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A parallel second order Cartesian method for elliptic interface problems

Abstract : We present in this paper a parallel Cartesian method to solve elliptic problems with complex immersed interfaces. This method is based on a finite difference scheme and second order accurate in the whole domain. We use a standard five point scheme for the discretization of the elliptic operator on all grid points, coupled with the discretization of transmission conditions across the interface. The originality of the method lies in the use of additional unknowns located on the interface, where the transmission conditions are imposed. We firstly describe the method itself and the details of its parallelization performed with the PETSc library. Then we present numerical validations in two dimensions, assorted with comparisons to other related methods, and a numerical study of the parallelized method.
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Submitted on : Tuesday, April 13, 2021 - 10:46:48 AM
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Marco Cisternino, Lisl Weynans. A parallel second order Cartesian method for elliptic interface problems. Communications in Computational Physics, Global Science Press, 2012, 12, pp.1562-1587. ⟨10.4208/cicp.160311.090112a⟩. ⟨inria-00577874v3⟩



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