Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients
In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product ba...
| Main Authors: | , |
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| Format: | Journal Article |
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Elsevier
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/51470 |
| _version_ | 1848758705773871104 |
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| author | Gao, L. Calo, Victor |
| author_facet | Gao, L. Calo, Victor |
| author_sort | Gao, L. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved. |
| first_indexed | 2025-11-14T09:48:14Z |
| format | Journal Article |
| id | curtin-20.500.11937-51470 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:14Z |
| publishDate | 2015 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-514702018-02-20T01:02:46Z Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients Gao, L. Calo, Victor In this paper, we combine the Alternating Direction Implicit (ADI) algorithm with the concept of preconditioning and apply it to linear systems discretized from the 2D steady-state diffusion equations with orthotropic heterogeneous coefficients by the finite element method assuming tensor product basis functions. Specifically, we adopt the compound iteration idea and use ADI iterations as the preconditioner for the outside Krylov subspace method that is used to solve the preconditioned linear system. An efficient algorithm to perform each ADI iteration is crucial to the efficiency of the overall iterative scheme. We exploit the Kronecker product structure in the matrices, inherited from the tensor product basis functions, to achieve high efficiency in each ADI iteration. Meanwhile, in order to reduce the number of Krylov subspace iterations, we incorporate partially the coefficient information into the preconditioner by exploiting the local support property of the finite element basis functions. Numerical results demonstrated the efficiency and quality of the proposed preconditioner. © 2014 Elsevier B.V. All rights reserved. 2015 Journal Article http://hdl.handle.net/20.500.11937/51470 10.1016/j.cam.2014.06.021 Elsevier fulltext |
| spellingShingle | Gao, L. Calo, Victor Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients |
| title | Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients |
| title_full | Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients |
| title_fullStr | Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients |
| title_full_unstemmed | Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients |
| title_short | Preconditioners based on the Alternating-Direction-Implicit algorithm for the 2D steady-state diffusion equation with orthotropic heterogeneous coefficients |
| title_sort | preconditioners based on the alternating-direction-implicit algorithm for the 2d steady-state diffusion equation with orthotropic heterogeneous coefficients |
| url | http://hdl.handle.net/20.500.11937/51470 |