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PIER PIER B PIER C PIER M PIER Letters
2015-03-08
New Efficient Implicit Time Integration Method for DGTD Applied to Sequential Multidomain and Multiscale Problems
By
Luis E. Tobon,

    Dr. Luis E. Tobon

    Department of Computer Science and Engineering

    Pontificia Universidad Javeriana-Cali

    Colombia

    Homepage

Qiang Ren,

    Dr. Qiang Ren

    Department of Electrical and Computer Engineering

    Duke University

    USA

    Homepage

Qingtao Sun,

    Dr. Qingtao Sun

    Department of Electrical and Computer Engineering

    Duke University

    USA

    Homepage

Jiefu Chen,

    Dr. Jiefu Chen

    Electrical Engineering

    University of Houston

    USA

    Homepage

Qing Huo Liu

    Dr. Qing Huo Liu

    Duke University

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 151, 1-8, 2015
doi:10.2528/PIER14112201
Abstract
The discontinuous Galerkin's (DG) method is an efficient technique for packaging problems. It divides an original computational region into several subdomains, i.e., splits a large linear system into several smaller and balanced matrices. Once the spatial discretization is solved, an optimal time integration method is necessary. For explicit time stepping schemes, the smallest edge length in the entire discretized domain determines the maximal time step interval allowed by the stability criterion, thus they require a large number of time steps for packaging problems. Implicit time stepping schemes are unconditionally stable, thus domains with small structures can use a large time step interval. However, this approach requires inversion of matrices which are generally not positive definite as in explicit shemes for the first-order Maxwell's equations and thus becomes costly to solve for large problems. This work presents an algorithm that exploits the sequential way in which the subdomains are usually placed for layered structures in packaging problems. Specifically, a reordering of interface and volume unknowns combined with a block LDU (Lower-Diagonal-Upper) decomposition allows improvements in terms of memory cost and time of execution, with respect to previous DGTD implementations.
Citation
Luis E. Tobon, Qiang Ren, Qingtao Sun, Jiefu Chen, and Qing Huo Liu, "New Efficient Implicit Time Integration Method for DGTD Applied to Sequential Multidomain and Multiscale Problems," Progress In Electromagnetics Research, Vol. 151, 1-8, 2015.
doi:10.2528/PIER14112201
References

1. Canouet, N., L. Fezoui, and S. Piperno, "Discontinuous Galerkin time-domain solution of Maxwell’s equations on locally-refined nonconforming cartesian grids," COMPEL: Int. J. for Computation and Maths. in Electrical and Electronic Eng., Vol. 24, No. 4, 1381-1401, 2005.
doi:10.1108/03321640510615670

2. Xiao, T. and Q. H. Liu, "Three-dimensional unstructured-grid discontinuous Galerkin method for Maxwell’s equations with well-posed perfectly matched layer," Microw. Opt. Technol. Lett., Vol. 46, No. 5, 459-463, 2005.
doi:10.1002/mop.21016

3. Hesthaven, J. S. and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications, Vol. 54, Vol. 54, Springer, 2007.

4. Lee, J.-H. and Q. H. Liu, "A 3-D spectral-element time-domain method for electromagnetic simulation," IEEE Trans. Microw. Theory Techn., Vol. 55, No. 5, 983-991, 2007.
doi:10.1109/TMTT.2007.895398

5. Lee, J.-H., J. Chen, and Q. H. Liu, "A 3-D discontinuous spectral element time-domain method for Maxwell’s equations," IEEE Trans. Antennas Propag., Vol. 57, No. 9, 2666-2674, 2009.
doi:10.1109/TAP.2009.2027731

6. Chen, J. and Q. H. Liu, "A hybrid spectral-element/finite-element method with the implicit-explicit Runge-Kutta time stepping scheme for multiscale computation," IEEE Intl. Symposium on Antennas and Propagation (APSURSI), 1-4, 2010.
doi:10.1155/2010/564357

7. Chen, J., Q. H. Liu, M. Chai, and J. A. Mix, "A nonspurious 3-D vector discontinuous Galerkin finite-element time-domain method," IEEE Micro. Wireless Comp. Lett., Vol. 20, No. 1, 1-3, 2010.
doi:10.1109/LMWC.2009.2035941

