ABSTRACT
Calculation of electro-and thermo-static fields in an infinite homogeneous medium with a heterogeneous isolated inclusion is considered in this work. It is reduced to the solution of integral equations for the fields inside the inclusion. Gaussian functions are used for the approximation of the unknown fields and discretization of the equations. For such functions, the elements of the matrix of discretized system are obtained in closed analytical forms. Coordinates of the nodes (centers of the Gaussian functions) are only necessary to carry out the method in the region occupied by the inclusion (i.e. a mesh-free method). Composed of a regular grid of nodes, the matrix of the discretized problem will have the Toeplitz structure. Fast Fourier transform technique (FFT) can be applied for the calculation of the matrix-vector products. This technique is used within the iterative solution of the system of linear algebraic equations of the discretized problem. The proposed algorithm is simple and fast and does not require much computer memory. The comparison of the numerical and exact solutions for electro-static fields inside spherical inclusions with radial variation of properties is presented and analyzed here.
