Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients.

Journal of Computational Physics
Kelin XiaGuo-Wei Wei

Abstract

Mesh deformation methods are a versatile strategy for solving partial differential equations (PDEs) with a vast variety of practical applications. However, these methods break down for elliptic PDEs with discontinuous coefficients, namely, elliptic interface problems. For this class of problems, the additional interface jump conditions are required to maintain the well-posedness of the governing equation. Consequently, in order to achieve high accuracy and high order convergence, additional numerical algorithms are required to enforce the interface jump conditions in solving elliptic interface problems. The present work introduces an interface technique based adaptively deformed mesh strategy for resolving elliptic interface problems. We take the advantages of the high accuracy, flexibility and robustness of the matched interface and boundary (MIB) method to construct an adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. The proposed method generates deformed meshes in the physical domain and solves the transformed governed equations in the computational domain, which maintains regular Cartesian meshes. The mesh deformation is realized by a mesh transformation PDE, which cont...Continue Reading

References

Jul 7, 2007·The Journal of Chemical Physics·Sining YuG W Wei
Sep 25, 2007·The Journal of Chemical Physics·Weihua GengGuowei Wei
Sep 17, 2010·Journal of Computational Chemistry·Duan ChenGuo-Wei Wei
Nov 23, 2010·Journal of Computational Physics·Weihua Geng, G W Wei

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