AuthorsA. Massing, M. G. Larson and A. Logg
TitleEfficient Implementation of Finite Element Methods on Nonmatching and Overlapping Meshes in Three Dimensions
AfilliationScientific Computing, Center for Biomedical Computing (SFF), Scientific Computing
Project(s)Center for Biomedical Computing (SFF)
StatusPublished
Publication TypeJournal Article
Year of Publication2013
JournalSIAM Journal on Scientific Computing
Volume35
Number1
PaginationC23-C47
Abstract

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.

DOI10.1137/11085949X
Citation KeySimula.simula.2404