An iterative method for solving a large dense matrix in the method of moments solution of an electrostatic problem

2003 ◽  
Vol 39 (5) ◽  
pp. 378-380 ◽  
Author(s):  
Ritu Singh ◽  
Surendra Singh
Keyword(s):  
Iterative Method ◽  
Method Of Moments ◽  
Dense Matrix ◽  
Electrostatic Problem

scholarly journals Comparison of Wavelet Packet and Wavelet in Solving Arbitrary Array of Parallel Wires Integral Equations in Electromagnetics

2020 ◽  
Vol 9 (3) ◽  
pp. 8-14
Author(s):  
M. Bayjja ◽  
G. Alsharahi ◽  
M. Aghoutane ◽  
N. A. Touhami
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Direct Method ◽  
Wavelet Packet ◽  
Dense Matrix ◽  
Impedance Matrix ◽  
Electric Field Integral Equation ◽  
Electromagnetic Problems ◽  
Number Of Zeros ◽  
Wavelet Packet Transformation

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.

scholarly journals The Terminal Responses of the Two-Wire Line in Multiaperture Cavities Based on Electromagnetic Topology and Method of Moments

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Ying Li ◽  
Jianshu Luo ◽  
Guyan Ni
Keyword(s):  
Iterative Method ◽  
Transmission Line ◽  
Method Of Moments ◽  
Electromagnetic Interference ◽  
Electromagnetic Interaction ◽  
Numerical Results ◽  
Frequency Range ◽  
Metallic Structures ◽  
Electromagnetic Interactions ◽  
Simulation Results

A simulation technique based on electromagnetic topology (EMT) theory is proposed for analyzing electromagnetic interference (EMI) coupling through apertures onto the two-transmission line enclosed within metallic structures. The electromagnetic interactions between apertures and the external-internal interactions were treated through the topological decomposition and the multistep iterative method. Then, the load responses of the two-wire transmission line are resolved by the the Baum-Liu-Tesche (BLT) equation. The simulation results both without and with the electromagnetic interaction are presented for the frequency range from 100 MHz to 3 GHz. These numerical results obtained by two methods imply that the electromagnetic interaction cannot be simply ignored, especially for the frequency range up to 1 GHz.

scholarly journals Accelerating the charge inversion algorithm with hierarchical matrices for gas insulated systems

2021 ◽  
Vol 2090 (1) ◽  
pp. 012136
Author(s):  
F Lucchini ◽  
N Marconato
Keyword(s):  
Industrial Applications ◽  
Hierarchical Matrices ◽  
Stable Operation ◽  
Dense Matrix ◽  
Memory Requirement ◽  
Inversion Algorithm ◽  
Surface Charges ◽  
Charge Inversion ◽  
Electrostatic Problem ◽  
Time Operation

Abstract Surface charges accumulating on dielectrics during long-time operation of Gas Insulated High Voltage Direct Current (HVDC-GIS) equipments may affect the stable operation and could possibly trigger surface flashovers. In industrial applications, to quantify and identify the location of the surface charge accumulation from experimental measurements, the surface potential distribution is evaluated using, e.g., electrostatic probes, then the charge density is determined by solving an electrostatic problem based on an inversion procedure known as Charge Inversion Algorithm. The major practical limitation of such procedure is the inversion and the storage of the fully dense matrix arising from the representation via Integral Equations of the electrostatic phenomenon, resulting in O(N 3) computational complexity and O(N 2) memory requirement. In this paper it is shown how hierarchical matrices can be efficiently used to accelerate the charge inversion algorithm and, more importantly, reduce the overall memory requirement.

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