Application of algebraic domain decomposition combined with Krylov subspace iterative methods to solve 3D vector finite element equations
In this paper, a parallel algorithm based on MPI (Message Passing Interface) parallel computing library for the finite element method is presented to analyze three‐dimensional electromagnetic devices. The algebraic domain decomposition method is used in the algorithm. The original problem is decompo...
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| Published in | Microwave and optical technology letters Vol. 49; no. 3; pp. 686 - 692 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.03.2007
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| ISSN | 0895-2477 1098-2760 |
| DOI | 10.1002/mop.22247 |
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| Abstract | In this paper, a parallel algorithm based on MPI (Message Passing Interface) parallel computing library for the finite element method is presented to analyze three‐dimensional electromagnetic devices. The algebraic domain decomposition method is used in the algorithm. The original problem is decomposed into several subproblems according to its features. Each of them is allocated to one process in one computation node and solved independently with a direct method. The data are exchanged by communication between adjacent subdomains with overlapped data based on the MPI network. The example of its application is given. Numerical shows that the proposed algorithm can get excellent performance vs. price ratio and can save much memory and CPU time than sequential computing. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 686–692, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22247 |
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| AbstractList | In this paper, a parallel algorithm based on MPI (Message Passing Interface) parallel computing library for the finite element method is presented to analyze three‐dimensional electromagnetic devices. The algebraic domain decomposition method is used in the algorithm. The original problem is decomposed into several subproblems according to its features. Each of them is allocated to one process in one computation node and solved independently with a direct method. The data are exchanged by communication between adjacent subdomains with overlapped data based on the MPI network. The example of its application is given. Numerical shows that the proposed algorithm can get excellent performance vs. price ratio and can save much memory and CPU time than sequential computing. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 686–692, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22247 In this paper, a parallel algorithm based on MPI (Message Passing Interface) parallel computing library for the finite element method is presented to analyze three-dimensional electromagnetic devices. The algebraic domain decomposition method is used in the algorithm. The original problem is decomposed into several subproblems according to its features. Each of them is allocated to one process in one computation node and solved independently with a direct method. The data are exchanged by communication between adjacent subdomains with overlapped data based on the MPI network. The example of its application is given. Numerical shows that the proposed algorithm can get excellent performance vs. price ratio and can save much memory and CPU time than sequential computing. In this paper, a parallel algorithm based on MPI (Message Passing Interface) parallel computing library for the finite element method is presented to analyze three-dimensional electromagnetic devices. The algebraic domain decomposition method is used in the algorithm. The original problem is decomposed into several subproblems according to its features. Each of them is allocated to one process in one computation node and solved independently with a direct method. The data are exchanged by communication between adjacent subdomains with overlapped data based on the MPI network. The example of its application is given. Numerical shows that the proposed algorithm can get excellent performance vs. price ratio and can save much memory and CPU time than sequential computing. copyright 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 686-692, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22247 |
