An investigation of near-zone preconditioning techniques for integral equation solutions by method of moments

Author(s):  
O. Wiedenmann ◽  
T.F. Eibert
2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Zhiwei Liu ◽  
Dan Tang ◽  
Zhanyang Zhang ◽  
Yueyuan Zhang ◽  
Xiaoli Wang ◽  
...  

Electromagnetic nondestructive evaluation of underground targets is of great significance for the safety of urban construction. Based on the accurate and efficient simulation of scattering, we can detect the underground targets successfully. As one of the most popular numerical methods in electromagnetics, surface integral equations solved by method of moments (MoM) are used to simulate the scattering from underground targets in this paper. The integral equation is discretized by RWG basis and Galerkin testing. Multilevel fast multipole algorithm (MLFMA) is used to decrease the computation complexity and memory cost. However, the octree used in MLFMA is not applied for rough surfaces and targets together; both the surface and target need to construct octree separately. Since the combination of MLFMA and ACA can build a more efficient method to compute scattering from underground targets, adaptive cross approximation (ACA) is used to compress the impedance matrix instead of MLFMA for the coupling action between the rough surface and target. That is to say that, when calculating the scattering of two targets, target self-interaction is suitable for MLFMA calculation and the coupling between targets is approximated by ACA. Numerical results demonstrate the accuracy and efficiency of our proposed method.


Geophysics ◽  
1976 ◽  
Vol 41 (5) ◽  
pp. 997-1015 ◽  
Author(s):  
Donald D. Snyder

A method has been developed for the solution of the resistivity and IP modeling problem for one or more two‐dimensional inhomogeneities buried in a space for which the Dirichlet Green’s function is known. The boundary‐value problem reduces to a Fredholm integral equation of the second kind which is parametrically a function of a spatial wavenumber. Using the method of moments, the integral equation is solved for a number of values of the wavenumber. An inverse Fourier transform is then performed in order to obtain the electric potential at any point of interest. The method agrees well with both experimental results and other numerical techniques.


1996 ◽  
Vol 74 (3-4) ◽  
pp. 122-131 ◽  
Author(s):  
H. Moheb ◽  
J. Shaker ◽  
L. Shafai

The equivalence principle and the generalized network formulation are used to model the tangential electric field on arbitrary apertures, backed by a rectangular wave guide or cavity, in terms of equivalent magnetic currents. The coupling is through the aperture whose characteristics are expressed by the aperture admittance matrices of the cavity and half-space regions. The aperture coupling is then expressed as the sum of the two independent aperture admittances, with source terms related to the incident field. The result is an integral equation for the unknown aperture current. This integral equation is then reduced to a matrix equation using the method of moments. The formulation is then used to, investigate the electrical characteristics, i.e., aperture field distribution, aperture admittance, and radiation patterns of low-gain antennas such as H, cross, end-loaded, and centre-loaded slots backed by a cavity. Experimental results are also provided to verify the numerical results.


2020 ◽  
Vol 9 (3) ◽  
pp. 8-14
Author(s):  
M. Bayjja ◽  
G. Alsharahi ◽  
M. Aghoutane ◽  
N. A. Touhami

In this paper, wavelets transformation (WT) and wavelet packet transformation (WPT) are used in solving, by the method of moments, a semicircular array of parallel wires electric field integral equation.  First, the integral equation is solved by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix.  Therefore, wavelet transformation and wavelet packet transformation are used to sparsify the impedance matrix, using two categories of wavelets functions, Biorthogonal (bior2.2) and Orthogonal (db4) wavelets.  The far-field scattering patterns and the comparison between wavelets transformation and wavelet packet transformation in term number of zeros in impedance matrix and CPU Time reduction are presented. Numerical results are presented to identify which technique is best suited to solve such scattering electromagnetic problems and compared with published results.


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