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Highly accurate surface and volume integration on implicit domains by means of moment-fitting

Müller, Björn and Kummer, Florian and Oberlack, Martin (2013):
Highly accurate surface and volume integration on implicit domains by means of moment-fitting.
96, In: International Journal for Numerical Methods in Engineering, (8), Wiley, pp. 512-528, ISSN 0029-5981, [Online-Edition: http://onlinelibrary.wiley.com/doi/10.1002/nme.4569/abstract],
[Article]

Abstract

We introduce a new method for the numerical integration over curved surfaces and volumes defined by a level set function. The method is based on the solution of a small linear system based on a simplified variant of the moment-fitting equations. Numerical experiments suggest that the accuracy of the resulting quadrature rules exceeds the accuracy of traditional methods by orders of magnitude. Using moments up to an order of p, the measured experimental orders of convergence exceed hp. Consequently, their construction is very efficient because only coarse computational grids are required. The conceptual simplicity allows for the application on very general grid types, which is demonstrated by numerical experiments on quadrilateral, triangular and hexahedral grids.

Item Type: Article
Erschienen: 2013
Creators: Müller, Björn and Kummer, Florian and Oberlack, Martin
Title: Highly accurate surface and volume integration on implicit domains by means of moment-fitting
Language: English
Abstract:

We introduce a new method for the numerical integration over curved surfaces and volumes defined by a level set function. The method is based on the solution of a small linear system based on a simplified variant of the moment-fitting equations. Numerical experiments suggest that the accuracy of the resulting quadrature rules exceeds the accuracy of traditional methods by orders of magnitude. Using moments up to an order of p, the measured experimental orders of convergence exceed hp. Consequently, their construction is very efficient because only coarse computational grids are required. The conceptual simplicity allows for the application on very general grid types, which is demonstrated by numerical experiments on quadrilateral, triangular and hexahedral grids.

Journal or Publication Title: International Journal for Numerical Methods in Engineering
Volume: 96
Number: 8
Publisher: Wiley
Uncontrolled Keywords: BoSSS
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Fluid Dynamics (fdy)
DFG-Collaborative Research Centres (incl. Transregio)
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
Exzellenzinitiative
Exzellenzinitiative > Clusters of Excellence
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Zentrale Einrichtungen
Exzellenzinitiative > Clusters of Excellence > Center of Smart Interfaces (CSI)
Date Deposited: 05 Sep 2013 12:34
Official URL: http://onlinelibrary.wiley.com/doi/10.1002/nme.4569/abstract
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