| Author | Chen, R. S. Ping, X. W. |
| Author_xml | – sequence: 1 givenname: X. W. surname: Ping fullname: Ping, X. W. organization: Department of Electrical Engineering, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China – sequence: 2 givenname: R. S. surname: Chen fullname: Chen, R. S. organization: Department of Electrical Engineering, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China |
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| Cites_doi | 10.1002/jnm.593 10.1109/9780470544655 10.1007/978-1-4615-5761-6 10.7551/mitpress/5712.001.0001 10.1109/8.537332 10.1109/8.558671 10.1109/12.127441 10.1109/8.546247 10.1109/20.877736 10.1109/22.85402 10.1016/0167-8191(93)90082-V 10.7551/mitpress/7056.001.0001 10.1002/mop.10480 10.1002/1097-0207(20010220)50:5<1077::AID-NME65>3.0.CO;2-P 10.1109/75.755039 10.1002/mop.10064 10.1109/8.855483 |
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| References | J.M. Jin, The finite element method in electromagnetics, Wiley, New York, 1993. K. Hoffman and J. Zou, Parallel efficiency of domain decomposition methods, Parallel Computing 19 (1993), 1375-1393. R.S. Chen, X.W. Ping, X.P. Wang, X.D. Ye, E.K.N. Yung, and K.W. Leung, Parallel realization of algebraic domain decomposition for the vector finite element analysis of 3D time-harmonic em field problems, Int J Numer Model 18 (2005), 481-492. X.H. Sun, H. Zhang, and L. Ni, Efficient tridiagonal solvers on multicomputers, IEEE Trans Comput 41 (1992), 286-296. K. Ise, K. Inoue, and M. Koshiba, Three-dimensional finite-element method with edge elements for electromagnetic waveguide discontinuities, IEEE Trans Microwave Theory Tech 39 (1991), 1289-1295. J. Dongarra, Introduction to MPI, Int J Supercomput Appl 8 (1994), 164-174. J.J.H. Wang, Generalized moment of methods in electromagnetics, Wiley, New York, 1990. Mardochee Magolu Monga Made, Incomplete factorization based preconditionings for solving the Helmholtz equation, Int J Numer Methods Eng 50 (2001), 1077-1101. W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable parallel programming with the message-passing interface, 2nd ed., MIT Press, Cambridge, MA, 1999. Y. Lu and C.Y. Shen, A domain decomposition finite-difference method for parallel numerical implementation of time-dependent Maxwell's equations, IEEE Trans Antennas Propag 45 (1997), 556-562. J.L. Volakis, A. Chatterjee, and L.C. Kempel, Finite element method for electromagnetic, IEEE Press, New York, 1998. M. Schinnerl, J. Shoberl, and M. Kaltenbacher, Nested multigrid methods for the fast numerical computation of 3D magnetic fields, IEEE Trans Magnetics 36 (2000), 1557-1560. A. Geist, A. Beguelin, J. Dongarra, W.C. Jiang, R. Manchek, and V. Sunderam, PVM: parallel virtual machine, MIT Press, 1994. Y. Saad, Iterative methods for sparse linear systems, PWS Publishing Company, Boston, 1995 S. Bruno, A fast domain decomposition method for the solution of electromagnetic scattering by large objects, IEEE Trans Antennas Propag 44 (1996), 1375-1385. 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. S. Bruno, A domain decomposition method for the vector wave equation, IEEE Trans Antennas Propag 48 (2000), 653-660. Yung Shirley Chio-Grogan, K. Eswar, P. Sadayappan, and R. Lee, Sequential and parallel implementations of the partitioning finite-element method, IEEE Trans Antennas Propag 44 (1996), 1609-1616. R.S. Chen, D.X. Wang, E.K.N. Yung, and J. M Jin, Application of the multifrontal method to the vector FEM for analysis of microwave filters, Microwave Opt Technol Lett 31 (2001), 465-470. G. Meurant, Computer solution of large linear system, Elsevier, New York, 1999. J.-M. Adamo, Multi-threaded object-oriented MPI-based messaging passing interface, the ARCH library, Kluwer, Boston, 1998. Y.Y. Botros and J.L. Volakis, Preconditioned generalized minimal residual iterative scheme for perfectly matched layer terminated application, IEEE Microwave Guided Wave Lett 9 (1999), 45-47. 1994; 8 2001; 50 1993; 19 1991; 39 1990 2000; 36 2000; 48 2002; 34 1997; 45 1998 1995 1994 1993 2005; 18 2001; 31 1992; 41 1999 1996; 44 1999; 9 Meurant G. (e_1_2_1_22_2) 1999 Geist A. (e_1_2_1_11_2) 1994 Wang J.J.H. (e_1_2_1_2_2) 1990 Dongarra J. (e_1_2_1_10_2) 1994; 8 Saad Y. (e_1_2_1_18_2) 1995 e_1_2_1_6_2 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_12_2 e_1_2_1_23_2 Jin J.M. (e_1_2_1_3_2) 1993 e_1_2_1_20_2 e_1_2_1_21_2 e_1_2_1_15_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_24_2 e_1_2_1_14_2 e_1_2_1_19_2 e_1_2_1_8_2 e_1_2_1_17_2 e_1_2_1_9_2 |
