A Comparison of Two Methods for Solving Electromagnetic Field Integral Equation

Jebli, L.

doi:10.1155/2011/169707

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…The MoM technique [22][23][24][25] has been widely used for different scattering problems to discretize the problem into a linear system of equations of the form Ax ¼ b. In this section, the CG version of the MoM forward solver for solving the scattering from inhomogeneous attenuation, density, and compressibility profiles will be described.…”

Section: Forward Solvermentioning

confidence: 99%

“…Note that in this paper the imaging domain is discretized into square cells using 2D pulse basis functions and Dirac delta weighting functions are utilized. 4,[22][23][24][25] The next task is to incorporate features in the numerical algorithm that will allow us to handle large numerical values of the contrast and also large objects as compared to the wavelength. The standard CG algorithm turns out to be too computationally expensive for the UT problem.…”

Section: A Mom Forward Solvermentioning

confidence: 99%

“…The steps of this algorithm can then be summarized as: 2, 5,7,8,39 (1) Set the unknown total pressure inside the imaging domain to be equal to the incident pressure in the first iteration (Born approximation), which is utilized in Eqs. (24) and (25). (3) Call the forward solver to find the total pressure inside the imaging domain based on the predicted contrast profiles of the previous step (see Sec.…”

Section: A Bimmentioning

confidence: 99%

“…In this paper, a Method of Moments (MoM) [22][23][24][25] forward solver, in conjunction with the Conjugate Gradient (CG) method, 26 is used to handle the scattering from inhomogeneous objects which simultaneously vary in compressibility, attenuation, and density. This forward solver can also deal with large high contrast objects.…”

Section: Introductionmentioning

confidence: 99%

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Ultrasound tomography for simultaneous reconstruction of acoustic density, attenuation, and compressibility profiles

Mojabi

LoVetri

2015

The Journal of the Acoustical Society of America

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A fast and efficient forward scattering solver is developed for use in ultrasound tomography. The solver is formulated so as to enable the calculation of scattering from large and relatively high-contrast objects with inhomogeneous physical properties that vary simultaneously in acoustic attenuation, compressibility, and density. It is based on the method of moments in conjunction with a novel implementation of the conjugate gradient algorithm which requires the use of the adjoints of the scattering operators. The solver takes advantage of the symmetric block Toeplitz matrix with symmetric Toeplitz blocks property of the Green's function matrix to increase efficiency and only stores the first row of this matrix to reduce memory requirements. This row is then used for the matrix-vector multiplication using the fast Fourier transform technique, thus, resulting in the computational complexity of O(n log n). The marching-on-source technique is also used to provide a good initial guess which allows the conjugate gradient technique to converge faster than initializing with an arbitrary guess. This feature is important in tomographic inversion algorithms which require that the object to be imaged be interrogated via several incident fields. Forward scattering and inversion examples, based on the Conjugate Gradient Least Squares regularized Born Iterative Method, are shown, in two-dimensions, for objects varying in all three physical properties.

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Section: Forward Solvermentioning

confidence: 99%