Today, modeling tasks are used in almost all areas - from modeling the stresses of the car frame, to tracking the dynamics of cell movement in the body. As we live in a world where technology is growing rapidly and the number of electronic devices: smartphones, tablets, sensors, PCs is increasing every second - by 2020, about 5.19 billion people own personal smartphones, the tasks of modeling and visualization of ongoing processes are extremely important.
In modern realities, during the production of devices, the cost of error is quite high. A special role is played by thermophysical problems for modeling thermal and thermoelastic processes that occur during the heating of elements. Such tasks require high accuracy, because incorrect determination of parameters leads to overheating or general destruction of the board and computer units. Modeling tasks play a huge role in industrial development and affect all areas of human activity: health, ecology, space technology, the military industry, industry, media, museums, entertainment, and more. The objects of research can be, as elementary wooden products, frames of metal structures, and extremely complex electronic computing systems, biological processes, space systems and real-time complexes, such as nuclear power plants and more. Therefore, the improvement and creation of new modeling tools make it possible to significantly improve the modern world. Important tasks are the problems of thermoelasticity and thermal conductivity to analyze heating processes and the interaction between piecewise homogeneous inclusions. At present, the related problem of thermoelasticity of piecewise homogeneous bodies has no discrete analogues using boundary element method (BEM), so modeling of this problem is relevant.
There are many software products that allow you to solve a range of modeling problems. These include: Ansys, Tesis, Materialize. The main method of modeling of such systems is FEM. On the one hand, it is quite simple and can numerically solve a wide range of problems, but on the other hand - for high accuracy it requires a large number of finite elements. For example, for thermoelasticity problems, you can use a more accurate method - BEM.
To date, there is no single concept and holistic methodology for solving a set of interconnected problems of computational geometry, which form the core of the problems for visual modeling of thermophysical processes.
Existing approaches to building a modeling system, in the vast majority, use a batch algorithmic model, which is a set of algorithms for a particular application problem, or a library of algorithms. In this case, almost each of the algorithms has its own data structures, data input and output format, pre-processing methods. Also, existing approaches do not allow the development of unified efficient algorithmic platforms for visual modeling systems.
Thus, for the first time the concept of building a model of a single algorithmic environment for solving a class of problems of computational geometry was proposed by V.M. Tereshchenko. In particular, in dissertation of VM Tereshchenko's the bases of the concept and basic methodological principles of construction of MUAE - model of uniform algorithmic environment are developed. A mathematical model of the parallel-recursive algorithm was presented, which allows to solve the following problems simultaneously: construction of the Voronoi diagram, Delaunay triangulation, construction of a convex hull, search for the nearest pair, etc. An example of another development of the MUAE concept is its application to image processing problems and the construction of polygon generator with given properties.
In general, the dissertation consists of two main components - the construction of discrete solutions of the connected quasi-static thermoelasticity problem, as well as the creation of a model of a single algorithmic environment for modeling and visualization of thermophysical phenomena and processes.
