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| HAL: inria-00577874, version 2 |
| DOI: 10.4208/cicp.160311.090112a |
| See detailed view |  BibTeX,EndNote,... |
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| Communications in Computational Physics 12 (2012) 1562-1587 |
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| Available versions | v1 (2011-03-19) | v2 (2011-03-31) |
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| A parallel second order Cartesian method for elliptic interface problems |
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| Marco Cisternino 1Lisl Weynans 2, 3 |
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| (2012-06-12) |
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| 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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| 1: | Dipartimento di Ingegneria Aeronautica e Spaziale [Torino] (DIASP) |
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Politecnico di Torino |
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| 2: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 3: | MC2 (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR |
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| Domain | : | Mathematics/Numerical Analysis |
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| Elliptic interface problem – Cartesian method – Second order scheme. |
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| inria-00577874, version 2 | |
| http://hal.inria.fr/inria-00577874 | |
| oai:hal.inria.fr:inria-00577874 | |
| From: Lisl Weynans | |
| Submitted on: Thursday, 31 March 2011 10:16:54 | |
| Updated on: Wednesday, 12 December 2012 16:34:03 | |
