Fast Simulation of Microwave Devices via a Data-Sparse and Explicit Finite-Element Time-Domain Method
Keywords:
Approximate inverse, electromagnetic simulation, finite-element time-domain (FETD), microwave devicesAbstract
An unconditionally stable and explicit finite-element time-domain (FETD) method is presented for the fast simulation of microwave devices. The Crank-Nicolson (CN) scheme is implemented leading to an unconditionally stable mixed FETD method. A data-sparse approximate inverse algorithm is introduced to provide a data-sparse way to approximate the inverse of FETD system matrix which is dense originally. This approximate inverse matrix can be constructed and stored with almost linear complexity, and then the FETD method can be computed explicitly at each time step without solving a sparse linear system. An efficient recompression technique is introduced to further accelerate the explicit solution at each time step. Some microwave devices are simulated to demonstrate the efficiency and accuracy of the proposed method.
Downloads
References
J. F. Lee, R. Lee, and A. Cangellaris, “Timedomain finite-element methods,” IEEE Trans. Antennas Propag., vol. 45, pp. 430-442, Mar. 1997.
D. A. White, “Orthogonal vector basis functions for time domain finite element solution of the vector wave equation,” IEEE Trans. Magn., vol. 35, no. 3, pp. 1458-1461, May 1999.
D. Jiao and J. M. Jin, “Three-dimensional orthogonal vector basis functions for time-domain finite element solution of vector wave equations,” IEEE Trans. Antennas Propag., vol. 51, no. 1, pp. 59-66, Jan. 2003.
J. H. Lee, T. Xiao, and Q. H. Liu, “A 3-D spectralelement method using mixed-order curl conforming vector basis functions for electromagnetic fields,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 1, pp. 437-444, Jan. 2006.
B. He and F. L. Teixeira, “Sparse and explicit FETD via approximate inverse Hodge (mass) matrix,” IEEE Microw. Wireless Compon. Lett., vol. 16, no. 6, pp. 348-350, June 2006.
J. Kim and F. L. Teixeira, “Parallel and explicit finite-element time-domain method for Maxwell’s equations,” IEEE Trans. Antennas Propag., vol. 59, no. 6, pp. 2350-2356, June 2011.
A. S. Moura, E. J. Silva, R. R. Saldanha, and W. G. Facco, “Performance of the alternating direction implicit scheme with recursive sparsification for the finite element time domain method,” IEEE Trans. Magn., vol. 51, no. 3, Mar. 2015.
M. Movahhedi, A. A. H. Ceric, A. Sheikholeslami, and S. Selberherr, “Alternation-direction implicit formulation of the finite-element time-domain method,” IEEE Trans. Microw. Theory Tech., vol. 55, no. 6, pp. 1322-1331, 2007.
R. S. Chen, L. Du, Z. B. Ye, and Y. Yang, “An efficient algorithm for implementing CrankNicolson scheme in the mixed finite-element timedomain method,” IEEE Trans. Antennas Propag., vol. 57, no. 10, pp. 3216-3222, Oct. 2009.
M. Bebendorf and W. Hackbusch, “Existence of H-matrix approximants to the inverse FE matrix of elliptic operators with L∞-coefficients,” Numer. Math., 95, pp. 1-28, 2003.
L. Grasedyck and W. Hackbusch, “Construction and arithmetics of H-matrices,” Computing, vol. 70, no. 4, pp. 295-344, Aug. 2003.
S. Börm, L. Grasedyck, and W. Hackbusch, “Introduction to hierarchical matrices with applications,” Engineering Analysis with Boundary Elements, no. 27, pp. 405-422, 2003.
H. Liu and D. Jiao, “Existence of H-matrix representations of the inverse finite-element matrix of electrodynamic problems and H-based fast direct finite-element solvers,” IEEE Trans. Microw. Theory Tech., vol. 58, no. 12, pp. 3697-3709, 2010.
S. Borm, “Data-sparse approximation by adaptive H2 -matrices,” Computing, vol. 69, no. 1, pp. 1-35, Sep. 2002.
M. Bozzi, L. Perregrini, and K. Wu, “Modeling of conductor, dielectric, and radiation losses in substrate integrated waveguide by the boundary integral-resonant mode expansion method,” IEEE Trans. Microw. Theory Tech., vol. 56, no. 12, pp. 3153-3161, 2008.
