Application of FPGA technology to accelerate the finite-difference time-domain (FDTD) method

ABSTRACT

The continuing advances in the field of electrical engineering, in areas like cellular communications, fiber optics, mobile and multi-gigahertz electronics have necessitated a computer-assisted design approach to the complex electromagnetic interactions and problems that arise. Finite-Difference Time-Domain (FDTD) Analysis is a very powerful tool for the modeling of electromagnetic phenomena. The algorithm is computationally intensive and simulations can run for a few hours to several days. Increasing the computation speed and decreasing the run times of this algorithm would bring greater productivity and new avenues of research to many facets of electrical engineering.The algorithm is transferred to custom FPGA-based hardware using a pipelined bit-serial arithmetic architecture. A one-dimensional resonator is used to verify the implementation and explore the hardware speed and costs. The computational speed is extremely fast and is not related to the number of computational cells in the simulation. Finally, a discussion of future research is presented.

REFERENCES

• 1: Taflove, Allen. Advances in Computational Electrodynamics - The Finite Difference Time Domain Method. Norwood, MA: Artech House Inc., 1998.
• 2: Marek, J.R., Mehalic, M.A. and Terzuoli, A.J. "A Dedicated VLSI Architecture for Finite-Difference Time Domain Calculations" 8th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, vol. 1, pp. 546-553, March, 1992.
• 3: Grinin, S.V.. "Integer-Arithmetic FDTD Codes for Computer Simulation of Internal, Near and Far Electromagnetic Fields Scattered by Three-Dimensional Conductive Complicated Form Bodies", Computer Physics Communications, vol. 102, no. 1--3, pp.109-131, May, 1997.
• 4: Mittra R. and Werner D.H.. Frontiers in Electromagnetics. IEEE Press, 1999.
• 5: Mittra R., Peterson, A.F. and Ray S.L.. Computational Methods for Electromagnetics. IEEE Press, 1997.
• 6: Yee, K.S., "Numerical Solution of initial boundary value problems solving Maxwell's equations in isotropic media," IEEE Trans. Antennas and Propagation, Vol. 14, 1966, pp.302-307
• 7: Taflove, Allen. Computational Electrodynamics - The Finite Difference Time-Domain Method. Norwood, MA: Artech House Inc., 1996.
• 8: Okoniewski, M., "Advances in FDTD Modeling: EMC and Numerical Dosimetry", Tutorial Slides, Zurich, 1999.
• 9: Bruton, L.T.. "Low sensitivity digital ladder filters," IEEE. Trans. Circuits Syst., vol CAS-22, pp.168-176, March 1975.
• 10: Gwarek, W.K.. "Analysis of Arbitrarily Shaped Two- Dimensional Microwave Circuits by Finite-Difference Time- Domain Method," IEEE Trans. Microwave Theory and Techniques, vol. 36, no. 4, pp.738-744.
• 11: XESS Development Corp. http://www.xess.com
• 12: Richard J. Hartley , Keshab K. Parhi, Digit-Serial Computation, Kluwer Academic Publishers, Norwell, MA, 1995
• 13: P. B. Denyer , David Renshaw, VLSI Signal Processing; A Bit-Serial Approach, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1985
• 14: Alfke, P. "Efficient Shift Registers, LSFR Counters and Long Pseudo-Random Sequence Generators, "Xilinx Application Note: XAPPP 052, July 7, 1996, http://www.xilinx.com.
• 15: Fettweis, A.. "On the connection between multiplier wordlength and roundoff noise in digital filters", IEEE Trans. on Circuit Theory, vol-19, no. 5, pp. 486- 491, September 1972.