PO-based characteristic basis finite element method (CBFEM-PO)-A parallel, iteration-free domain decomposition algorithm using perfectly matched layers for large-scale electromagnetic scattering problems
In this article, we introduce a new type of Characteristic Basis Finite Element Method (CBFEM), which is based on the concepts of Physical Optics (PO) and Perfectly Matched Layers (PMLs), for solving large‐scale electromagnetic scattering problems in a rigorous and efficient manner. This parallel an...
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| Veröffentlicht in: | Microwave and optical technology letters Jg. 52; H. 5; S. 1053 - 1060 |
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| Abstract | In this article, we introduce a new type of Characteristic Basis Finite Element Method (CBFEM), which is based on the concepts of Physical Optics (PO) and Perfectly Matched Layers (PMLs), for solving large‐scale electromagnetic scattering problems in a rigorous and efficient manner. This parallel and iteration‐free technique, called CBFEM‐PO, decomposes the computational domain into a number of subdomains, and generates three types of characteristic basis functions (CBFs) that are specially‐tailored to each individual subdomain. Of these, the first two types of CBFs are comprised of primary and secondary bases arising from the self‐interactions in each subdomain and mutual‐couplings between different subdomains, respectively. They are obtained by solving the localized problem in each subdomain, isolated by PML regions. The third‐type of CBFs are derived by using the PO fields for different incident angles, polarization, and frequency. Two important salutary features of the proposed technique are: considerable reduction in the matrix size, which makes it feasible to use direct solvers; and convenient parallelizability that enables us to decrease the overall computation time by utilizing parallel platforms. We present a number of representative examples to illustrate the versatility of the method in solving 3D electromagnetic scattering problems. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1053–1060, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25134 |
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| AbstractList | In this article, we introduce a new type of Characteristic Basis Finite Element Method (CBFEM), which is based on the concepts of Physical Optics (PO) and Perfectly Matched Layers (PMLs), for solving large-scale electromagnetic scattering problems in a rigorous and efficient manner. This parallel and iteration-free technique, called CBFEM-PO, decomposes the computational domain into a number of subdomains, and generates three types of characteristic basis functions (CBFs) that are specially-tailored to each individual subdomain. Of these, the first two types of CBFs are comprised of primary and secondary bases arising from the self-interactions in each subdomain and mutual-couplings between different subdomains, respectively. They are obtained by solving the localized problem in each subdomain, isolated by PML regions. The third-type of CBFs are derived by using the PO fields for different incident angles, polarization, and frequency. Two important salutary features of the proposed technique are: considerable reduction in the matrix size, which makes it feasible to use direct solvers; and convenient parallelizability that enables us to decrease the overall computation time by utilizing parallel platforms. We present a number of representative examples to illustrate the versatility of the method in solving 3D electromagnetic scattering problems. In this article, we introduce a new type of Characteristic Basis Finite Element Method (CBFEM), which is based on the concepts of Physical Optics (PO) and Perfectly Matched Layers (PMLs), for solving large‐scale electromagnetic scattering problems in a rigorous and efficient manner. This parallel and iteration‐free technique, called CBFEM‐PO, decomposes the computational domain into a number of