8. Chen, J., L. Tobon, M. Chai, J. Mix, and Q. H. Liu, "Efficient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures," IEEE Trans. Compon. Packag. Manuf. Technol., Vol. 1, No. 9, 1438-1446, 2011.
doi:10.1109/TCPMT.2011.2162726

9. Tobon, L., J. Chen, and Q. H. Liu, "Multilayer microwave filter design using a locally implicit discontinuous Galerkin finite-element time-domain (DG-FETD) method," 2011 IEEE Intl. Symposium on Antennas and Propagation (APSURSI), 2972-2975, 2011.
doi:10.1109/APS.2011.5997153

10. Courant, R., K. Friedrichs, and H. Lewy, "On the partial difference equations of mathematical physics," IBM. J. Res. Dev., Vol. 11, No. 2, 215-234, 1967.
doi:10.1147/rd.112.0215

11. Sun, G. and C. W. Trueman, "Unconditionally stable Crank-Nicolson scheme for solving two-dimensional Maxwell’s equations," Electron. Lett., Vol. 39, No. 7, 595-597, 2003.
doi:10.1049/el:20030416

12. Sun, G. and C. W. Trueman, "Unconditionally-stable FDTD method based on Crank-Nicolson scheme for solving three-dimensional Maxwell equations," Electron. Lett., Vol. 40, No. 10, 2004.
doi:10.1049/el:20040420

13. Sun, G. and C. W. Trueman, "Efficient implementations of the Crank-Nicolson scheme for the finite-difference time-domain method," IEEE Trans. Microw. Theory Techn., Vol. 54, No. 5, 2275-2284, 2006.
doi:10.1109/TMTT.2006.873639

14. Yang, Y., R. S. Chen, and E. K. N. Yung, "The unconditionally stable Crank-Nicolson FDTD method for three-dimensional Maxwell’s equations," Micro. Opt. Techn. Lett., Vol. 48, No. 8, 1619-1622, 2006.
doi:10.1002/mop.21684

15. Chen, R. S., L. Du, Z. Ye, and Y. Yang, "An efficient algorithm for implementing the Crank-Nicolson scheme in the mixed finite-element time-domain method," IEEE Trans. Antennas Propag., Vol. 57, No. 10, 3216-3222, 2009.
doi:10.1109/TAP.2009.2028675

16. Nedelec, J. C., "Mixed finite elements in R3," Numer. Math., Vol. 35, No. 3, 315-341, 1980.
doi:10.1007/BF01396415

17. Bossavit, A., "Whitney forms: A class of finite elements for three-dimensional computations in electromagnetism," Proc. Inst. Elect. Eng., Vol. 135, No. 8, 493-500, 1988.

18. Lee, J.-H., T. Xiao, and Q. H. Liu, "A 3-D spectral-element method using mixed-order curl conforming vector basis functions for electromagnetic fields," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 1, 437-444, 2006.
doi:10.1109/TMTT.2005.860502

19. Chen, J. and Q. H. Liu, "A non-spurious vector spectral element method for Maxwell’s equations," Progress In Electromagnetics Research, Vol. 96, 205-215, 2009.
doi:10.2528/PIER09082705

20. Shankar, V., A. H. Mohammadian, and W. F. Hall, "A time-domain, finite-volume treatment for the Maxwell equations," Electromagnetics, Vol. 10, 127-145, 1990.
doi:10.1080/02726349008908232

21. Mohammadian, A. H., V. Shankar, and W. F. Hall, "Computation of electromagnetic scattering and radiation using a time-domain finite-volume discretization procedure," Comput. Phys. Commun., Vol. 68, 175-196, 1991.
doi:10.1016/0010-4655(91)90199-U

22. Liu, Q. H., "The PSTD algorithm: A time-domain method requiring only two cells per wavelength," Microw. Opt. Techn. Lett., Vol. 15, No. 3, 158-165, 1997.
doi:10.1002/(SICI)1098-2760(19970620)15:3<158::AID-MOP11>3.0.CO;2-3

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