Domain decomposition preconditioning for elliptic problems with jumps in coefficients

Sungmin Cho; S. V. Nepomnyaschikh; Eun Jae Park

doi:10.1016/j.camwa.2014.08.011

Domain decomposition preconditioning for elliptic problems with jumps in coefficients

Sungmin Cho, S. V. Nepomnyaschikh, Eun Jae Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We propose an effective iterative preconditioning method to solve elliptic problems with jumps in coefficients. The algorithm is based on the additive Schwarz method (ASM). First, we consider a domain decomposition method without cross points on the interfaces between subdomains and next, we treat the cross points case. In both cases the main computational cost is an implementation of preconditioners for the Laplace operator in whole domain and in subdomains. Iterative convergence is independent of jumps in coefficients and mesh size. Several numerical examples are given to demonstrate the performance of proposed algorithm and theory developed in the paper.

Original language	English
Pages (from-to)	2292-2313
Number of pages	22
Journal	Computers and Mathematics with Applications
Volume	68
Issue number	12
DOIs	https://doi.org/10.1016/j.camwa.2014.08.011
Publication status	Published - 2014 Dec 1

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF-2012R1A2A2A01046471 .

Publisher Copyright:
© 2014 Elsevier Ltd. All rights reserved.

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2014.08.011

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title = "Domain decomposition preconditioning for elliptic problems with jumps in coefficients",

abstract = "We propose an effective iterative preconditioning method to solve elliptic problems with jumps in coefficients. The algorithm is based on the additive Schwarz method (ASM). First, we consider a domain decomposition method without cross points on the interfaces between subdomains and next, we treat the cross points case. In both cases the main computational cost is an implementation of preconditioners for the Laplace operator in whole domain and in subdomains. Iterative convergence is independent of jumps in coefficients and mesh size. Several numerical examples are given to demonstrate the performance of proposed algorithm and theory developed in the paper.",

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note = "Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF-2012R1A2A2A01046471 . Publisher Copyright: {\textcopyright} 2014 Elsevier Ltd. All rights reserved.",

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AU - Cho, Sungmin

AU - Nepomnyaschikh, S. V.

AU - Park, Eun Jae

N1 - Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology NRF-2012R1A2A2A01046471 . Publisher Copyright: © 2014 Elsevier Ltd. All rights reserved.

PY - 2014/12/1

Y1 - 2014/12/1

N2 - We propose an effective iterative preconditioning method to solve elliptic problems with jumps in coefficients. The algorithm is based on the additive Schwarz method (ASM). First, we consider a domain decomposition method without cross points on the interfaces between subdomains and next, we treat the cross points case. In both cases the main computational cost is an implementation of preconditioners for the Laplace operator in whole domain and in subdomains. Iterative convergence is independent of jumps in coefficients and mesh size. Several numerical examples are given to demonstrate the performance of proposed algorithm and theory developed in the paper.

AB - We propose an effective iterative preconditioning method to solve elliptic problems with jumps in coefficients. The algorithm is based on the additive Schwarz method (ASM). First, we consider a domain decomposition method without cross points on the interfaces between subdomains and next, we treat the cross points case. In both cases the main computational cost is an implementation of preconditioners for the Laplace operator in whole domain and in subdomains. Iterative convergence is independent of jumps in coefficients and mesh size. Several numerical examples are given to demonstrate the performance of proposed algorithm and theory developed in the paper.

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 12

ER -

Domain decomposition preconditioning for elliptic problems with jumps in coefficients

Abstract

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