subdomains, and generates three types of characteristic basis functions (CBFs) that are specially‐tailored to each individual subdomain. Of these, the first two types of CBFs are comprised of primary and secondary bases arising from the self‐interactions in each subdomain and mutual‐couplings between different subdomains, respectively. They are obtained by solving the localized problem in each subdomain, isolated by PML regions. The third‐type of CBFs are derived by using the PO fields for different incident angles, polarization, and frequency. Two important salutary features of the proposed technique are: considerable reduction in the matrix size, which makes it feasible to use direct solvers; and convenient parallelizability that enables us to decrease the overall computation time by utilizing parallel platforms. We present a number of representative examples to illustrate the versatility of the method in solving 3D electromagnetic scattering problems. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 1053–1060, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25134 |
| Author | Mittra, Raj Kuzuoglu, Mustafa Ozgun, Ozlem |
| Author_xml | – sequence: 1 givenname: Ozlem surname: Ozgun fullname: Ozgun, Ozlem email: ozgunozlem@gmail.com organization: Department of Electrical Engineering, Middle East Technical University, Northern Cyprus Campus, Guzelyurt, Mersin 10, Turkey – sequence: 2 givenname: Raj surname: Mittra fullname: Mittra, Raj organization: Electromagnetic Communication Laboratory, Pennsylvania State University, University Park, PA 16802 – sequence: 3 givenname: Mustafa surname: Kuzuoglu fullname: Kuzuoglu, Mustafa organization: Department of Electrical Engineering, Middle East Technical University, Ankara 06531, Turkey |
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| Cites_doi | 10.1163/156939308784160668 10.1002/mop.10685 10.1016/j.jcp.2008.12.002 10.1109/8.537332 10.1002/mop.10480 10.1002/mop.11247 10.1002/mop.11085 10.1109/TADVP.2008.2002910 10.1002/mop.22757 10.1109/6040.784484 10.1109/TAP.2007.891865 10.1016/j.jcp.2007.04.017 10.1016/j.jcp.2007.08.025 10.1080/00207169208804091 10.1109/8.833077 10.1109/MAP.2006.1645557 |
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| References | M. Carr and J.L. Volakis, A generalized framework for hybrid simulation of multi-component structures using iterative field refinement, IEEE Antennas Propag Mag 48 ( 2006), 22-32. O. Ozgun and M. Kuzuoglu, Forward-backward domain decomposition method for finite element solution of boundary value problems, Microwave Opt Technol Lett 49 ( 2007), 2582-2590. C.T. Wolfe, U. Navsariwala, and S.D. Gedney, A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium, IEEE Trans Antennas Propag 48 ( 2000), 278-284. R.S. Chen, E.K.N. Yung, C.H. Chan, D.X. Wang, and J.M. Jin, An algebraic domain decomposition algorithm for the vector finite-element analysis of 3D electromagnetic field problems, Microwave Opt Technol Lett 34 ( 2002), 414-417. V.V. Prakash and R. Mittra, Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations, Microwave Opt Technol Lett 36 ( 2003), 95-100. W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable parallel programming with the message-passing interface, MIT Press, Cambridge, 1994. A. Schadle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, Domain decomposition method for Maxwell's equations: Scattering off periodic structures, J Comput Phys 226 ( 2007), 477-493. O. Ozgun and M. Kuzuoglu, Finite element analysis of electromagnetic wave problems via iterative leap-field domain decomposition method, J Electromagn Waves Appl 22 ( 2008), 251-266. O. Ozgun and M. Kuzuoglu, Non-Maxwellian locally-conformal PML absorbers for finite element mesh truncation, IEEE Trans Antennas Propag 55 ( 2007), 931-937. J. Yeo, V.V.S. Prakash, and R. Mittra, Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM), Microwave Opt Technol Lett 39 ( 2003), 456-464. O. Ozgun and M. Kuzuoglu, Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations, J Comput Phys 