Grid-operator approach to programming mathematical physics problems

Abstract:

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.

Keywords:

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