А modification of the superelement method is proposed for calculation of layered medium when physical properties are greatly varied in one direction. Such problems appear in geophysics, microelectronics, science of materials, researches of oil and gas fields. The main elements of the method are showed for solving the 3D heat-conduction equation. The suggested scheme uses the finite elements in uniform cells and super-elements in cells crossed by thin layers. An approach to approximate the equation on a domain boundary when boundary intersects a cell is considered. We suppose that generalization of the approach for solving various differential equations including case of anisotropic coefficients is possible.

finite superelement method, layered medium

Mathematical problems and theory of numerical methods