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.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes / Raeli, Alice; Michell, Bermann; Iollo, Angelo. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - ELETTRONICO. - 355:(2018), pp. 55-77. [10.1016/j.jcp.2017.11.007]

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

RAELI, ALICE;Angelo Iollo
2018

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2722806
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