2018/07/09 by Jürgen Dölz, Dölz, Jürgen, Stefan Kurz +5
Computer Science · Engineering · Mathematics · #65D07 #65N38 #65Y20 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Polynomial and algebraic computation #cs.NA #math.NA #msc:65D07 #msc:65N38 #msc:65Y20
paper · pdf · doi:10.48550/arxiv.1807.03097
openalex publication_date 2018/07/09 · arxiv created 2019/06/27 · arxiv updated 2019/06/28 · openalex created_date 2022/08/04 · openalex updated_date 2026/08/01
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.