Commun. Comput. Phys., 12 (2012), pp. 1562-1587.


A Parallel Second Order Cartesian Method for Elliptic Interface Problems

Marco Cisternino 1, Lisl Weynans 2*

1 Dipartimento di Ingegneria Aeronautica e Spaziale, Politecnico di Torino C.so Duca degli Abruzzi 24, 10129 Torino, Italy.
2 Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France. CNRS, IMB, UMR 5251, F-33400 Talence, France. INRIA, F-33400 Talence, France.

Received 16 March 2011; Accepted (in revised version) 9 January 2012
Available online 4 June 2012
doi:10.4208/cicp.160311.090112a

Abstract

We present a parallel Cartesian method to solve elliptic problems with complex immersed interfaces. This method is based on a finite-difference scheme and is second-order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express straightforwardly the interface transmission conditions. We describe the method 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.

AMS subject classifications: 65N06, 65N12, 65Y05

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Key words: Elliptic interface problem, Cartesian method, second-order scheme, interface unknowns.

*Corresponding author.
Email: marco.cisternino@polito.it (M. Cisternino), lisl.weynans@math.u-bordeaux1.fr (L. Weynans)
 

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