Analysis of low frequency scattering from penetrable scatterers

A method is presented for solving the surface integral equation using the method of moments (MoM) at very low frequencies, which finds applications in geoscience. The nature of the Helmholtz decomposition leads the authors to choose loop-tree basis functions to represent the surface current. Careful analysis of the frequency scaling property of each operator allows them to introduce a frequency normalization scheme to reduce the condition number of the MoM matrix. After frequency normalization, the MoM matrix can be solved using LU decomposition. The poor spectral properties of the matrix, however, makes it ill-suited for an iterative solver. A basis rearrangement is used to improve this property of the MoM matrix. The basis function rearrangement (BFR), which involves inverting the connection matrix, can be viewed as a pre-conditioner. The complexity of BFR is reduced to O(N), allowing this method to be combined with iterative solvers. Both rectilinear and curvilinear patches have been used in the simulations. The use of curvilinear patches reduces the number of unknowns significantly, thereby making the algorithm more efficient. This method is capable of solving Maxwell's equations from quasistatic to electrodynamic frequency range. This capability is of great importance in geophysical applications because the sizes of the simulated objects can range from a small fraction of a wavelength to several wavelengths.

[1]  Roger F. Harrington,et al.  An E-Field solution for a conducting surface small or comparable to the wavelength , 1984 .

[2]  R. J. Adams,et al.  An iterative solution of one-dimensional rough surface scattering problems based on a factorization of the Helmholtz operator , 1999 .

[3]  L. Knizhnerman,et al.  Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains , 1994 .

[4]  Jiming Song,et al.  Fast Illinois solver code (FISC) , 1998 .

[5]  Stephen M. Wandzura,et al.  Electric Current Basis Functions for Curved Surfaces , 1992 .

[6]  Weng Cho Chew,et al.  The Fast Illinois Solver Code: requirements and scaling properties , 1998 .

[7]  Krzysztof A. Michalski,et al.  On the existence of branch points in the eigenvalues of the electric field integral equation operator in the complex frequency plane , 1983 .

[8]  Roberto D. Graglia,et al.  On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle , 1993 .

[9]  L. N. Medgyesi-Mitschang,et al.  Generalized method of moments for three-dimensional penetrable scatterers , 1994 .

[10]  Akira Ishimaru,et al.  Backscattering enhancement of electromagnetic waves from two-dimensional perfectly conducting random rough surfaces: a comparison of Monte Carlo simulations with experimental data , 1996 .

[11]  W. Chew,et al.  Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies , 2000 .

[12]  Weng Cho Chew,et al.  NEW HIGH SPEED TECHNIQUE FOR CALCULATING SYNTHETIC INDUCTION AND DPT LOGS. , 1984 .

[13]  Weng Cho Chew,et al.  Moment method solutions using parametric geometry , 1995 .

[14]  L Tsang,et al.  Scattering of electromagnetic waves from dense distributions of spheroidal particles based on Monte Carlo simulations. , 1998, Journal of the Optical Society of America. A, Optics, image science, and vision.

[15]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[16]  E. S. Li,et al.  Modeling and measurements of scattering from road surfaces at millimeter-wave frequencies , 1997 .

[17]  Donald R. Wilton,et al.  Modeling Scattering From and Radiation by Arbitrary Shaped Objects with the Electric Field Integral Equation Triangular Surface Patch Code , 1990 .

[18]  K. J. Glover,et al.  Electromagnetic Computation Using Parametric Geometry , 1990 .