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Efficient implementation of finite element methods on nonmatching AND overlapping meshes in three dimensions
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2013 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, no 1, C23-C47 p.Article in journal (Refereed) Published
Abstract [en]

In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on nonmatching or overlapping meshes. Examples of such methods are the fictitious domain method, the extended finite element method, and Nitsche's method. In all these methods, integrals must be computed over cut cells or subsimplices, which is challenging to implement, especially in three space dimensions. In this note, we address the main challenges of such an implementation and demonstrate good performance of a fully general code for automatic detection of mesh intersections and integration over cut cells and subsimplices. As a canonical example of an overlapping mesh method, we consider Nitsche's method, which we apply to Poisson's equation and a linear elastic problem.

Place, publisher, year, edition, pages
2013. Vol. 35, no 1, C23-C47 p.
Keyword [en]
overlapping mesh, non-matching mesh, Nitsche method, discontinuous Galerkin method, immersed interface, extended finite element method, algorithm, implementation, computational geometry
National Category
URN: urn:nbn:se:umu:diva-68276DOI: 10.1137/11085949XISI: 000315575000039OAI: diva2:616192
Available from: 2013-04-15 Created: 2013-04-15 Last updated: 2013-04-15Bibliographically approved

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Larson, Mats G.
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Department of Mathematics and Mathematical Statistics
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