A Finite-Element-Based Domain Decomposition Method for Efficient Simulation of Nonlinear Electromechanical Problems

The dual-primal finite-element tearing and interconnecting (FETI-DP) method is combined with the Newton-Raphson method to expand the capability and improve the efficiency of 3-D finite-element analysis (FEA) of nonlinear electromechanical problems. Despite its modeling capability and high degree of accuracy, FEA has high computational complexity, especially for nonlinear analysis. The FETI-DP method is a robust domain decomposition method, which has been enhanced and applied to solve electromechanical problems involving linear materials. In this paper, the FETI-DP method is extended with the Newton-Raphson method to address problems involving nonlinearity and saturation. Using parallel computing techniques, the total computation time is reduced significantly. Linear and nonlinear regions are separated using the FETI-DP method. This further improves simulation efficiency and flexibility. Cubic splines and relaxation techniques are adopted to ensure stable and fast convergence of the Newton-Raphson method. The performance of the proposed method is compared with infolytica's MagNet, a commercial 3-D FEA solver.

[1]  Jian-Ming Jin,et al.  A dual‐primal finite‐element tearing and interconnecting method combined with tree‐cotree splitting for modeling electromechanical devices , 2013 .

[2]  Jian-Ming Jin,et al.  A Highly Efficient Domain Decomposition Method Applied to 3-D Finite-Element Analysis of Electromechanical and Electric Machine Problems , 2012, IEEE Transactions on Energy Conversion.

[3]  C. Sadarangani,et al.  Loss Distribution on Solid Pole Plates of Wound-Rotor Synchronous Motors Fed From Inverters Using Direct Torque Control , 2012, IEEE Transactions on Energy Conversion.

[4]  M. Cosovic,et al.  The effects of magnetic circuit geometry on characteristics of switched reluctance motors , 2011, 2011 IEEE International Electric Machines & Drives Conference (IEMDC).

[5]  M Moallem,et al.  Double-Stator Switched Reluctance Machines (DSSRM): Fundamentals and Magnetic Force Analysis , 2010, IEEE Transactions on Energy Conversion.

[6]  Marco Amrhein,et al.  Induction Machine Modeling Approach Based on 3-D Magnetic Equivalent Circuit Framework , 2010, IEEE Transactions on Energy Conversion.

[7]  L L Lai,et al.  Performance of an Axial-Flux Permanent Magnet Synchronous Generator From 3-D Finite-Element Analysis , 2010, IEEE Transactions on Energy Conversion.

[8]  M. Kuczmann.  Using the Newton–Raphson Method in the Polarization Technique to Solve Nonlinear Static Magnetic Field Problems , 2010, IEEE Transactions on Magnetics.

[9]  S. Ho,et al.  An Efficient Two-Grid Finite-Element Method of 3-D Nonlinear Magnetic-Field Computation , 2009, IEEE Transactions on Magnetics.

[10]  P.T. Krein,et al.  Force Calculation in 3-D Magnetic Equivalent Circuit Networks With a Maxwell Stress Tensor , 2009, IEEE Transactions on Energy Conversion.

[11]  P.T. Krein,et al.  3-D Magnetic Equivalent Circuit Framework for Modeling Electromechanical Devices , 2009, IEEE Transactions on Energy Conversion.

[12]  Jian-Ming Jin,et al.  Parallel implementation of the FETI-DPEM algorithm for general 3D EM simulations , 2009, J. Comput. Phys..

[13]  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.

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

[15]  B. Fahimi,et al.  A field reconstruction method for optimal excitation of permanent magnet synchronous machines , 2006, IEEE Transactions on Energy Conversion.

[16]  H. Kanayama,et al.  Effectiveness of A-/spl phi/ method in a parallel computing with an iterative domain decomposition method , 2006, IEEE Transactions on Magnetics.

[17]  Chang Seop Koh,et al.  Convergence acceleration of the Newton-Raphson method using successive quadratic function approximation of residual , 2006, IEEE Transactions on Magnetics.

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

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

[20]  A.M. Knight,et al.  Efficient parallel solution of time-stepped multislice eddy-current induction motor models , 2004, IEEE Transactions on Magnetics.

[21]  Thomas Weiland,et al.  Numerical calculation of nonlinear transient field problems with the Newton-Raphson method , 2000 .

[22]  A. El-Antably,et al.  Analytical model for permanent magnet motors with surface mounted magnets , 1999, IEEE International Electric Machines and Drives Conference. IEMDC'99. Proceedings (Cat. No.99EX272).

[23]  Timothy J. Flack,et al.  On the domain decomposition and transmission line modelling finite element method for time-domain induction motor analysis , 1999 .

[24]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[25]  A. Kost,et al.  Convergence properties of the Newton-Raphson method for nonlinear problems , 1998 .

[26]  J. Brauer,et al.  Polyphase induction motor performance computed directly by finite elements , 1997, 1997 IEEE International Electric Machines and Drives Conference Record.

[27]  S. Ho,et al.  Solution of a 3-D complex finite element model of skewed rotor induction motors using an iterative method , 1997, 1997 IEEE International Electric Machines and Drives Conference Record.

[28]  D. Lavers,et al.  Numerical solution of transient 2-D eddy current problem by domain decomposition algorithms , 1996 .

[29]  Essam S Hamdi,et al.  Design of Small Electrical Machines , 1994 .

[30]  D. R. Fokkema,et al.  BICGSTAB( L ) FOR LINEAR EQUATIONS INVOLVING UNSYMMETRIC MATRICES WITH COMPLEX , 1993 .

[31]  Koji Fujiwara,et al.  Method for determining relaxation factor for modified Newton-Raphson method , 1993 .

[32]  S.R.H. Hoole,et al.  The subregion method in magnetic field analysis and design optimization , 1992 .

[33]  Koji Fujiwara,et al.  Improvements of convergence characteristics of Newton-Raphson method for nonlinear magnetic field analysis , 1992 .

[34]  N. Takahashi,et al.  Effects of permeability of magnetic materials on errors of the T- Omega method , 1990 .

[35]  S. J. Salon,et al.  Finite element analysis of electrical machines , 1995 .