Recursive algorithm for wave-scattering solutions using windowed addition theorem

A review of a recursive algorithm with a more succinct derivation is first presented. This algorithm, which calculates the scattering solution from an inhomogeneous body, first divides the body into N subscatterers. The algorithm then uses an aggregate T matrix and translation formulas to solve for the solution of n+1 subscatterers from the solution for n subscatterers. This recursive algorithm has reduced computational complexity. Moreover, the memory requirement is proportional to the number of unknowns. This algorithm has been used successfully to solve for the volume scattering solution of two-dimensional scatterers for Ez -polarized waves. However, for Hz -polarized waves, a straightforward application of the recursive algorithm yields unsatisfactory solutions due to the violation of the restricted regime of the addition theorem. But by windowing the addition theorem, the restricted regime of validity is extended. Consequently, the recursive algorithm with the windowed addition theorem works well eve...

[1]  Weng Cho Chew,et al.  Reflection and transmission operators for strips or disks embedded in homogenous and layered media , 1988 .

[2]  E.D. Denman,et al.  An introduction to invariant imbedding , 1977, Proceedings of the IEEE.

[3]  Gene H. Golub,et al.  Matrix computations , 1983 .

[4]  Y. M. Wang,et al.  Limited‐Angle inverse scattering problems and their applications for geophysical explorations , 1990, Int. J. Imaging Syst. Technol..

[5]  Weng Cho Chew,et al.  An efficient algorithm for solution of a scattering problem , 1990 .

[6]  A. Papoulis,et al.  The Fourier Integral and Its Applications , 1963 .

[7]  Weng Cho Chew,et al.  A fast algorithm for solution of a scattering problem using a recursive aggregate τ matrix method , 1990 .

[8]  J. Kong.  Electromagnetic Wave Theory , 1986 .

[9]  J. Richmond,et al.  TE-wave scattering by a dielectric cylinder of arbitrary cross-section shape , 1966 .

[10]  Weng Cho Chew,et al.  An N2 algorithm for the multiple scattering solution of N scatterers , 1989 .

[11]  N. Vilenkin.  Special Functions and the Theory of Group Representations , 1968 .

[12]  Weng Cho Chew,et al.  A multiple scattering solution for the effective permittivity of a sphere mixture , 1990 .

[13]  Raphael Kastner,et al.  An 'add-on' method for the analysis of scattering from large planar structures , 1989 .

[14]  Yi-Ming Wang.  Theory and applications of scattering and inverse scattering problems , 1991 .

[15]  Om P. Gandhi,et al.  Comparison of the FFT Conjugate Gradient Method and the Finite-Difference Time-Domain Method for the 2-D Absorption Problem , 1987 .

[16]  V. Rokhlin.  Rapid Solution of Integral Equations of Scattering Theory , 1990 .

[17]  Ching-Chuan Su,et al.  Calculation of electromagnetic scattering from a dielectric cylinder using the conjugate gradient method and FFT , 1987 .

[18]  W. Chew,et al.  Recursive algorithms for calculating the scattering from N strips or patches , 1990 .

[19]  P. Waterman,et al.  New Formulation of Acoustic Scattering , 1969 .

[20]  J. Kong,et al.  Theory of microwave remote sensing , 1985 .

[21]  K. J. Glover,et al.  The discrete Fourier transform method of solving differential-integral equations in scattering theory , 1989 .

[22]  Weng Cho Chew,et al.  Application of the fast recursive algorithm to a large inhomogeneous scatterer for TM polarization , 1991 .

[23]  B. Peterson,et al.  T matrix for electromagnetic scattering from an arbitrary number of scatterers and representations of E(3) , 1973 .