227 ( 2007), 1225-1245. O. Ozgun, R. Mittra, and M. Kuzuoglu, Multi-Level Characteristic Basis Finite Element Method (ML-CBFEM)-An efficient version of a parallel, non-iterative domain decomposition algorithm for direct solution of large-scale electromagnetic problems, IEEE Trans Antennas Propag, in press. V.V. Veremey and R. Mittra, Efficient computation of interconnect capacitances using the domain decomposition approach, IEEE Trans Adv Packaging 22 ( 1999), 348-355. O. Ozgun, R. Mittra, and M. Kuzuoglu, CBFEM-MPI: A parallelized version of characteristic basis finite element method for extraction of 3D interconnect capacitances, IEEE Trans Adv Packaging 32 ( 2009), 164-174. T.N. Philips, Preconditioned iterative methods for elliptic problems on decomposed domains, Int J Comput Math 44 ( 1992), 5-18. S.J. Kwon, K. Du, and R. Mittra, Characteristic basis function method: A numerically efficient technique for analyzing microwave and RF circuits, Microwave Opt Technol Lett 38 ( 2003), 444-448. J.F. Lee, R. Lee, and F. Teixeira, Hierarchical vector finite elements with p-type non-overlapping Schwarz method for modeling waveguide discontinuities, Comput Model Eng Sci 5 ( 2004), 423-434. B. Stupfel, A fast-domain decomposition method for the solution of electromagnetic scattering by large objects, IEEE Trans Antennas Propag 44 ( 1996), 1375-1385. O. Ozgun, R. Mittra, and M. Kuzuoglu, Parallelized characteristic basis finite element method (CBFEM-MPI)-A non-iterative domain decomposition algorithm for electromagnetic scattering problems, J Comput Phys 228 ( 2009), 2225-2238. 2007; 226 2009; 32 2007; 227 2000; 48 2002; 34 2005; 2B 2006; 48 2003; 2 2003; 36 1999; 22 2004; 5 2003; 38 2003; 39 1994 2008; 22 2009; 228 2007; 55 1992; 44 1996; 44 2007; 49 Kuzuoglu M. (e_1_2_1_14_2) 2003 Abd‐El‐Raouf H. (e_1_2_1_15_2) 2005 Gropp W. (e_1_2_1_23_2) 1994 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_2_2 e_1_2_1_11_2 e_1_2_1_22_2 e_1_2_1_3_2 e_1_2_1_12_2 e_1_2_1_20_2 e_1_2_1_10_2 e_1_2_1_21_2 Ozgun O. (e_1_2_1_19_2) e_1_2_1_16_2 e_1_2_1_13_2 Ozgun O. (e_1_2_1_17_2) Lee J.F. (e_1_2_1_6_2) 2004; 5 e_1_2_1_8_2 e_1_2_1_9_2 e_1_2_1_18_2 |
| References_xml | – reference: V.V. Veremey and R. Mittra, Efficient computation of interconnect capacitances using the domain decomposition approach, IEEE Trans Adv Packaging 22 ( 1999), 348-355. – reference: W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable parallel programming with the message-passing interface, MIT Press, Cambridge, 1994. – reference: S.J. Kwon, K. Du, and R. Mittra, Characteristic basis function method: A numerically efficient technique for analyzing microwave and RF circuits, Microwave Opt Technol Lett 38 ( 2003), 444-448. – reference: O. Ozgun, R. Mittra, and M. Kuzuoglu, CBFEM-MPI: A parallelized version of characteristic basis finite element method for extraction of 3D interconnect capacitances, IEEE Trans Adv Packaging 32 ( 2009), 164-174. – reference: J.F. Lee, R. Lee, and F. Teixeira, Hierarchical vector finite elements with p-type non-overlapping Schwarz method for modeling waveguide discontinuities, Comput Model Eng Sci 5 ( 2004), 423-434. – reference: V.V. Prakash and R. Mittra, Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations, Microwave Opt Technol Lett 36 ( 2003), 95-100. – reference: A. Schadle, L. Zschiedrich, S. Burger, R. Klose, and F. Schmidt, Domain decomposition method for Maxwell's equations: Scattering off periodic structures, J Comput Phys 226 ( 2007), 477-493. – reference: J. Yeo, V.V.S. Prakash, and R. Mittra, Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM), Microwave Opt Technol Lett 39 ( 2003), 456-464. – reference: O. Ozgun, R. Mittra, and M. Kuzuoglu, Multi-Level Characteristic Basis Finite Element Method (ML-CBFEM)-An efficient version of a parallel, non-iterative domain decomposition algorithm for direct solution of large-scale electromagnetic problems, IEEE Trans Antennas Propag, in press. – reference: T.N. Philips, Preconditioned iterative methods for elliptic problems on