An N2 algorithm for the multiple scattering solution of N scatterers

The scattering solution from N scatterers, each of whose scattered field is approximated by M harmonics is an NM unknown problem. A straightforward solution to this problem can be obtained by casting it into an NM linear algebraic equation. The solution of the linear algebraic equation will involve order N3M3 flouting point operations. However, via the use of a recursive algorithm and the translation formula, an order N2M3 algorithm to solve such a problem is possible.

[1]  P. Waterman,et al.  Multiple Scattering of Waves. II. ``Hole Corrections'' in the Scalar Case , 1964 .

[2]  Weng Cho Chew,et al.  Propagation of electromagnetic waves through geological beds in a geophysical probing environment , 1985 .

[3]  Y. Lo,et al.  Multiple scattering of EM waves by spheres part I--Multipole expansion and ray-optical solutions , 1971 .

[4]  Schwartz,et al.  Electromagnetic propagation in close-packed disordered suspensions. , 1985, Physical review. B, Condensed matter.

[5]  A. Bansil,et al.  effective-medium theory of electronic states in structurally disordered metals: Application to liquid Cu , 1981 .

[6]  D. M. Wood,et al.  Long-wavelength electromagnetic propagation in heterogeneous media , 1980 .

[7]  P. Waterman.  Matrix formulation of electromagnetic scattering , 1965 .

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

[9]  L. Schwartz.  Electronic states in liquid and amorphous metals. I. Optical theorem and multiple-scattering theory , 1980 .

[10]  Leung Tsang,et al.  Multiple scattering of electromagnetic waves by random distributions of discrete scatterers with coherent potential and quantum mechanical formalism , 1980 .

[11]  L. Tsang.  Scattering of electromagnetic waves from a half space of nonspherical particles , 1984 .

[12]  M. Lax.  MULTIPLE SCATTERING OF WAVES. II. THE EFFECTIVE FIELD IN DENSE SYSTEMS , 1952 .

[13]  Michael Danos,et al.  Multipole Matrix Elements of the Translation Operator , 1965 .

[14]  V. Twersky.  On Scattering of Waves by Random Distributions. I. Free‐Space Scatterer Formalism , 1962 .

[15]  S. Ström,et al.  Matrix formulation of acoustic scattering from an arbitrary number of scatterers , 1974 .