Published

An Interface-Fitted Mesh Generator and Virtual Element Methods for Elliptic Interface Problems

Long Chen, Huayi Wei, and Min Wen

Journal of Computational Physics. 334(1), 2017, 327–348.

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ABSTRACT:

 A simple and efficient interface-fitted mesh algorithm which
can produce a semi-unstructured 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.