decomposed domains, Int J Comput Math 44 ( 1992), 5-18. – reference: O. Ozgun and M. Kuzuoglu, Finite element analysis of electromagnetic wave problems via iterative leap-field domain decomposition method, J Electromagn Waves Appl 22 ( 2008), 251-266. – reference: O. Ozgun and M. Kuzuoglu, Non-Maxwellian locally-conformal PML absorbers for finite element mesh truncation, IEEE Trans Antennas Propag 55 ( 2007), 931-937. – reference: O. Ozgun and M. Kuzuoglu, Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations, J Comput Phys 227 ( 2007), 1225-1245. – reference: R.S. Chen, E.K.N. Yung, C.H. Chan, D.X. Wang, and J.M. Jin, An algebraic domain decomposition algorithm for the vector finite-element analysis of 3D electromagnetic field problems, Microwave Opt Technol Lett 34 ( 2002), 414-417. – reference: O. Ozgun, R. Mittra, and M. Kuzuoglu, Parallelized characteristic basis finite element method (CBFEM-MPI)-A non-iterative domain decomposition algorithm for electromagnetic scattering problems, J Comput Phys 228 ( 2009), 2225-2238. – reference: O. Ozgun and M. Kuzuoglu, Forward-backward domain decomposition method for finite element solution of boundary value problems, Microwave Opt Technol Lett 49 ( 2007), 2582-2590. – reference: M. Carr and J.L. Volakis, A generalized framework for hybrid simulation of multi-component structures using iterative field refinement, IEEE Antennas Propag Mag 48 ( 2006), 22-32. – reference: B. Stupfel, A fast-domain decomposition method for the solution of electromagnetic scattering by large objects, IEEE Trans Antennas Propag 44 ( 1996), 1375-1385. – reference: C.T. Wolfe, U. Navsariwala, and S.D. Gedney, A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium, IEEE Trans Antennas Propag 48 ( 2000), 278-284. – volume: 5 start-page: 423 year: 2004 end-page: 434 article-title: Hierarchical vector finite elements with p‐type non‐overlapping Schwarz method for modeling waveguide discontinuities publication-title: Comput Model Eng Sci – volume: 226 start-page: 477 year: 2007 end-page: 493 article-title: Domain decomposition method for Maxwell's equations: Scattering off periodic structures publication-title: J Comput Phys – volume: 44 start-page: 1375 year: 1996 end-page: 1385 article-title: A fast‐domain decomposition method for the solution of electromagnetic scattering by large objects publication-title: IEEE Trans Antennas Propag – article-title: Multi‐Level Characteristic Basis Finite Element Method (ML‐CBFEM)—An efficient version of a parallel, non‐iterative domain decomposition algorithm for direct solution of large‐scale electromagnetic problems publication-title: IEEE Trans Antennas Propag – volume: 2 start-page: 1072 year: 2003 end-page: 1075 – volume: 55 start-page: 931 year: 2007 end-page: 937 article-title: Non‐Maxwellian locally‐conformal PML absorbers for finite element mesh truncation publication-title: IEEE Trans Antennas Propag – volume: 44 start-page: 5 year: 1992 end-page: 18 article-title: Preconditioned iterative methods for elliptic problems on decomposed domains publication-title: Int J Comput Math – volume: 36 start-page: 95 year: 2003 end-page: 100 article-title: Characteristic basis function method: A new technique for efficient solution of method of moments matrix equations publication-title: Microwave Opt Technol Lett – volume: 48 start-page: 22 year: 2006 end-page: 32 article-title: A generalized framework for hybrid simulation of multi‐component structures using iterative field refinement publication-title: IEEE Antennas Propag Mag – volume: 34 start-page: 414 year: 2002 end-page: 417 article-title: An algebraic domain decomposition algorithm for the vector finite‐element analysis of 3D electromagnetic field problems publication-title: Microwave Opt Technol Lett – volume: 22 start-page: 251 year: 2008 end-page: 266 article-title: Finite element analysis of electromagnetic wave problems via iterative leap‐field domain decomposition method publication-title: J Electromagn Waves Appl – volume: 48 start-page: 278 year: 2000 