Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations
Hierarchical (H-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU t...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Antennas and Propagation |
| Online Access: | http://dx.doi.org/10.1155/2012/756259 |
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| author | Han Guo Jun Hu Hanru Shao Zaiping Nie |
| author_facet | Han Guo Jun Hu Hanru Shao Zaiping Nie |
| author_sort | Han Guo |
| collection | DOAJ |
| description | Hierarchical (H-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures. |
| format | Article |
| id | doaj-art-a8c7ce2f880f43f6b69a0c83430dbccf |
| institution | Kabale University |
| issn | 1687-5869 1687-5877 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Antennas and Propagation |
| spelling | doaj-art-a8c7ce2f880f43f6b69a0c83430dbccf2025-02-03T01:10:30ZengWileyInternational Journal of Antennas and Propagation1687-58691687-58772012-01-01201210.1155/2012/756259756259Hierarchical Matrices Method and Its Application in Electromagnetic Integral EquationsHan Guo0Jun Hu1Hanru Shao2Zaiping Nie3School of Electronic Engineering, University of Electronic Science and Technology of China, Sichuan, Chengdu 611731, ChinaSchool of Electronic Engineering, University of Electronic Science and Technology of China, Sichuan, Chengdu 611731, ChinaSchool of Electronic Engineering, University of Electronic Science and Technology of China, Sichuan, Chengdu 611731, ChinaSchool of Electronic Engineering, University of Electronic Science and Technology of China, Sichuan, Chengdu 611731, ChinaHierarchical (H-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics, H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solve H-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure of H-matrices are also available along with high efficiency and accuracy, which is a unique advantage compared to other fast algorithms. In this paper, a novel sparse approximate inverse (SAI) preconditioner in multilevel fashion is proposed to accelerate the convergence rate of Krylov iterations for solving H-matrices system in electromagnetic applications, and a group of parallel fast direct solvers are developed for dealing with multiple right-hand-side cases. Finally, numerical experiments are given to demonstrate the advantages of the proposed multilevel preconditioner compared to conventional “single level” preconditioners and the practicability of the fast direct solvers for arbitrary complex structures.http://dx.doi.org/10.1155/2012/756259 |
| spellingShingle | Han Guo Jun Hu Hanru Shao Zaiping Nie Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations International Journal of Antennas and Propagation |
| title | Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations |
| title_full | Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations |
| title_fullStr | Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations |
| title_full_unstemmed | Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations |
| title_short | Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations |
| title_sort | hierarchical matrices method and its application in electromagnetic integral equations |
| url | http://dx.doi.org/10.1155/2012/756259 |
| work_keys_str_mv | AT hanguo hierarchicalmatricesmethodanditsapplicationinelectromagneticintegralequations AT junhu hierarchicalmatricesmethodanditsapplicationinelectromagneticintegralequations AT hanrushao hierarchicalmatricesmethodanditsapplicationinelectromagneticintegralequations AT zaipingnie hierarchicalmatricesmethodanditsapplicationinelectromagneticintegralequations |