An Explicit and Unconditionally Stable FDTD Method for Electromagnetic Analysis

In this paper, an explicit and unconditionally stable finite-difference time-domain (FDTD) method is developed for electromagnetic analysis. Its time step is not restricted by the space step, and its accuracy is ensured for the time step chosen based on accuracy. The strength of the conventional explicit FDTD is thus preserved in avoiding a system matrix solution, while the shortcoming of the conventional FDTD is eliminated in the time step's dependence on space step. Numerical experiments in both 2-D and 3-D simulations have demonstrated the performance of the proposed method in stability and efficiency without sacrificing accuracy.

[2]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

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

[4]  Costas D. Sarris,et al.  A three-dimensional spatially filtered FDTD with controllable stability beyond the courant limit , 2012, 2012 IEEE/MTT-S International Microwave Symposium Digest.

[5]  Dan Jiao,et al.  An explicit and unconditionally stable FDTD method for 3-D electromagnetic analysis , 2013, 2013 IEEE MTT-S International Microwave Symposium Digest (MTT).

[6]  Dan Jiao,et al.  Explicit and unconditionally stable FDTD method without eigenvalue solutions , 2016, 2016 IEEE MTT-S International Microwave Symposium (IMS).

[7]  Houle Gan,et al.  Explicit Time-Domain Finite-Element Method Stabilized for an Arbitrarily Large Time Step , 2012, IEEE Transactions on Antennas and Propagation.

[8]  Q.H. Liu,et al.  The unconditionally stable pseudospectral time-domain (PSTD) method , 2003, IEEE Microwave and Wireless Components Letters.

[9]  J. Yamauchi,et al.  Efficient implicit FDTD algorithm based on locally one-dimensional scheme , 2005 .

[10]  Hasan U. Akay,et al.  Digital Filtering Techniques for Parallel Computation of Explicit Schemes , 1998 .

[11]  Dan Jiao,et al.  An Explicit and Unconditionally Stable FDTD Method for the Analysis of General 3-D Lossy Problems , 2015, IEEE Transactions on Antennas and Propagation.

[12]  Dan Jiao,et al.  A theoretical study on the rank's dependence with electric size of the inverse finite element matrix for large-scale electrodynamic analysis , 2012, Proceedings of the 2012 IEEE International Symposium on Antennas and Propagation.

[13]  Rob F. Remis,et al.  On the Stability of the Finite-Difference Time-Domain Method , 2000 .

[14]  Jian-Ming Jin,et al.  A general approach for the stability analysis of time-domain finite element method , 2001, IEEE Antennas and Propagation Society International Symposium. 2001 Digest. Held in conjunction with: USNC/URSI National Radio Science Meeting (Cat. No.01CH37229).

[15]  Dan Jiao,et al.  Alternative Method for Making Explicit FDTD Unconditionally Stable , 2015, IEEE Transactions on Microwave Theory and Techniques.

[16]  Peter P. Silvester,et al.  Analytic solutions for the finite‐difference time‐domain and transmission‐line‐matrix methods , 1994 .

[17]  Chun Chang,et al.  A Spatially Filtered Finite-Difference Time-Domain Scheme With Controllable Stability Beyond the CFL Limit: Theory and Applications , 2013, IEEE Transactions on Microwave Theory and Techniques.

[18]  Yan-Tao Duan,et al.  A New Efficient Algorithm for the Unconditionally Stable 2-D WLP-FDTD Method , 2013, IEEE Transactions on Antennas and Propagation.

[19]  Houle Gan.  Time-domain finite-element reduction-recovery methods for large-scale electromagnetics-based analysis and design of next-generation integrated circuits , 2010 .

[20]  Costas D Sarris.  Extending the Stability Limit of the FDTD Method With Spatial Filtering , 2011, IEEE Microwave and Wireless Components Letters.

[21]  F. Teixeira,et al.  Split-field PML implementations for the unconditionally stable LOD-FDTD method , 2006, IEEE Microwave and Wireless Components Letters.

[22]  Cheng-Kok Koh,et al.  A Quadratic Eigenvalue Solver of Linear Complexity for 3-D Electromagnetics-Based Analysis of Large-Scale Integrated Circuits , 2012, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[23]  Zhizhang Chen,et al.  A finite-difference time-domain method without the Courant stability conditions , 1999 .

[24]  T. Namiki,et al.  A new FDTD algorithm based on alternating-direction implicit method , 1999 .

[25]  Luca Roselli,et al.  Optimum mesh grading for finite-difference method , 1996 .

[26]  C. Holloway,et al.  Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation , 2003 .

[27]  Qing He,et al.  An explicit time-domain finite-element method that is unconditionally stable , 2011, 2011 IEEE International Symposium on Antennas and Propagation (APSURSI).

[28]  C. W. Trueman,et al.  Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell's equations , 2003 .

[29]  Dan Jiao,et al.  Theoretical Study on the Rank of Integral Operators for Broadband Electromagnetic Modeling From Static to Electrodynamic Frequencies , 2013, IEEE Transactions on Components, Packaging and Manufacturing Technology.

[30]  Eng Leong Tan,et al.  Fundamental Schemes for Efficient Unconditionally Stable Implicit Finite-Difference Time-Domain Methods , 2008, IEEE Transactions on Antennas and Propagation.

[31]  Duo Chen,et al.  Minimal-order circuit model based fast electromagnetic simulation , 2013, 2013 IEEE 22nd Conference on Electrical Performance of Electronic Packaging and Systems.

[32]  Bengt Fornberg,et al.  A split step approach for the 3-D Maxwell's equations , 2003 .

[33]  P B Hoffer,et al.  Computerized three-dimensional segmented human anatomy. , 1994, Medical physics.

[34]  Tapan K. Sarkar,et al.  An unconditionally stable scheme for the finite-difference time-domain method , 2003 .

[35]  Bin Chen,et al.  A New Unconditionally Stable Scheme for FDTD Method Using Associated Hermite Orthogonal Functions , 2014, IEEE Transactions on Antennas and Propagation.

[36]  L. Trefethen.  Group velocity in finite difference schemes , 1981 .