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A Parallel Second Order Cartesian Method for Elliptic Interface Problems

Published online by Cambridge University Press:  20 August 2015

Marco Cisternino  and
Lisl Weynans
Marco Cisternino*
Affiliation:
Dipartimento di Ingegneria Aeronautica e Spaziale, Politecnico di Torino C.so Duca degli Abruzzi 24, 10129 Torino, Italy
Lisl Weynans*
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France. CNRS, IMB, UMR 5251, F-33400 Talence, France. INRIA, F-33400 Talence, France
*
Corresponding author.Email address:lisl.weynans@math.u-bordeaux1.fr
Email address:marco.cisternino@polito.it
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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.

Keywords

65N0665N1265Y05Elliptic interface problemCartesian methodsecond-order schemeinterface unknowns
Type
Research Article
Information
Communications in Computational Physics , Volume 12 , Issue 5 , November 2012 , pp. 1562 - 1587
Copyright
Copyright © Global Science Press Limited 2012

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