Shift-operator finite-element time-domain dealing with dispersive media

Abstract A new technique of finite-element time-domain (FETD) for dealing with dispersive media is presented. First, the basic theory of FETD is discussed, mainly includes electric field ( E ) and electric displacement vector ( D ). An iteration equation contains D and E is presented. Followed by an introduction of shift operator to the FETD method, a recursive formulation of constitutive between D and E in time domain is given. Then the achievement of shift-operator finite-element time-domain (SO-FETD) is developed through combining the above two equations. Finally, the feasibility of this technique is validated with 3- dimension numerical examples.

[1]  O. C. Zienkiewicz.  A new look at the newmark, houbolt and other time stepping formulas. A weighted residual approach , 1977 .

[2]  Michael S. Yeung.  Application of the hybrid FDTD–FETD method to dispersive materials , 1999 .

[3]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[4]  Qing He,et al.  Explicit and Unconditionally Stable Time-Domain Finite-Element Method with a More Than “Optimal” Speedup , 2014 .

[5]  F. Teixeira,et al.  Full-wave FETD-based PIC algorithm with local explicit update , 2016, 2016 IEEE International Symposium on Antennas and Propagation (APSURSI).

[6]  A Fast Explicit FETD Method Based on Compressed Sensing , 2017 .

[7]  Jian-Ming Jin,et al.  A Hybrid FETD-GSM Algorithm for Broadband Full-Wave Modeling of Resonant Waveguide Devices , 2017, IEEE Transactions on Microwave Theory and Techniques.

[8]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[9]  Jian-Ming Jin,et al.  Time-domain finite element modeling of dispersive media , 2001, IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.01CH37229).

[10]  Yaqiu Jin,et al.  Efficient TDFEM schemes with second-order PML based on different temporal basis functions , 2011 .

[11]  Hongzhu Cai,et al.  Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series , 2017, Computational Geosciences.

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

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

[14]  Bin Zhang,et al.  Specific evaluation of tunnel lining multi-defects by all-refined GPR simulation method using hybrid algorithm of FETD and FDTD , 2018, Construction and Building Materials.

[15]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[16]  Wu Yue,et al.  Shift operator method applied for dispersive medium in FDTD analysis , 2003 .

[17]  Salvatore Caorsi,et al.  Assessment of the performances of first‐ and second‐order time‐domain ABC's for the truncation of finite element grids , 2003 .

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

[19]  Jian-Ming Jin,et al.  Total- and scattered-field decomposition technique for the finite-element time-domain method , 2005, 2005 IEEE Antennas and Propagation Society International Symposium.

[20]  Xiao-wei Shi,et al.  A Dispersive Conformal FDTD Technique for Accurate Modeling Electromagnetic Scattering of THz Waves by Inhomogeneous Plasma Cylinder Array , 2013 .

[21]  Z. Nie,et al.  Application of diagonally perturbed incomplete factorization preconditioned conjugate gradient algorithms for edge finite-element analysis of Helmholtz equations , 2006, IEEE Transactions on Antennas and Propagation.

[22]  Jin-Fa Lee,et al.  Whitney elements time domain (WETD) methods , 1995 .