Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations

A parallel implementation of the electromagnetic dual-primal finite element tearing and interconnecting algorithm (FETI-DPEM) is designed for general three-dimensional (3D) electromagnetic large-scale simulations. As a domain decomposition implementation of the finite element method, the FETI-DPEM algorithm provides fully decoupled subdomain problems and an excellent numerical scalability, and thus is well suited for parallel computation. The parallel implementation of the FETI-DPEM algorithm on a distributed-memory system using the message passing interface (MPI) is discussed in detail along with a few practical guidelines obtained from numerical experiments. Numerical examples are provided to demonstrate the efficiency of the parallel implementation.

[1]  C. Farhat,et al.  FETI-DPH: A DUAL-PRIMAL DOMAIN DECOMPOSITION METHOD FOR ACOUSTIC SCATTERING , 2005 .

[2]  Jian-Ming Jin,et al.  A Vector Dual-Primal Finite Element Tearing and Interconnecting Method for Solving 3-D Large-Scale Electromagnetic Problems , 2006 .

[3]  Jin-Fa Lee,et al.  Treatment of cement variables in the domain decomposition method for Maxwell’s equations , 2007, 2007 IEEE Antennas and Propagation Society International Symposium.

[4]  Charbel Farhat,et al.  A FETI‐DP method for the parallel iterative solution of indefinite and complex‐valued solid and shell vibration problems , 2005 .

[5]  Jian-Ming Jin,et al.  Fast full-wave analysis of large-scale three-dimensional photonic crystal devices , 2007 .

[6]  Zheng Lou,et al.  Modeling and simulation of broad-band antennas using the time-domain finite element method , 2005 .

[7]  Charbel Farhat,et al.  A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems , 2000, Numerische Mathematik.

[8]  Jian-Ming Jin,et al.  Implementation of the 2nd-order ABC with auxiliary variables in the FETI-DPEM method for 3D EM problems , 2008, 2008 IEEE Antennas and Propagation Society International Symposium.

[9]  DIAS DA CUNHA A PARALLEL IMPLEMENTATION OF THE RESTARTED GMRES ITERATIVE METHOD FOR NONSYMMETRIC SYSTEMS OF LINEAR EQUATIONS , 1993 .

[10]  John L. Volakis,et al.  A hybridization of finite-element and high-frequency methods for pattern prediction for antennas on aircraft structures , 1996 .

[11]  Stephen D. Gedney,et al.  A parallel finite-element tearing and interconnecting algorithm for solution of the vector wave equation with PML absorbing medium , 2000 .

[12]  Jian-Ming Jin,et al.  Simulation of photonic crystal nanocavity using the FETI‐DPEM method , 2008 .

[13]  Michel Lesoinne,et al.  An Efficient FETI Implementation on Distributed Shared Memory Machines with Independent Numbers of Subdomains and Processors , 1998 .

[14]  D. Rixen,et al.  FETI‐DP: a dual–primal unified FETI method—part I: A faster alternative to the two‐level FETI method , 2001 .

[15]  Jian-Ming Jin,et al.  Implementation of the Second-Order ABC in the FETI-DPEM Method for 3D EM Problems , 2008, IEEE Transactions on Antennas and Propagation.

[16]  J. P. Webb Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements , 1999 .

[17]  Jian-Ming Jin,et al.  A New Dual-Primal Domain Decomposition Approach for Finite Element Simulation of 3-D Large-Scale Electromagnetic Problems , 2007, IEEE Transactions on Antennas and Propagation.

[18]  Daniel Rixen,et al.  Application of the FETI method to ASCI problems—scalability results on 1000 processors and discussion of highly heterogeneous problems , 2000 .

[19]  Jian-Ming Jin,et al.  Analysis of conformal antennas on a complex platform , 2003, IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450).

[20]  Stéphane Lanteri,et al.  TOP/DOMDEC : a software tool for mesh partitioning and parallel processing and applications to CSM a , 1995 .

[21]  Michel Lesoinne,et al.  FETI-DP: An Efficient, Scalable and Unified Dual-Primal FETI Method , 2000 .

[22]  S.D. Gedney,et al.  Preconditioning the FETI Method for Accelerating the Solution of Large EM Scattering Problems , 2007, IEEE Antennas and Wireless Propagation Letters.

[23]  Jian-Ming Jin,et al.  Finite‐element analysis of phased‐array antennas , 2004 .

[24]  Timothy Walsh,et al.  Experiences with FETI-DP in a Production Level Finite Element Application , 2002 .

[25]  Tim Hopkins,et al.  A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations , 1994, Adv. Comput. Math..