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Isogeometric boundary elements in electromagnetism: rigorous analysis, fast methods, and examples. (English) Zbl 07123202

Summary: We analyze 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.

MSC:

65D07 Numerical computation using splines
65N38 Boundary element methods for boundary value problems involving PDEs
65Y20 Complexity and performance of numerical algorithms

Software:

Bembel; hlib; GeoPDEs
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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