| References_xml | – reference: K. Ise, K. Inoue, and M. Koshiba, Three-dimensional finite-element method with edge elements for electromagnetic waveguide discontinuities, IEEE Trans Microwave Theory Tech 39 (1991), 1289-1295. – reference: K. Hoffman and J. Zou, Parallel efficiency of domain decomposition methods, Parallel Computing 19 (1993), 1375-1393. – reference: Mardochee Magolu Monga Made, Incomplete factorization based preconditionings for solving the Helmholtz equation, Int J Numer Methods Eng 50 (2001), 1077-1101. – reference: S. Bruno, A fast domain decomposition method for the solution of electromagnetic scattering by large objects, IEEE Trans Antennas Propag 44 (1996), 1375-1385. – reference: G. Meurant, Computer solution of large linear system, Elsevier, New York, 1999. – reference: W. Gropp, E. Lusk, and A. Skjellum, Using MPI: Portable parallel programming with the message-passing interface, 2nd ed., MIT Press, Cambridge, MA, 1999. – reference: Y. Lu and C.Y. Shen, A domain decomposition finite-difference method for parallel numerical implementation of time-dependent Maxwell's equations, IEEE Trans Antennas Propag 45 (1997), 556-562. – reference: R.S. Chen, D.X. Wang, E.K.N. Yung, and J. M Jin, Application of the multifrontal method to the vector FEM for analysis of microwave filters, Microwave Opt Technol Lett 31 (2001), 465-470. – reference: J.L. Volakis, A. Chatterjee, and L.C. Kempel, Finite element method for electromagnetic, IEEE Press, New York, 1998. – reference: S. Bruno, A domain decomposition method for the vector wave equation, IEEE Trans Antennas Propag 48 (2000), 653-660. – reference: A. Geist, A. Beguelin, J. Dongarra, W.C. Jiang, R. Manchek, and V. Sunderam, PVM: parallel virtual machine, MIT Press, 1994. – reference: Y. Saad, Iterative methods for sparse linear systems, PWS Publishing Company, Boston, 1995 – reference: J.J.H. Wang, Generalized moment of methods in electromagnetics, Wiley, New York, 1990. – reference: R.S. Chen, X.W. Ping, X.P. Wang, X.D. Ye, E.K.N. Yung, and K.W. Leung, Parallel realization of algebraic domain decomposition for the vector finite element analysis of 3D time-harmonic em field problems, Int J Numer Model 18 (2005), 481-492. – reference: J. Dongarra, Introduction to MPI, Int J Supercomput Appl 8 (1994), 164-174. – reference: Yung Shirley Chio-Grogan, K. Eswar, P. Sadayappan, and R. Lee, Sequential and parallel implementations of the partitioning finite-element method, IEEE Trans Antennas Propag 44 (1996), 1609-1616. – reference: M. Schinnerl, J. Shoberl, and M. Kaltenbacher, Nested multigrid methods for the fast numerical computation of 3D magnetic fields, IEEE Trans Magnetics 36 (2000), 1557-1560. – reference: Y.Y. Botros and J.L. Volakis, Preconditioned generalized minimal residual iterative scheme for perfectly matched layer terminated application, IEEE Microwave Guided Wave Lett 9 (1999), 45-47. – reference: J.-M. Adamo, Multi-threaded object-oriented MPI-based messaging passing interface, the ARCH library, Kluwer, Boston, 1998. – reference: X.H. Sun, H. Zhang, and L. Ni, Efficient tridiagonal solvers on multicomputers, IEEE Trans Comput 41 (1992), 286-296. – reference: J.M. Jin, The finite element method in electromagnetics, Wiley, New York, 1993. – 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. – 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 – volume: 50 start-page: 1077 year: 2001 end-page: 1101 article-title: Mardochee Magolu Monga Made, Incomplete factorization based preconditionings for solving the Helmholtz equation publication-title: Int J Numer Methods Eng – volume: 19 start-page: 