Application of Invariant Approximations Technique to Electrical Field Analysis

The paper deals with the solution of the boundary value problem of a steady-state electric field distributed in a linear uniform substance, provided by applying the finite-differences method and the methodology of invariant functions´ approximation. The research constitutes the first attempt to apply the foresaid methodology, that guarantees the invariance of the solution in respect to the group of linear transformations of Cartesian co-ordinate system, i.e. preserves the tensor characteristics of initial Maxwell´s equations, to the simulation of electrical grounds´ field that is inherently three-dimensional and cannot be substituted by the series of two-dimensional tasks. In result, the considered domain for electric field analysis comprises the internal subset of nodes located strictly inside the domain, the boundary subsets of nodes located on grounds´ surface, the boundary subset of nodes with Neumann relation, and the boundary subset of nodes with Dirichlet relation. The proposed model was tested by means of comparison of its results with analytical solution obtained by application of mirror refractions method and average potential method. The technique proved to be efficient for arbitrary configuration of electrical field distribution domain and can be extended to non-linear case in future research