Abstract:

In the integral equation for the direct current electrical field the kernel function is the magnetic dyadic Green’s function. In comparison to the electrical Green’s function, the magnetic Green’s function has a different mathematical formulation. As a result, one cannot use the published singularity removal formulas directly to the magnetic Green’s function, because the formulas are developed solely for the electrical Green’s function. To find a way for removing the singularity of the magnetic Green’s function, we present the concept of the quasi-source dyadic for the magnetic Green’s function, after the corresponding work done for the electrical Green’s function. Furthermore, we compute the quasi-source dyadic for some forms of neighborhoods of the singular point of the magnetic Green’s function, such as spheres and cubes. Using the computed quasi-source dyadic in the integral equation for the direct current field, we can establish a numerical scheme only containing regular integrals. If the numerical scheme is used in the quasi-analytical theory on the direct current field, the fast modeling of the direct current electrical field can be carried out.

Key words: the quasi-analytical method, D.C. electrical field, singularity, dyadic Green’function, the quasi source dyadic