A numerical method for the solution of thermo- and electro-static problems for a medium with isolated inclusions

Gaussian approximating functions are used for the solution of the volume integral equation of thermo- and electro-statics for a medium with isolated inhomogeneous inclusions. These functions essentially simplify the construction of the final matrix of the system of linear algebraic equations to which the problem is reduced after the discretization. The method is developed for the solution of 2D and 3D problems and the numerical results are compared with the exact solutions of the problems for spherically layered inclusions. The so-called Edge Gaussian approximating functions are proposed for the improvement of the numerical solution near the borders of the inclusions.