Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem

Niall Madden

doi:10.1007/978-3-319-67168-0_4

Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem

Niall Madden

Mathematics

Research output: Chapter in Book or Conference Publication/Proceeding › Chapter › peer-review

Abstract

The solution of linear systems of equations that arise when singularly perturbed partial differential equations are discretized can be difficult: direct solvers scale poorly, but are also known not to be robust with respect to the perturbation parameter, while the design of parameter robust preconditioners is not trivial, primarily due to the specialised layer adapted meshes used for such problems; see MacLachlan and Madden (SIAM J Sci Comput 35:A2225A2254, 2013). Here we present a multigrid solver strategy that circumvents this problem by using a robust patched mesh method proposed by de Falco and ORiordan (BAIL 2008-Boundary and Interior Layers vol. 69, pp. 117127. Springer, Berlin, 2009), as well as permitting parallelization. Numerical results demonstrate the efficiency of the method.

Original language	English (Ireland)
Title of host publication	Modeling, Simulation and Optimization of Complex Processes HPSC 2015
Publisher	Springer
ISBN (Electronic)	978-3-319-67167-3
ISBN (Print)	978-3-319-67167-3
DOIs	https://doi.org/10.1007/978-3-319-67168-0_4
Publication status	Published - 1 Jan 2017

Authors (Note for portal: view the doc link for the full list of authors)

Authors
José Luis Gracia, Niall Madden, Thái Anh Nhan

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10.1007/978-3-319-67168-0_4

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abstract = "The solution of linear systems of equations that arise when singularly perturbed partial differential equations are discretized can be difficult: direct solvers scale poorly, but are also known not to be robust with respect to the perturbation parameter, while the design of parameter robust preconditioners is not trivial, primarily due to the specialised layer adapted meshes used for such problems; see MacLachlan and Madden (SIAM J Sci Comput 35:A2225A2254, 2013). Here we present a multigrid solver strategy that circumvents this problem by using a robust patched mesh method proposed by de Falco and ORiordan (BAIL 2008-Boundary and Interior Layers vol. 69, pp. 117127. Springer, Berlin, 2009), as well as permitting parallelization. Numerical results demonstrate the efficiency of the method. ",

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PY - 2017/1/1

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N2 - The solution of linear systems of equations that arise when singularly perturbed partial differential equations are discretized can be difficult: direct solvers scale poorly, but are also known not to be robust with respect to the perturbation parameter, while the design of parameter robust preconditioners is not trivial, primarily due to the specialised layer adapted meshes used for such problems; see MacLachlan and Madden (SIAM J Sci Comput 35:A2225A2254, 2013). Here we present a multigrid solver strategy that circumvents this problem by using a robust patched mesh method proposed by de Falco and ORiordan (BAIL 2008-Boundary and Interior Layers vol. 69, pp. 117127. Springer, Berlin, 2009), as well as permitting parallelization. Numerical results demonstrate the efficiency of the method.

AB - The solution of linear systems of equations that arise when singularly perturbed partial differential equations are discretized can be difficult: direct solvers scale poorly, but are also known not to be robust with respect to the perturbation parameter, while the design of parameter robust preconditioners is not trivial, primarily due to the specialised layer adapted meshes used for such problems; see MacLachlan and Madden (SIAM J Sci Comput 35:A2225A2254, 2013). Here we present a multigrid solver strategy that circumvents this problem by using a robust patched mesh method proposed by de Falco and ORiordan (BAIL 2008-Boundary and Interior Layers vol. 69, pp. 117127. Springer, Berlin, 2009), as well as permitting parallelization. Numerical results demonstrate the efficiency of the method.

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PB - Springer

ER -

Applying a Patched Mesh Method to Efficiently Solve a Singularly Perturbed Reaction-Diffusion Problem

Abstract

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