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Efficient implementation of finite element methods on nonmatching and overlapping meshes in three dimensions

A. Massing ; M.G. Larson ; Anders Logg (Institutionen för matematiska vetenskaper, matematik)
SIAM Journal on Scientific Computing (1064-8275). Vol. 35 (2013), 1, p. C23-C47.
[Artikel, refereegranskad vetenskaplig]

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. © 2013 Society for Industrial and Applied Mathematics.

Nyckelord: Algorithm , Computational geometry , Discontinuous Galerkin method , Extended finite element method , Immersed interface , Implementation , Nitsche method , Non-matching mesh , Overlapping mesh



Denna post skapades 2014-01-05. Senast ändrad 2015-02-16.
CPL Pubid: 191172

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik
Beräkningsmatematik

Chalmers infrastruktur