The objectives of this thesis are to develop a programming approach that allows you to compactly record and effectively implement a class of mathematical formulas and develop an experimental software package that shows the possibility of implementing this approach to solve a wide class of problems in mathematical physics. A new programming approach has been developed for the class of mathematical calculations on various types of grids, both regular and arbitrary irregular. Within the framework of the developed approach, a new system of concepts is introduced, which ensures the effective implementation of the approach. A set of software libraries has been developed that demonstrate the possibility of effective software implementation of the proposed programming approach for various types of grids.

grid operator, regular grids and arbitrary irregular grids, parallel platform NVIDIA CUDA, OpenMP, solving the Euler equation by the discontinuous Galerkin method, three-dimensional heat conduction problem

Programming, parallel computing, multimedia