Convergence analysis of a balalncing domain decomposition method for solving interior Helmholtz equations

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A variant of balancing domain decomposition method by constraints (BDDC) is proposed for solving a class of indefinite system of linear equations, which arises from the finite element discretization of the Helmholtz equation of time-harmonic wave propagation in a bounded interior domain. The proposed BDDC algorithm is closely related to the dual-primal finite element tearing and interconnecting algorithm for solving Helmholtz equations (FETI-DPH). Under the condition that the diameters of the subdomains are small enough, the rate of convergence is established which depends polylogarithmically on the dimension of the individual subdomain problems and which improves with the decrease of the ... continued below

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Li,Jing & Tu, Xuemin December 10, 2008.

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A variant of balancing domain decomposition method by constraints (BDDC) is proposed for solving a class of indefinite system of linear equations, which arises from the finite element discretization of the Helmholtz equation of time-harmonic wave propagation in a bounded interior domain. The proposed BDDC algorithm is closely related to the dual-primal finite element tearing and interconnecting algorithm for solving Helmholtz equations (FETI-DPH). Under the condition that the diameters of the subdomains are small enough, the rate of convergence is established which depends polylogarithmically on the dimension of the individual subdomain problems and which improves with the decrease of the subdomain diameters. These results are supported by numerical experiments of solving a Helmholtz equation on a two-dimensional square domain.

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  • Journal Name: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS

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  • Report No.: LBNL-1315E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 945049
  • Archival Resource Key: ark:/67531/metadc902561

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  • December 10, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 8, 2016, 1:18 p.m.

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Li,Jing & Tu, Xuemin. Convergence analysis of a balalncing domain decomposition method for solving interior Helmholtz equations, article, December 10, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc902561/: accessed September 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.