A NEW 2D NON-SPURIOUS DISCONTINUOUS GALERKIN FINITE ELEMENT TIME DOMAIN (DG-FETD) METHOD FOR MAXWELL'S EQUATIONS

A new discontinuous Galerkin Finite Element Time Domain (DG-FETD) method for Maxwell's equations is developed. It can suppress spurious modes using basis functions based on polynomials with the same order of interpolation for electric fleld intensity E and magnetic ∞ux density B. Compared to FETD based on EH scheme, which requires difierent orders of interpolation polynomials for electric and magnetic fleld intensities, this method uses fewer unknowns and reduces the computation load. The discontinuous Galerkin method is employed to implement domain decomposition for the EB scheme based FETD. In addition, a well-posed time-domain perfectly matched layer (PML) is extended to the EB scheme to simulate the unbounded problem. Leap frog method is utilized for explicit time stepping. Numerical results demonstrate that the above proposed methods are efiective and e-cient for 2D time domain TMz multi-domain problems.

[1]  Joab R. Winkler,et al.  Elimination of spurious modes in finite element analysis , 1984 .

[2]  Qing Huo Liu,et al.  Efficient Implicit–Explicit Time Stepping Scheme With Domain Decomposition for Multiscale Modeling of Layered Structures , 2011, IEEE Transactions on Components, Packaging and Manufacturing Technology.

[3]  Qing Huo Liu,et al.  A strongly well-posed PML in lossy media , 2003 .

[4]  F. Teixeira,et al.  Conformal Perfectly Matched Layer for the Mixed Finite Element Time-Domain Method , 2008, IEEE Transactions on Antennas and Propagation.

[5]  H. Asai,et al.  Mixed finite element time domain method based on iterative leapfrog scheme for fast simulations of electromagnetic problems , 2011, 2011 IEEE International Symposium on Electromagnetic Compatibility.

[6]  Wei Cai,et al.  Discontinuous galerkin time-domain method for GPR simulation in dispersive media , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Constantine A. Balanis,et al.  The finite-element method for modeling circuits and interconnects for electronic packaging , 1997 .

[8]  Houle Gan,et al.  A Time-Domain Layered Finite Element Reduction Recovery (LAFE-RR) Method for High-Frequency VLSI Design , 2007, IEEE Transactions on Antennas and Propagation.

[9]  Nikolaos V. Kantartzis,et al.  A fully explicit Whitney element-time domain scheme with higher order vector finite elements for thr , 1998 .

[10]  Yan Shi,et al.  SIMULATIONS OF THE LEFT-HANDED MEDIUM USING DISCONTINUOUS GALERKIN METHOD BASED ON THE HYBRID DOMAINS , 2006 .

[11]  Jian-Ming Jin,et al.  A three-dimensional time-domain finite-element formulation for periodic structures , 2006, IEEE Transactions on Antennas and Propagation.

[12]  Noureddine Takorabet,et al.  Transient Finite Element Analysis of Induction Machines with Stator Winding Turn Fault , 2009 .

[13]  Qing Huo Liu,et al.  A Non-Spurious Vector Spectral Element Method for Maxwell's Equations , 2009 .

[14]  John L. Volakis,et al.  Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics , 1999 .

[15]  Qing Huo Liu,et al.  The PSTD algorithm: A time-domain method requiring only two cells per wavelength , 1997 .

[16]  G. Mur.  The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media , 1992 .

[17]  U. Navsariwala,et al.  An unconditionally stable finite element time-domain solution of the vector wave equation , 1995 .

[18]  Jianming Jin,et al.  A general approach for the stability analysis of the time-domain finite-element method for electromagnetic simulations , 2002 .

[19]  J. Nédélec.  A new family of mixed finite elements in ℝ3 , 1986 .

[20]  O. Picon,et al.  A finite element method based on Whitney forms to solve Maxwell equations in the time domain , 1995 .

[21]  M.F. Wong,et al.  A new global time domain electromagnetic simulator of microwave circuits including lumped elements based on finite element method , 1997, 1997 IEEE MTT-S International Microwave Symposium Digest.

[22]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[23]  T. Kramer,et al.  The Discontinuous Galerkin Finite Element Time Domain method (DGFETD) , 2008, 2008 IEEE International Symposium on Electromagnetic Compatibility.

[24]  Peter P. Silvester,et al.  Finite Elements for Electrical Engineers , 1983 .

[25]  L. Fezoui,et al.  Discontinuous Galerkin time‐domain solution of Maxwell's equations on locally‐refined nonconforming Cartesian grids , 2005 .

[26]  F. Maradei,et al.  An explicit-implicit solution scheme to analyze fast transients by finite elements , 1997 .

[27]  Tatsuo Itoh,et al.  An unconditionally stable extended (USE) finite-element time-domain solution of active nonlinear microwave circuits using perfectly matched layers , 2001, IMS 2001.

[28]  Qing Huo Liu,et al.  Spurious solutions in mixed finite element method for Maxwell's equations: Dispersion analysis and new basis functions , 2011, J. Comput. Phys..

[29]  J. Volakis,et al.  Hybrid finite-element methodologies for antennas and scattering , 1997 .

[30]  F. Faghihi,et al.  A Combination of Time Domain Finite Element-Boundary Integral and with Time Domain Physical Optics for Calculation of Electromagnetic Scattering of 3-D Structures , 2008 .

[31]  E. Tonti.  Finite Formulation of the Electromagnetic Field , 2001 .

[32]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[33]  Andreas C. Cangellaris,et al.  Point-matched time domain finite element methods for electromagnetic radiation and scattering , 1987 .

[34]  Gary H. Cohen,et al.  Non Spurious Spectral-Like Element Methods for Maxwell's Equations , 2007 .

[35]  F. Teixeira,et al.  Mixed Finite-Element Time-Domain Method for Transient Maxwell Equations in Doubly Dispersive Media , 2008, IEEE Transactions on Microwave Theory and Techniques.

[36]  A.C. Cangellaris,et al.  Domain decomposition and multi-scale finite elements for electromagnetic analysis of integrated electronic systems , 2005, 2005 International Symposium on Electromagnetic Compatibility, 2005. EMC 2005..

[37]  Jian-Ming Jin,et al.  Time-domain finite-element simulation of three-dimensional scattering and radiation problems using perfectly matched layers , 2003 .

[38]  Jin-Fa Lee,et al.  Time-domain finite-element methods , 1997 .