Habitat for Creative Electromagneticists

Computational Electromagnetics


Goals

We have developed a variety of finite difference time domain (FDTD) algorithms to solve Maxwell’s equations in the presence of complex media and structures. We have developed unstructured grid approaches. We have analyzed these unstructured grid approaches in terms of differential forms and their topological properties. We have developed a variety of physics-based absorbing boundary conditions (ABCs). We have developed moving window FDTD approaches.

 

Papers

  1. C. Kaus and R. W. Ziolkowski, “Topological and geometrical considerations for Maxwell’s equations on unstructured meshes,” Electromagnetics, vol. 28, no. 1&2, pp. 42-53, January 2008.  

  2. R. Holtzman, R. Kastner, E. Heyman, and R. W. Ziolkowski, “Ultra wide band cylindrical antenna design using the Green’s function method (GFM) as an absorbing boundary condition (ABC) and radiated field propagator in a genetic optimization approach,”  Microwave Opt. Tech. Lett., vol. 48, pp. 348-354, February 2006.  

  3. R. Holtzman, R. Kastner, E. Heyman, and R. W. Ziolkowski, “Stability analysis of the Green’s function method (GFM) used as an ABC for arbitrarily shaped boundaries,” IEEE Trans. Antennas Propagat., vol. 50, no. 7, pp. 1017-1029, July 2002.  

  4. D. C. Wittwer and R. W. Ziolkowski, “The effect of dielectric loss in FDTD simulations of microstrip structures,” IEEE Trans. Microwave Theory Tech., Vol. 49, No. 2, pp. 250-262, February 2001.  

  5. Z. Wu and R. W. Ziolkowski, “Electromagnetic effects associated with a cavity backed aperture loaded with nonlinear elements,” J. Electromagn. Waves and Appl., Vol. 14, pp. 615-616, 2000.  

  6.  D. C. Wittwer and R. W. Ziolkowski, “Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy media,” IEEE Trans. Antennas and Propagat., Vol. 48, No. 2, pp. 192-199, February 2000.  

  7. D. C. Wittwer and R. W. Ziolkowski, “Maxwellian material based absorbing boundary conditions for lossy media in 3D,” IEEE Trans. Antennas and Propagat., Vol. 48, No. 2, pp. 200-213, February 2000.  

  8. Y. Pemper, E. Heyman, R. Kastner, and R. W. Ziolkowski, “Hybrid-ray moving coordinate frame approach for long range tracking of collimated wavepackets,” J. Electromagnetic Waves and Appl., Vol. 15, pp. 1115-1117, 2000.  

  9. Y. Pemper, V. Lomakin, E. Heyman, R. Kastner, and R. W. Ziolkowski, “Moving coordinate frame FDTD analysis of long range tracking of pulsed fields in graded index waveguides,” J. Electromagn. Waves and Appl., Vol. 14, pp. 493-496, 2000.  

  10. R. W. Ziolkowski, “Maxwell material based absorbing boundary conditions,” Special Issue on Advances in Computational Methods in Electromagnetics, Comput. Methods Appl. Mech. Engr., Vol. 169, pp. 237-262, 1999.

  11. B. Fidel, E. Heyman, R. Kastner, and R. W. Ziolkowski, “Hybrid ray-FDTD moving frame approach to pulse propagation,” Journal of Computational Physics, Vol. 138, pp. 480-500, December 1997.  

  12. R. W. Ziolkowski, “Time derivative Lorentz-material based absorbing boundary conditions,” IEEE Antennas Propagat., Vol. 45, No. 10, pp. 1530-1535, October 1997.  

  13. R. W. Ziolkowski, “Time derivative Lorentz-materials and their utilization as electromagnetic absorbers,” Phys. Rev. E, Vol. 55, No. 6, pp. 7696-7703, June 1997  

  14. R. W. Ziolkowski, “The design of Maxwellian absorbers for numerical boundary conditions and for practical applications using engineered artificial materials,” IEEE Antennas Propagat., Vol. 45, No. 4, pp. 656-671, April 1997.  

  15. R. W. Ziolkowski, “The incorporation of microscopic material models into the FDTD approach for ultrafast optical pulse simulations,” IEEE Trans. Antennas and Propagat., Vol. 45, No. 3, pp. 375-391, March 1997.  

  16. D. C. Wittwer and R. W. Ziolkowski, “How to design the imperfect Berenger PML,” Special Issue on Absorbing Boundary Conditions, Electromagnetics, Vol. 16, pp. 465-485, July-August 1996.  

  17. D. B. Davidson and R. W. Ziolkowski, “A connection machine (CM-2) implementation of a three-dimensional parallel finite difference time-domain code for electromagnetic field simulation,” Int. J. Num. Modeling: Electronic Networks, Devices and Fields, Vol. 8, pp. 221-232, May 1995.  

  18. M. J. Barth, R. R. McLeod, and R. W. Ziolkowski, “A near and far-field projection algorithm for finite-difference time-domain codes,” J. Electromagnetic Waves and Appl., Vol. 6(1), pp. 5-18, 1992.  

  19. N. K. Madsen and R. W. Ziolkowski, “A 3D Modified Finite Volume Technique for Maxwell's Equations,” Invited Paper, Electromagnetics, Vol. 10, pp. 147-161, 1990.  

  20. N. K. Madsen and R. W. Ziolkowski, “A numerical solution of Maxwell's equations in the time domain using irregular nonorthogonal grids,” Invited Paper, Wave Motion, Vol. 10, pp. 583-596, 1988.  

  21. R. W. Ziolkowski, N. K. Madsen, and R. C. Carpenter, “Three-dimensional computer modeling of electromagnetic fields: A global lookback lattice truncation scheme,” J. Comp. Phys., Vol. 50(3), pp. 360-408, 1983.