Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples
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DOI：
10.1137/18m1227251
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发表时间：
2018-07
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影响因子：
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通讯作者：
Jürgen Dölz;S. Kurz;S. Schöps;Felix Wolf
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文献类型：
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作者：
Jürgen Dölz;S. Kurz;S. Schöps;Felix Wolf
提出了一种求解三维电磁散射问题的快速等几何边界元方法。从周围的电场积分方程的理论设置在等几何框架内的调查，我们显示的存在性，唯一性和准最优的等几何方法。为了快速和有效的计算，我们然后介绍和分析了一个基于插值的快速多极子方法量身定制的等几何设置，承认竞争力的算法和复杂性。接下来是一系列工业范围的数值示例，以及对结果的详细介绍和解释。
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.