1375 year: 1993 end-page: 1393 article-title: Parallel efficiency of domain decomposition methods publication-title: Parallel Computing – volume: 36 start-page: 1557 year: 2000 end-page: 1560 article-title: Nested multigrid methods for the fast numerical computation of 3D magnetic fields publication-title: IEEE Trans Magnetics – volume: 41 start-page: 286 year: 1992 end-page: 296 article-title: Efficient tridiagonal solvers on multicomputers publication-title: IEEE Trans Comput – volume: 45 start-page: 556 year: 1997 end-page: 562 article-title: A domain decomposition finite‐difference method for parallel numerical implementation of time‐dependent Maxwell's equations publication-title: IEEE Trans Antennas Propag – 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: 44 start-page: 1609 year: 1996 end-page: 1616 article-title: Sequential and parallel implementations of the partitioning finite‐element method publication-title: IEEE Trans Antennas Propag – volume: 18 start-page: 481 year: 2005 end-page: 492 article-title: Parallel realization of algebraic domain decomposition for the vector finite element analysis of 3D time‐harmonic em field problems publication-title: Int J Numer Model – year: 1995 – volume: 8 start-page: 164 year: 1994 end-page: 174 article-title: Introduction to MPI publication-title: Int J Supercomput Appl – volume: 31 start-page: 465 year: 2001 end-page: 470 article-title: Application of the multifrontal method to the vector FEM for analysis of microwave filters publication-title: Microwave Opt Technol Lett – year: 1990 – year: 1993 – volume: 48 start-page: 653 year: 2000 end-page: 660 article-title: A domain decomposition method for the vector wave equation publication-title: IEEE Trans Antennas Propag – year: 1994 – volume: 9 start-page: 45 year: 1999 end-page: 47 article-title: Preconditioned generalized minimal residual iterative scheme for perfectly matched layer terminated application publication-title: IEEE Microwave Guided Wave Lett – year: 1998 – volume: 39 start-page: 1289 year: 1991 end-page: 1295 article-title: Three‐dimensional finite‐element method with edge elements for electromagnetic waveguide discontinuities publication-title: IEEE Trans Microwave Theory Tech – year: 1999 – volume: 8 start-page: 164 year: 1994 ident: e_1_2_1_10_2 article-title: Introduction to MPI publication-title: Int J Supercomput Appl – ident: e_1_2_1_20_2 doi: 10.1002/jnm.593 – volume-title: The finite element method in electromagnetics year: 1993 ident: e_1_2_1_3_2 – ident: e_1_2_1_4_2 doi: 10.1109/9780470544655 – volume-title: Generalized moment of methods in electromagnetics year: 1990 ident: e_1_2_1_2_2 – ident: e_1_2_1_12_2 doi: 10.1007/978-1-4615-5761-6 – volume-title: PVM: parallel virtual machine year: 1994 ident: e_1_2_1_11_2 doi: 10.7551/mitpress/5712.001.0001 – ident: e_1_2_1_15_2 doi: 10.1109/8.537332 – ident: e_1_2_1_17_2 doi: 10.1109/8.558671 – ident: e_1_2_1_8_2 doi: 10.1109/12.127441 – ident: e_1_2_1_14_2 doi: 10.1109/8.546247 – ident: e_1_2_1_5_2 doi: 10.1109/20.877736 – volume-title: Iterative methods for sparse linear systems year: 1995 ident: e_1_2_1_18_2 – ident: e_1_2_1_24_2 doi: 10.1109/22.85402 – ident: e_1_2_1_13_2 – ident: e_1_2_1_7_2 doi: 10.1016/0167-8191(93)90082-V – ident: e_1_2_1_9_2 doi: 10.7551/mitpress/7056.001.0001 – ident: e_1_2_1_19_2 doi: 10.1002/mop.10480 – ident: e_1_2_1_6_2 doi: 10.1002/1097-0207(20010220)50:5<1077::AID-NME65>3.0.CO;2-P – ident: e_1_2_1_23_2 doi: 10.1109/75.755039 – ident: e_1_2_1_21_2 doi: 10.1002/mop.10064 – ident: e_1_2_1_16_2 doi: 10.1109/8.855483 – volume-title: Computer solution of large linear system year: 1999 ident: e_1_2_1_22_2 |
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| SubjectTerms | Algebra algebraic domain decomposition Algorithms Devices Finite element method Krylov subspace iterative methods Mathematical analysis Mathematical models Message passing Microwaves MPI parallel computing vector finite element method |
| Title | Application of algebraic domain decomposition combined with Krylov subspace iterative methods to solve 3D vector finite element equations |
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