An interface-fitted mesh generator and virtual element methods for elliptic interface problems

A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-structured interface-fitted mesh in two and three dimensions quickly is developed in this paper. Elements in such interface-fitted meshes are not restricted to simplices but can be polygons or polyhedra. Espec...

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Bibliographic Details
Published in:Journal of computational physics 2017-04, Vol.334, p.327-348
Main Authors: Chen, Long, Wei, Huayi, Wen, Min
Format: Article
Language:English
Subjects:
Algebra
Computational physics
Control systems
Delaunay triangulation
Elliptic interface problem
Interface-fitted mesh
Linear algebra
Mesh generation
Nonlinear equations
Nonlinear systems
Polyhedra
Semi-structured
Slivers
Solvers
Stochastic control theory
Stochastic models
Virtual element method
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Summary:A simple and efficient interface-fitted mesh generation algorithm which can produce a semi-structured interface-fitted mesh in two and three dimensions quickly is developed in this paper. Elements in such interface-fitted meshes are not restricted to simplices but can be polygons or polyhedra. Especially in 3D, the polyhedra instead of tetrahedra can avoid slivers. Virtual element methods are applied to solve elliptic interface problems with solutions and flux jump conditions. Algebraic multigrid solvers are used to solve the resulting linear algebraic system. Numerical results are presented to illustrate the effectiveness of our method.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2017.01.004