TY - JOUR

T1 - Fast-forward solvers for the low-frequency detection of buried dielectric objects

AU - Cui, Tie Jun

AU - Chew, Weng Cho

AU - Aydiner, Alaeddin A.

AU - Zhang, Yunhua H.

N1 - Funding Information:
Manuscript received February 27, 2002; revised March 8, 2003. This work was supported by the Department of Energy under Grant DOE DEFG07-97ER 14835, by the Air Force Office of Scientific Research under MURI Grant F49620-96-1-0025, and by the National Science Foundation under Grant NSF ECS 99-06651. The work of T. J. Cui was supported by the National Science Foundation of China for Distinguished Young Scholars under Grant 60225001, China.

PY - 2003/9

Y1 - 2003/9

N2 - It is known that the extended Born approximation (ExBorn) is much faster than the method of moments (MoM) in the study of electromagnetic scattering by three-dimensional (3-D) dielectric objects, while it is much more accurate than the Born approximation at low frequencies. Hence, it is more applicable in the low-frequency numerical simulation tools. However, the conventional ExBorn is still too slow to solve large-scale problems because it requires O(N2) computational load, where N is the number of unknowns. In this paper, a fast ExBorn algorithm is proposed for the numerical simulation of 3-D dielectric objects buried in a lossy earth. When the buried objects are discretized with uniform rectangular mesh and the Green's functions are extended appropriately, the computational load can be reduced to O(N log N) using the cyclic convolution, cyclic correlation, and fast Fourier transform (FFT). Numerical analysis shows that the fast ExBorn provides good approximations if the buried target has a small or moderate contrast. If the contrast is large, however, ExBorn will be less accurate. In this case, a preconditioned conjugate-gradient FFT (CG-FFT) algorithm is developed, where the solution of the fast ExBorn is chosen as the initial guess and the preconditioner. Numerical results are given to test the validity and efficiency of the fast algorithms.

AB - It is known that the extended Born approximation (ExBorn) is much faster than the method of moments (MoM) in the study of electromagnetic scattering by three-dimensional (3-D) dielectric objects, while it is much more accurate than the Born approximation at low frequencies. Hence, it is more applicable in the low-frequency numerical simulation tools. However, the conventional ExBorn is still too slow to solve large-scale problems because it requires O(N2) computational load, where N is the number of unknowns. In this paper, a fast ExBorn algorithm is proposed for the numerical simulation of 3-D dielectric objects buried in a lossy earth. When the buried objects are discretized with uniform rectangular mesh and the Green's functions are extended appropriately, the computational load can be reduced to O(N log N) using the cyclic convolution, cyclic correlation, and fast Fourier transform (FFT). Numerical analysis shows that the fast ExBorn provides good approximations if the buried target has a small or moderate contrast. If the contrast is large, however, ExBorn will be less accurate. In this case, a preconditioned conjugate-gradient FFT (CG-FFT) algorithm is developed, where the solution of the fast ExBorn is chosen as the initial guess and the preconditioner. Numerical results are given to test the validity and efficiency of the fast algorithms.

KW - Buried objects

KW - Conjugate-gradient fast fourier transform (CG-FFT) algorithm

KW - Cyclic convolution

KW - Cyclic correlation

KW - Fast extended born approximation

KW - Half space

KW - Low-frequency numerical simulation

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U2 - 10.1109/TGRS.2003.813502

DO - 10.1109/TGRS.2003.813502

M3 - Article

AN - SCOPUS:0141940252

SN - 0196-2892

VL - 41

SP - 2026

EP - 2036

JO - IEEE Transactions on Geoscience and Remote Sensing

JF - IEEE Transactions on Geoscience and Remote Sensing

IS - 9 PART I

ER -