A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz Problems

Felix Wolf; Helmut Harbrecht; J\"urgen D\"olz; Sebastian Sch\"ops; Stefan Kurz

arxiv: 1708.09162 · v2 · pith:MMBEKZCXnew · submitted 2017-08-30 · 🧮 math.NA

A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz Problems

J\"urgen D\"olz , Helmut Harbrecht , Stefan Kurz , Sebastian Sch\"ops , Felix Wolf This is my paper

classification 🧮 math.NA

keywords problemsboundaryelementfasthelmholtzhighermethodnumerical

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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.

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A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation
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A higher-order isogeometric discretization of the augmented EFIE using NURBS geometry representation that avoids low-frequency breakdown via deflation and demonstrates convergence on academic and realistic cases.