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

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arxiv 1708.09162 v2 pith:MMBEKZCX submitted 2017-08-30 math.NA cs.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 cs.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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  1. A Low-Frequency-Stable Higher-Order Isogeometric Discretization of the Augmented Electric Field Integral Equation

    cs.CE 2024-01 unverdicted novelty 5.0

    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.