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

Dölz, Jürgen and Harbrecht, Helmut and Kurz, Stefan and Schöps, Sebastian and Wolf, Felix (2018):
A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz Problems.
In: Computer Methods in Applied Mechanics and Engineering, Elsevier, pp. 83-101, 330, ISSN 0045-7825, DOI: 10.1016/j.cma.2017.10.020, [Online-Edition: https://doi.org/10.1016/j.cma.2017.10.020],
[Article]

Abstract

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.

Item Type: Article
Erschienen: 2018
Creators: Dölz, Jürgen and Harbrecht, Helmut and Kurz, Stefan and Schöps, Sebastian and Wolf, Felix
Title: A Fast Isogeometric BEM for the Three Dimensional Laplace- and Helmholtz Problems
Language: English
Abstract:

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.

Journal or Publication Title: Computer Methods in Applied Mechanics and Engineering
Volume: 330
Publisher: Elsevier
Uncontrolled Keywords: iga, bem
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute of Electromagnetic Field Theory (from 01.01.2019 renamed Institute for Accelerator Science and Electromagnetic Fields)
18 Department of Electrical Engineering and Information Technology > Institute of Electromagnetic Field Theory (from 01.01.2019 renamed Institute for Accelerator Science and Electromagnetic Fields) > Computational Engineering (from 01.01.2019 renamed Computational Electromagnetics)
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 20 Nov 2017 06:21
DOI: 10.1016/j.cma.2017.10.020
Official URL: https://doi.org/10.1016/j.cma.2017.10.020
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