Методи та засоби розподілення обчислень в задачах теплового проектування електронних пристроїв

Abstract

The thesis is devoted to problems of distributed computing — an effective way to solve a particular class of resource-intensive problems through the use of network infrastructure and many computers' computing resources. The thesis copes with a major problem of raising solving efficiency for such electronic devices' thermal design problems that can be reduced to solving high dimensional systems of linear algebraic equations with block-banded matrices. The mathematical support and software developed allows to optimize utilization of existing computing infrastructure. In the first section, an analysis of historical evolution and current state of distributed computing was performed, differences between parallel computing and distributed computing were considered, a scope of distributed computing was outlined and modern tools for distributed computing were organized. In addition, the section shows the need for solving high dimensional systems of linear algebraic equations during electronic devices' thermal design, presents an overview of existing tools for high-performance solving systems of linear algebraic equations and notes their main disadvantages. According to the proposed classification, architectures of distributed computing systems can be segregated by their structures into such groups: one-tier systems (also known as «client−server» systems), two-tier systems (for instance, systems based on grid technology) and N-tier systems (particularly hierarchically structured systems). The second section deals with a problem of designing methods for distributed solving high dimensional systems of linear algebraic equations with block-banded matrices. The method for evaluating the effectiveness and time losses of distributed computing systems was developed. Also, three different algorithms for sectioning high dimensional banded matrices were developed and named according to the principle of operation: One-Directional Sectioning Algorithm (OD), Bidirectional Sectioning Algorithm (BD) and Adjustable Sectioning Algorithm (AD). For iterative improvement of high dimensional banded matrices sectioning results, received using one of the algorithms mentioned above, the Iterative Algorithm (IT) was developed. Use of the Iterative Algorithm cannot worsen existing results. In the third section, an architecture of distributed system for electronic devices' thermal design was developed. The architecture contains subsystem for distributed computing with N-tier hierarchical structure and features of adaptability. The choice and substantiation of software technologies and programming languages were performed. The data model based on XML was described. Guidelines for creating such a system were formulated. The problem of implementing an adaptive approach to distributed solving systems of linear algebraic equations was resolved. Based on the created algorithms, software of subsystem for distributed computing was developed. The fourth section is focused upon application of the developed subsystem for distributed computing by solving miscellaneous mathematical models. An analysis of steady-state temperature field in multilayer circuit board with eleven heat sources was performed. The developed subsystem for distributed computing can be used to solve other problems of mathematical physics, which require solving high dimensional systems of linear algebraic equations with block-banded matrices. To demonstrate versatility of the software developed, a simulation of stressedly-deformed state of the lower jaw with fixed partial denture was performed. Диссертация посвящена вопросам распределения вычислений — способу эффективного решения определённого класса ресурсоёмких задач благодаря использованию сетевой инфраструктуры и вычислительных ресурсов множества компьютеров. В диссертационной работе решена важная задача повышения эффективности решения проблем теплового проектирования электронных устройств, которые сводятся к решению систем линейных алгебраических уравнений большой размерности с матрицами блоково-ленточной структуры. Разработанное математическое и программное обеспечение даёт возможность оптимизировать использование имеющейся вычислительной инфраструктуры. Дисертація присвячена питанням розподілення обчислень — способу ефективного вирішення певного класу ресурсомістких задач завдяки використанню мережевої інфраструктури та обчислювальних ресурсів багатьох комп’ютерів. У дисертаційній роботі розв’язано важливу задачу підвищення ефективності вирішення проблем теплового проектування електронних пристроїв, які зводяться до розв’язування систем лінійних алгебраїчних рівнянь великої розмірності з матрицями блоково-стрічкової структури. Розроблене математичне та програмне забезпечення дає можливість оптимізувати використання наявної обчислювальної інфраструктури.