The method of geometrical immersion and calculations for boundary-value elastic problem

The method of geometrical immersion (MGI) is intended to constuct the generalised solution of the boundary-value elastic problem in a region of complex space configuration by realization of the iteration sequence of the variational problems in a region of simple (canonical) form entirely involving the initial. Application of MGI permits us to obtain efficient numerical algorithms for solving elastic problems. Based on the finite element and finite difference methods, the formulation of the finite-dimensional analog of MGI has been performed. Differential analog of the variational equation MGI is the iteration procedure for boundary integral equation. High practical efficiency of the proposed numerical algorithms is supported by comparison of the numerical results obtained from the solution of some plane and three-dimensional problems by the MGI.