Solution Of The Variable Coefficient Poisson Equation On Cartesian Hierarchical Meshes In Parallel: Applications To Phase Changing Materials

Alice Raeli 1, 2
2 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We consider problems governed by a linear elliptic equation with varying coefficients 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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Submitted on : Monday, December 18, 2017 - 3:38:26 PM
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Alice Raeli. Solution Of The Variable Coefficient Poisson Equation On Cartesian Hierarchical Meshes In Parallel: Applications To Phase Changing Materials. Numerical Analysis [math.NA]. IMB - Institut de Mathématiques de Bordeaux, 2017. English. ⟨tel-01666340⟩

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