Prof. Chew's book
ECE 350 lecture notes
Former graduate students
Former post-doctoral and visiting scholars
Image formation and processing group
Recent conference presentations
Papers on Efficient Addition Theorem Calculations
My physics colleague told me that these papers can be useful to the physics community.
The calculation of the addition theorem usually involves the calculation of Gaunt coefficients and 3j symbols. The techniques outlined in these papers avoid those
Recurrence Relations for Three-Dimensional Scalar Addition Theorem. Journal of Electromagnetic Waves and Applications. pp. 133-142 vol. 6 no. 2, 1992.
Efficient Ways to Compute the Vector Addition Theorem. Journal of Electromagnetic Waves and Applications. pp. 651-665 vol. 7 no. 5, 1993.
Many people have asked for the codes in the papers above. I have codes written by Yiming Wang under my supervision when he was a Ph.D. student here. Instead of letting those age-old codes sit on my shelf doing nothing, I am givin them away with no support. If you find the codes useful, just acknowledge us. I looked through the code quickly. It seems that we wrote a vector addtion theorem by calling the scalar addition theorem (one of the suggestions in the paper). I can't find the code that does it directly--probably tucked away somewhere else. The translators are called alpha, beta, and alpha as are named in my book WFIM. Also, if any one of you care to translate the codes to C or C++, I will appreciate receiving a copy.
Scattering by a cluster of spheres written in Fortran 77.
Here are other gems on efficient addition theorem calculation if you want to translate only in the z direction. One can perform a general translation by first rotating the coordinates, followed by a z translation, and then by a back rotation.
J.H. Bruning and Y.T.Lo, "Multiple Scattering by Spheres," UIUC EM Lab Technical Report, May 1969.
J.H. Bruning and Y.T.Lo, "Multiple Scattering of EM Waves by Spheres, Part I," IEEE Trans. Antennas Propag. vol. AP-19, pp. 378-400, 1971.
J.H. Bruning and Y.T.Lo, "Multiple Scattering of EM Waves by Spheres, Part II," IEEE Trans. Antennas Propag. vol. AP-19, pp. 378-400, 1971.