Reduced forward operator for electromagnetic wave scattering problems

The paper describes a reduced forward operator for solving electromagnetic scattering problems using a volume integral equation in conjunction with a conjugate gradient fast Fourier transform scheme. The reduction is obtained by decoupling of the interaction between the locations in the spatial computational domain at which there is non-zero contrast and those positions at which there is zero contrast. The decoupling is achieved by multiplication of the kernel by a diagonal matrix whose entries reflect the presence or absence of contrast at the associated point. Analysis supported by numerical experiments shows that the conjugate gradient algorithm applied to the reduced system converges more rapidly than when it is applied to the original system.

[1]  T. Sarkar,et al.  Comments on "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies" , 1986 .

[2]  P. M. van den Berg,et al.  Iterative Methods for Solving Integral Equations , 1991, Progress In Electromagnetics Research.

[3]  W. Wright,et al.  A reduced forward operator for acoustic scattering problems , 2005 .

[4]  R. Mathias.  Two theorems on singular values and eigenvalues , 1990 .

[5]  A. T. Hoop,et al.  Handbook of Radiation and Scattering of Waves: Acoustic Waves in Fluids, Elastic Waves in Solids, Electromagnetic Waves , 2001 .

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

[7]  P. M. van den Berg,et al.  A weak form of the conjugate gradient FFT method for plate problems , 1991 .

[8]  Caicheng Lu.  A fast algorithm based on volume integral equation for analysis of arbitrarily shaped dielectric radomes , 2003 .

[9]  Qing Huo Liu,et al.  Microwave breast imaging: 3-D forward scattering simulation , 2003, IEEE Transactions on Biomedical Engineering.

[10]  Tapan K. Sarkar,et al.  Application of Conjugate Gradient Method to Electromagnetics and Signal Analysis , 1991 .

[11]  Y. Gan,et al.  A fast combined field volume integral equation solution to EM scattering by 3-D dielectric objects of arbitrary permittivity and permeability , 2006, IEEE Transactions on Antennas and Propagation.

[12]  Qing Huo Liu,et al.  A volume adaptive integral method (VAIM) for 3-D inhomogeneous objects , 2002 .

[13]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[14]  Qing Huo Liu,et al.  RCS computation of large inhomogeneous objects using a fast integral equation solver , 2003 .