Laboratory "Mathematical Modeling"

Head of the laboratory: Nail A. Gumerov Staff


Сотрудники лаборатории компьютерного моделирования
Prof. Iskander Akhatov (on the left), Prof. Nail Gumerov (in the center) and staff of the laboratory "Advanced Computer Modeling of Micro- and Nanoscale Processes"

Development and application of highly efficient methods for simulation of dispersed flows in micro- and nanoscales is very important for theory and experiments. One reason for that is that experiments on such scales are usually difficult and costly. For example, the wavelength of visible light is about 500 nanometers, which creates difficulties for application of conventional visualization techniques for particles of sizes below 1 micron. In addition, the disperse systems are multiparametric, that is why computational methods are especially important for planning of experiments, development and validation of mathematical models, and optimizations.

Low complexity algorithms for solution of basic equations of mathematical physics in three dimensions on unstructured sets are in the focus of the laboratory. These algorithms form a basis for application of direct methods for simulation of dispersed flows and affect computational complexity of the entire numerical approach. The laboratory is a pioneer in Russia in development and application of the fast multipole method (FMM). It achieved significant results in simulations of 3D Stokes flows, 3D bubble dynamics, and 3D molecular dynamics simulations using this method. Contemporary high-end computing architectures (heterogeneous systems based on multi-core CPUs and GPUs) are also in the focus of the laboratory. Particularly, substantial activities are related to implementation of scalable algorithms on such hardware. It can be noticed that only a few advanced research groups in the world currently develop this approach for computational mechanics. The laboratory pays a substantial attention to training of its staff. This includes lab seminars and special courses, such as the FMM course and high performance computing course taught in American universities. In 2013 three employees had several months training in the Institute for Advanced Computer Studies of University of Maryland. Also, in 2012-2014 the results obtained in the laboratory were presented on several Russian and International conferences and meetings held in the United States, United Kingdom, Singapore, Canada, and Germany.

The topics listed below reflect current activities of the laboratory: