Вычислительный эксперимент – обезразмеривание уравнений, вычислительная устойчивость и тестирование программ

Abstract

From the stages of the computational experiment, the stage of non-dimensionalization of the initial equation (system of equations) of the problem is considered - the replacement of its variables by the product of the corresponding dimensionless quantities by their units of measurement with subsequent transformations. Such a transition from a physical model to a mathematical (dimensionless) one makes it possible to obtain software implementations for research. A critical evaluation of its complexity is carried out and possible errors in the results are evaluated. At the same time, new versions of software are formed. Object-oriented programming tools and version control systems (for example, git) allow you to create versions of software tools adapted to different conditions of their use and for different types of users. Parallelization of work on versions is carried out. At the same time, for further software implementation, the set-theoretic language of formulas with partially recursive functions is effective. To implement versions with large amounts of calculations and data, high-performance computing systems based on software and hardware acceleration, parallel information processing and cloud architectures are used. As a rule, a difference model of the problem and iterative methods for solving it are constructed for a program version. Computational stability conditions are usually stipulated in modern instructions for standard program libraries. For new algorithms, it is necessary to analyze the stability of difference schemes based on the refinement of their spectral properties and the use of functional analysis methods. For storage and subsequent application of the results of computational experiments, it is advisable to use modern databases. As a kind of computational experiment, testing of alpha and beta versions of programs and their releases is also considered.