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Volume 12, Issue 5
A Parallel Second Order Cartesian Method for Elliptic Interface Problems

Marco Cisternino & Lisl Weynans

DOI: 10.4208/cicp.160311.090112a

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

Published online: 2012-12

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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. 

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@Article{CiCP-12-1562, author = {Marco Cisternino and Lisl Weynans}, title = {A Parallel Second Order Cartesian Method for Elliptic Interface Problems}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {5}, pages = {1562--1587}, 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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.160311.090112a}, url = {http://global-sci.org/intro/article_detail/cicp/7347.html} }
TY - JOUR T1 - A Parallel Second Order Cartesian Method for Elliptic Interface Problems AU - Marco Cisternino & Lisl Weynans JO - Communications in Computational Physics VL - 5 SP - 1562 EP - 1587 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.160311.090112a UR - https://global-sci.org/intro/article_detail/cicp/7347.html KW - AB -

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. 

Marco Cisternino and Lisl Weynans. (2012). A Parallel Second Order Cartesian Method for Elliptic Interface Problems. Communications in Computational Physics. 12 (5). 1562-1587. doi:10.4208/cicp.160311.090112a
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