Магистратура
2018/2019
Многомасштабное компьютерное моделирование
Лучший по критерию «Полезность курса для расширения кругозора и разностороннего развития»
Статус:
Курс обязательный (Математические методы моделирования и компьютерные технологии)
Направление:
01.04.02. Прикладная математика и информатика
Кто читает:
Департамент прикладной математики
Когда читается:
2-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Прогр. обучения:
Математические методы моделирования и компьютерные технологии
Язык:
английский
Кредиты:
3
Контактные часы:
50
Course Syllabus
Abstract
The course «Computer multiscale modelling and simulation» is aimed at the teaching students with a wide spectrum of methods, technologies and problems in the field of multiscale modelling and simulation and material properties. Different levels of theoretical description at various space and time scales are considered as well as the connections between them and computational technologies oriented on the hardware of the pre-exaflops era supercomputers.
Learning Objectives
- The objectives of this course are at the suding of a wide spectrum of methods, technologies and problems in the field of multiscale modelling and simulation and material properties
Expected Learning Outcomes
- know: the principles of the theoretical and computational description of matter at various scales. the basic algorithms for application of software for numerical solution of problems at each scale. the principles of bridging the gaps between the scale for solving particular problems and to have the corresponding experience
- be capable of: Estimation the computational complexity of the multiscale problems and the amount of computational resources for their solution; Analyzing scient ific problems and physical processes, realizing in practice fundamental knowledge obtained in the course of training; Adaptation new problematics, knowledge, scientific terminology and methodology, to possess the skills of independent learning;
- be capable of: Application in the given subject area statistical methods of processing experimental data, numerical methods, methods of mathematical and computational modeling of complex systems; Understanding meaning of the tasks appearing in the course of professional activity and employment the related physico-mathematical apparatus for description and solving the above tasks; Using the knowledge of physical and mathematical subjects for further learning according to the training profile;
- get experience in: Formulation of computational tasks in studies of complex systems; Preparing and running computer simulations of various systems; Correct processing of modeling results and their comparison with available experimental and literature data; Theoretical analysis of real problems related to atomic-scale studies
Course Contents
- Multiscale levels of theoretical description of matterQuantum manybody problem and ab initio modelling and simulation. The notion of quantum chromodynamics and qantum electrodynamics. Introduction into the methods of quantum theory of solids and quantum chemistry. Hartry-Fock method and multiconfiguration approaches. Density functional theory. Classical many body problem. Molecular dynamics method and other particle methods. Horizon of predictability and stochastic properties. Empirical models of interatomic interaction. Pair potentials. Many body potentials.Central symmetric and non-central symmetric models. Force fields of molecular systems. Methods for development of coarse-grained models for complex molecular systems
- Principles of bridging the gaps between the scalesSeparation of fast and slow dynamics. Integrators that distinguish slow processes. Car-Parinello method. Combining first-principles calculation of forces with classical atomic dynamics. Division of a model into quantum and classical parts (QM/MM methods). Combining atomistic and continuum description in a single model. Calculation rare events barriers. Kinetic Monte Carlo methods
- Computational aspects of multiscale modelling and simulationSupercomputers of pre-exaflops era. SIMD and MIMD parallelisation strategies for computations. Interconnect topology. Moore’s law. Parallel scaling of algorithms. Ahmdal’s law. Parallel efficiency in strong and weak sense. Typical features of data transfers in classical and quantum molecular dynamics algorithms. Data processing at supercomputer calculations of multiscale models. Parallel input/output. On-the-fly data analysis
- Examples of the development and deployment of multiscale models in different fieldsRadiation damage of solids. Fractureand movement of cracks. Molecular machines. Properties of polymer composites. Active motion on complex systems and selforganisation
Bibliography
Recommended Core Bibliography
- Frenkel D., Smit B. Understanding Molecular Simulation: From Algorithms to Applications. –Elsevier, 2002.
- Rapaport, D. C. The art of molecular dynamics simulation. –Cambridge university press, 2004.
Recommended Additional Bibliography
- Precision Physics of Simple Atomic Systems, S.G. KarshenboimV.B. Smirnov (Eds.), Springer, 2003.
- Schweitzer F., Browning Agents and Active Particles Collective Dynamics in the Natural and Social Sciences, Springer, 2003