Solution of the variable coefficients Poisson equation on Cartesian hierarchical meshes in parallel : applications to phase changing materials.

Alice Raeli 1, 2
1 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
Inria Bordeaux - Sud-Ouest, IMB - Institut de Mathématiques de Bordeaux
Abstract : We consider problems governed by a linear elliptic equation with varying coéficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second order accuracy. Numerical illustrations relevant for actual applications are presented in two and three-dimensional configurations.
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Alice Raeli. Solution of the variable coefficients Poisson equation on Cartesian hierarchical meshes in parallel : applications to phase changing materials.. Numerical Analysis [cs.NA]. Université de Bordeaux, 2017. English. ⟨NNT : 2017BORD0669⟩. ⟨tel-02005700⟩

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