. (English) Zbl 1439.65208

Summary: We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract the problems arising due to the dense matrices produced by boundary element methods. By solving Laplace and Helmholtz problems via a single layer approach we show, through a series of numerical examples suitable for easy comparison with other numerical schemes, that one can indeed achieve extremely high rates of convergence of the pointwise potential through the utilisation of higher order B-spline-based ansatz functions.

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
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