Topological methods in one numerical scheme of solving three-dimensional continuum mechanics problems

We discuss finite element numerical schemes for solving the continuum mechanics problems. Previously a method of acceleration of calculations was developed which uses the simplicial mesh inscribed in the original cubic cell partition of a three-dimensional body. In this work we show that the obstacle to the construction of this design may be described in terms of homology groups modulo 2. The main goal of the work is to develop a method of removing this obstacle. The achievement of the goal is based on efficient algorithms for computing bases of the homology groups which are dual with respect to the intersection form.