A numerical solution for conducting bodies of arbitrary shape

1990 ◽  
Vol 68 (6) ◽  
pp. 459-468 ◽  
Author(s):  
H. Moheb ◽  
L. Shafai
Keyword(s):  
Electromagnetic Scattering ◽  
Arbitrary Shape ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Surface Current ◽  
Basis Functions ◽  
The Other ◽  
Current Component ◽  
Discrete Surfaces ◽  
Conducting Bodies

An efficient numerical technique based on a Fourier expansion of the surface current is developed to study the electromagnetic scattering from three-dimensional geometries of arbitrary shape. In this method, the discrete domain representing the structure surface is geometrically represented by two orthogonal contours. One is selected along the intersection of the x–z plane with the object's surface, and the other along the corresponding one in the x–y plane. Entire domain basis functions are selected for the current component in the x–y plane, and subdomain linear basis functions are used to represent the other current component. The method of moments is used to solve the problem numerically. The technique is then applied to study the scattering from discrete surfaces such as squares and rectangles, to compare them with those of the coordinate-transformation technique developed earlier. The behavior of the solutions with the number of modes is investigated to determine their coupling.

ELECTROMAGNETIC SCATTERING FROM CYLINDERS OF ARBITRARY CROSS‐SECTION IN A CONDUCTIVE HALF‐SPACE

Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 67-100 ◽  
Author(s):  
J. R. Parry ◽  
S. H. Ward
Keyword(s):  
Half Space ◽  
Cross Section ◽  
Electromagnetic Scattering ◽  
Numerical Technique ◽  
Surface Current ◽  
Arbitrary Cross Section ◽  
Integral Representations ◽  
Radius Of Curvature ◽  
Current Densities ◽  
Conducting Cylinders

A general numerical technique is presented for solving the problem of electromagnetic scattering by conducting cylinders of arbitrary cross‐section located in a conductive half‐space. Solutions to the electromagnetic wave equation are required for the free space above the half‐space, for the half‐space surrounding the cylinder, and for the cylinder. The problem is formulated by choosing an integral representation for the electromagnetic fields in each of the three homogeneous regions. By enforcing the boundary conditions on tangential E and H, we obtain a set of coupled integral equations which can be solved numerically for the unknown equivalent surface current densities on the interface bounding each homogeneous region. Once these current densities have been estimated, the fields can be calculated at any point from the general integral representations. The following conclusions are among those of importance to AFMAG and VLF surveys: 1) the ratio of Re (H) to Im (H) is a function of traverse position and of ground conductivity, as well as of cylinder conductivity and of survey frequency; 2) in no case was a zero phase observed, even for perfectly conducting cylinders; and 3) reverse crossovers in Im (H) can occur in the field scattered by a single conductor whenever the radius of curvature on the upper portion of a “poor” conductor is small.

Multinode Unsteady Surface Element Method With Application to Contact Conductance Problem

1986 ◽  
Vol 108 (2) ◽  
pp. 257-263 ◽  
Author(s):  
B. Litkouhi ◽  
J. V. Beck
Keyword(s):  
Numerical Technique ◽  
Three Dimensional ◽  
The Other ◽  
Surface Element ◽  
Variable Boundary ◽  
Transient Problems ◽  
Different Temperatures ◽  
Perfect Contact ◽  
Transfer Problems ◽  
Element Method

The unsteady surface element method is a powerful numerical technique for solution of linear transient two- and three-dimensional heat transfer problems. Its development originated with the need of solving certain transient problems for which similar or dissimilar bodies are attached one to the other over a part of their surface boundaries. In this paper a multinode unsteady surface element (MUSE) method for two arbitrary geometries contacting over part of their surface boundaries is developed and formulated. The method starts with Duhamel’s integral (for arbitrary time and space variable boundary conditions) which is then approximated numerically in a piecewise manner over time and the boundaries of interest. To demonstrate the capability of the method, it is applied to the problem of two semi-infinite bodies initially at two different temperatures suddenly brought into perfect contact over a small circular region. The results show excellent agreement between the MUSE solution and the other existing solutions.

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