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Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples

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arxiv 1807.03097 v2 pith:ZHW4FAA5 submitted 2018-07-09 math.NA cs.NA

Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples

J\"urgen D\"olz , Stefan Kurz , Sebastian Sch\"ops , Felix Wolf This is my paper
classification math.NA cs.NA
keywords isogeometricfastapproachboundaryexamplesmethodssettingadmits
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We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within the isogeometric framework, we show existence, uniqueness, and quasi-optimality of the isogeometric approach. For a fast and efficient computation, we then introduce and analyze an interpolation-based fast multipole method tailored to the isogeometric setting, which admits competitive algorithmic and complexity properties. This is followed by a series of numerical examples of industrial scope, together with a detailed presentation and interpretation of the results.

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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.