V.I. Drozdova, E.I. Nikolaev, G.V. Shagrova

This paper describes the features of the application of numerical methods for solving problems of mathematical physics in the relational architecture. Considered tools of relational database management systems (RDBMS) for the implementation of the basic steps of the numerical simulation: mesh generation, discretization of the equations of the original model, solving the system of linear algebraic equations (SLAE), analysis and interpretation of results. The approaches to the construction of algorithms and formats of data storage in the relational architecture at every stage of the computational experiment are described. In this work considered the mesh generation algorithms for the finite difference method (FDM) and finite element method (FEM), describes the data structures to represent non-uniform structured and unstructured grids. An algorithm for discretization of the equations of the original model and build a matrix of SLAE using stored procedures in SQL is proposed. In this work is proposed an algorithm for solving SLAE of large-scale empty-matrix iterative method of Krylov type in the relational architecture. An algorithm for the calculation of integral characteristics of the fields calculated value using SQL is proposed. The capabilities provided by the RDBMS to export and processing of data obtained during the numerical calculations are described. It also describes how to build unstructured triangular mesh finite element. The results of calculation of the magnetic scalar potential with the help of FDM, the magnetic vector potential by using the FEM and the results of calculation of the magnetic force by using different numerical methods are presented.