A balancing domain decomposition method by constraints for advection-diffusion problems

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The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for ... continued below

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

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The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.

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  • Journal Name: Communications in Applied Mathematics and Computational Science; Journal Volume: 3; Related Information: Journal Publication Date: 2008

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  • Report No.: LBNL-1301E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 944569
  • Archival Resource Key: ark:/67531/metadc900278

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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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Tu, Xuemin & Li, Jing. A balancing domain decomposition method by constraints for advection-diffusion problems, article, December 10, 2008; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc900278/: accessed November 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.