Hlova A. Development of the software and mathematical instruments for modelling of evolutionary processes

Evolutionary processes are characterized by continuous system state changes over time. Their mathematical models are mixed problems for second order differential equations with constant coefficients. In the dissertation, a combination of boundary integral equations (BIE) method with the Laguerre transform over the time is applied to obtain solutions. Galerkin method is used to find solutions of BIE, namely its implementation in the form of boundary element method (BEM). Such a combination of the Laguerre transform and BEM allows the generalization of computational schemes for all evolutionary problems considered in the dissertation and formulation of requirements for the development of specialized software, called MultiMathFramework (MMF). To ensure the maximum flexibility of the system, the division of software modules into four levels is applied. Each of these levels is formed by program modules, which are logically coupled. However, the dependency between modules at different levels is limited and weak. Due to the designed architecture, the amount of program code for individual problems is relatively small. In particular, these are modules, which are responsible for the calculation of the matrices of the obtained systems of algebraic equations (SLAE). After highlighting the main architectural and algorithmic aspects of the framework, the implementation of the proposed approaches is considered in the example of building a problem solver module for the wave equation with dynamic boundary condition. The use of infrastructure elements, base classes and kernel interfaces are consistently shown. Particular attention is paid to the mathematical justification of key aspects of the proposed approaches. In order to demonstrate the application of the mathematical instruments and software, the results of a series of numerical experiments for evolutionary problems are presented. They confirm the correctness of the theory and show the effectiveness of the framework.