An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method
An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain....
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MDPI AG
2023-04-01
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| Online Access: | https://www.mdpi.com/1099-4300/25/4/693 |
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| author | Jia-Fen Chen Xian-Ming Gu Liang Li Ping Zhou |
| author_facet | Jia-Fen Chen Xian-Ming Gu Liang Li Ping Zhou |
| author_sort | Jia-Fen Chen |
| collection | DOAJ |
| description | An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective. |
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| id | doaj.art-ca0ae08875604b40b5e333a65b1221b7 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T05:02:27Z |
| publishDate | 2023-04-01 |
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| spelling | doaj.art-ca0ae08875604b40b5e333a65b1221b72023-11-17T19:09:46ZengMDPI AGEntropy1099-43002023-04-0125469310.3390/e25040693An Optimized Schwarz Method for the Optical Response Model Discretized by HDG MethodJia-Fen Chen0Xian-Ming Gu1Liang Li2Ping Zhou3School of Mathematics and Computer Science, Chongqing College of International Business and Economics, Chongqing 401520, ChinaSchool of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, ChinaSchool of Mathematics and Computer Science, Chongqing College of International Business and Economics, Chongqing 401520, ChinaAn optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective.https://www.mdpi.com/1099-4300/25/4/693local optical response modelhybridizable discontinuous Galerkin methodoptimized Schwarz methodKrylov subspace methoddomain decomposition method |
| spellingShingle | Jia-Fen Chen Xian-Ming Gu Liang Li Ping Zhou An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method Entropy local optical response model hybridizable discontinuous Galerkin method optimized Schwarz method Krylov subspace method domain decomposition method |
| title | An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method |
| title_full | An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method |
| title_fullStr | An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method |
| title_full_unstemmed | An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method |
| title_short | An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method |
| title_sort | optimized schwarz method for the optical response model discretized by hdg method |
| topic | local optical response model hybridizable discontinuous Galerkin method optimized Schwarz method Krylov subspace method domain decomposition method |
| url | https://www.mdpi.com/1099-4300/25/4/693 |
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