A Finite-Difference Method for the Variable Coefficient Poisson Equation on Hierarchical Cartesian Meshes

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 are presented in two and three-dimensional configurations. Finite difference method; Hierarchical Cartesian grid; Octree/Quadtree; Variable coefficient Poisson equation 1
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Alice Raeli, Michel Bergmann, Angelo Iollo. A Finite-Difference Method for the Variable Coefficient Poisson Equation on Hierarchical Cartesian Meshes. Journal of Computational Physics, Elsevier, 2017, 355, pp.59-77. ⟨10.1016/j.jcp.2017.11.007⟩. ⟨hal-01662050⟩

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