Fast multipole accelerated chebyshev pseudospectral time domain algorithm

The Chebyshev pseudospectral time domain (PSTD) method has become a flexible and efficient approach in Electromagnetic (EM) transient analysis. The major computation cost of PSTD method comes from the evaluation of differentiation matrix multiplication. To alleviate and improve the efficiency, the fast multipole method has been explored. By making use of the similarity of the N-body problem and the Chebyshev interpolation, a new fast multipole accelerated PSTD method is developed. Our numerical comparison confirms the efficiency of the proposed method and the error analysis of the proposed method is also conducted.

[1]  Jan S. Hesthaven,et al.  Spectral Simulations of Electromagnetic Wave Scattering , 1997 .

[2]  Qing Huo Liu,et al.  Unconditionally stable multidomain pseudospectral time-domain (PSTD) method , 2003, IEEE Antennas and Propagation Society International Symposium. Digest. Held in conjunction with: USNC/CNC/URSI North American Radio Sci. Meeting (Cat. No.03CH37450).

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

[4]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

[5]  Chang-Hong Liang,et al.  Two dimensional multidomain pseudospectral time-domain algorithm based on alternating-direction implicit method , 2006, IEEE Transactions on Antennas and Propagation.

[6]  W. J. Gordon,et al.  Transfinite element methods: Blending-function interpolation over arbitrary curved element domains , 1973 .

[7]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[8]  J. Boyd.  Multipole expansions and pseudospectral cardinal functions: A new generalization of the fast fourier transform , 1992 .

[9]  T. Eibert,et al.  A diagonalized multilevel fast multipole method with spherical harmonics expansion of the k-space Integrals , 2005, IEEE Transactions on Antennas and Propagation.

[10]  Leslie Greengard,et al.  The numerical solution of the N-body problem , 1990 .

[11]  B. Ooi,et al.  Efficient hybrid TDFEM-PSTD method , 2005 .

[12]  Vincent K. N. Lau.  Spatial-multiplexing phase-sweep transmit diversity (SM-PSTD) for multiantenna base stations with mobile-assisted scheduling and incremental rate feedback , 2006, IEEE Transactions on Vehicular Technology.

[13]  S. Wakao,et al.  Large-scale analysis of eddy-current problems by the hybrid finite element-boundary element method combined with the fast multipole method , 2006, IEEE Transactions on Magnetics.

[14]  Qing Huo Liu,et al.  The 2.5-D multidomain pseudospectral time-domain algorithm , 2003 .