end-page: 284 article-title: A parallel finite‐element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium publication-title: IEEE Trans Antennas Propag – volume: 38 start-page: 444 year: 2003 end-page: 448 article-title: Characteristic basis function method: A numerically efficient technique for analyzing microwave and RF circuits publication-title: Microwave Opt Technol Lett – volume: 227 start-page: 1225 year: 2007 end-page: 1245 article-title: Near‐field performance analysis of locally‐conformal perfectly matched absorbers via Monte Carlo simulations publication-title: J Comput Phys – year: 1994 – volume: 22 start-page: 348 year: 1999 end-page: 355 article-title: Efficient computation of interconnect capacitances using the domain decomposition approach publication-title: IEEE Trans Adv Packaging – volume: 49 start-page: 2582 year: 2007 end-page: 2590 article-title: Forward‐backward domain decomposition method for finite element solution of boundary value problems publication-title: Microwave Opt Technol Lett – volume: 2B start-page: 2 year: 2005 end-page: 5 – volume: 32 start-page: 164 year: 2009 end-page: 174 article-title: CBFEM‐MPI: A parallelized version of characteristic basis finite element method for extraction of 3D interconnect capacitances publication-title: IEEE Trans Adv Packaging – volume: 228 start-page: 2225 year: 2009 end-page: 2238 article-title: Parallelized characteristic basis finite element method (CBFEM‐MPI)—A non‐iterative domain decomposition algorithm for electromagnetic scattering problems publication-title: J Comput Phys – volume: 39 start-page: 456 year: 2003 end-page: 464 article-title: Efficient analysis of a class of microstrip antennas using the characteristic basis function method (CBFM) publication-title: Microwave Opt Technol Lett – ident: e_1_2_1_10_2 doi: 10.1163/156939308784160668 – ident: e_1_2_1_11_2 doi: 10.1002/mop.10685 – ident: e_1_2_1_16_2 doi: 10.1016/j.jcp.2008.12.002 – ident: e_1_2_1_19_2 article-title: Multi‐Level Characteristic Basis Finite Element Method (ML‐CBFEM)—An efficient version of a parallel, non‐iterative domain decomposition algorithm for direct solution of large‐scale electromagnetic problems publication-title: IEEE Trans Antennas Propag – ident: e_1_2_1_2_2 doi: 10.1109/8.537332 – ident: e_1_2_1_5_2 doi: 10.1002/mop.10480 – ident: e_1_2_1_13_2 doi: 10.1002/mop.11247 – ident: e_1_2_1_12_2 doi: 10.1002/mop.11085 – ident: e_1_2_1_18_2 doi: 10.1109/TADVP.2008.2002910 – start-page: 1072 year: 2003 ident: e_1_2_1_14_2 – ident: e_1_2_1_9_2 doi: 10.1002/mop.22757 – start-page: 2 year: 2005 ident: e_1_2_1_15_2 – ident: e_1_2_1_3_2 doi: 10.1109/6040.784484 – ident: e_1_2_1_20_2 doi: 10.1109/TAP.2007.891865 – volume: 5 start-page: 423 year: 2004 ident: e_1_2_1_6_2 article-title: Hierarchical vector finite elements with p‐type non‐overlapping Schwarz method for modeling waveguide discontinuities publication-title: Comput Model Eng Sci – ident: e_1_2_1_8_2 doi: 10.1016/j.jcp.2007.04.017 – volume-title: IEEE Antennas and Propagation Society International Symposium ident: e_1_2_1_17_2 – ident: e_1_2_1_21_2 doi: 10.1016/j.jcp.2007.08.025 – ident: e_1_2_1_22_2 doi: 10.1080/00207169208804091 – ident: e_1_2_1_4_2 doi: 10.1109/8.833077 – ident: e_1_2_1_7_2 doi: 10.1109/MAP.2006.1645557 – volume-title: Using MPI: Portable parallel programming with the message‐passing interface year: 1994 ident: e_1_2_1_23_2 |
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| SubjectTerms | Algorithms characteristic basis functions Computation domain decomposition Electromagnetic scattering Finite element method finite element method (FEM) Mathematical analysis parallel processing perfectly matched layer (PML) Perfectly matched layers Physical optics Three dimensional |
| Title | PO-based characteristic basis finite element method (CBFEM-PO)-A parallel, iteration-free domain decomposition algorithm using perfectly matched layers for large-scale electromagnetic scattering problems |
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