Time-Domain Near-to-Far Field Transformation for Underwater Simulations at Elf Frequencies

1. Time-Domain Near-to-Far Field Transformation for Underwater Simulations at Elf Frequencies Das Butherus, Yang Xia, MS, and Dennis Sullivan, Ph.D. Department of Electrical and Computer Engineering University of Idaho Moscow, ID USA, 83844-1023

2. Collaborators: University of Idaho Professor Jeffrey Young Dr. Chris Wagner Alireza Mansoori, M.S. Washington State University Professor Robert Olsen Zhi Li This work is funded by the ONR under grant number N000014-07-1-0811 in collaboration with NAVESEA, Carderock Division.

3. Motivation: The navy is moving to an all-electric fleet. Surface ships will use fossil fuel to generate power, but the power train will be electric. There is concern that this will lead to a larger electric signature

4. The biggest danger to ships is mines. Mines are no longer detonated exclusively by contact, but can detect a ship by the electrical signature. The navy is particularly interested in the electrical signal given off by a surface ship in shallow water.

5. The finite-difference time-domain (FDTD) method is being used to simulate the propagation of EM signals at extremely low frequencies (ELF).

6. This project could require simulations over some very long distances. The uniform gridding of FDTD could result in some very large problem spaces. EM Source Mine

7. We have already developed a “Near field, far field” method to help address this. The source is modeled with relatively small cells (10 m cubed), while the far field is modeled is modeled with larger cells (50 m cubed). Dual Problem Space FDTD Simulation for Underwater ELF Applications, Y. Xia, et al, IEEE AWPL, Vol. 8, 2009

8. Dual Problem Space FDTD Simulation for Underwater ELF Applications, Y. Xia, et al, IEEE AWPL, Vol. 8, 2009 This method stored the amplitudes and phases of selected frequencies at the boundary, and used them to generate individual sinusoids in the far field.

9. We are now wondering if it wouldn’t be better to store the time domain data at the near-field, far-field boundary. In this manner, we are not restricted to only selecting discrete frequencies for far-field results.

10. Problem: In the near-to-far-field transformation, every E field on all six surfaces are needed. This could potentially require a huge amount of data storage.

11. Wavelets are being used as a means of data compression Analysis proceeds by convolving and decimating (down-sampling). Synthesis is accomplished by up-sampling and convolving. Analysis Synthesis h0 and f0 are low pass filters; h1 and f1 are high pass filters

12. h0 and f0 are low pass filters; h1 and f1 are high pass filters

13. Analysis Synthesis

14. Analysis (3 Levels) The c0 coefficients are from the low-pass branch. They are filtered down to fewer and fewer terms, i.e., c0(3) has half as many terms as c0(2), etc. c0(4) has only 1/8 then number of terms as x(n). The c1 terms are the high-pass terms. If they are zero or near zero, they can be discarded.

15. An input signal of 800 time steps. We would like to compress this down to a smaller number of points using a five step filter bank.

16. Blue lines: low pass output; Red lines: high-pass output

17. All of the high pass terms are zero, until we come to level 6. Then we have to keep low pass and high pass terms to get perfect reconstruction. We might as well just stop at level 5, which only has low pass terms.

18. Using only the low-pass branches of the analysis and synthesis, the original function was reconstructed from about 50 non-zero numbers.

19. The signals from our ELF FDTD simulation look more like this: The best filters found so far are these:

20. Since we are only going to keep the low-pass terms, the filter banks reduce to this form:

21. The above can be written as loops: Each of these requires about 10 additional lines of code in in the FDTD programs.

22. In the analysis, the number of points is reduced by half at each stage.

23. After 8 levels, the original 5,000 points have been reduced to about 40.

24. The synthesis reconstructs the original

25. Procedure The near field FDTD program is run. The time-domain data at the boundary is stored. The data is compressed and written to a file. The compressed data is read and uncompressed. This data is used as the source at the boundary of the far field FDTD program.

26. The time-domain E fields at the boundary are compressed and stored in data files. Each face is 30x30 cells. The data files are read in, uncompressed, and used as the source at the near field-far field boundary. Each face is 6x6 cells.

27. The following are time-domain simulations, first in the near field, and then in the far field. The source in the near field is a dipole. The near field problem space is 80 cells cubed and uses cells of 10 m cubed. The far field problem space is 60 cells cubed and uses cells of 50 m cubed.

44. Test configuration

46. Summary A time-domain, near-field, far-field formulation has been developed. The time-domain data in the near field is compressed using wavelets. It is likely that a better wavelet filter pair can be found to reduce the amount of data to be stored.