A cascadic multigrid algorithm in the finite element method for the plane elasticity problem

For the plane elasticity problem a standard scheme of the finite element method with the use of piecewise linear elements on triangles is discussed. For its solution on a sequence of embedded triangulations, a cascadic arrangement of two iterative algorithms is used, which gives the simplest version of multigrid methods without preconditioning and restriction onto a coarser grid. The cascadic algorithm begins on the coarsest grid where the grid problem is solved by direct method. To obtain approximate solutions on finer grids, the iterative method is used; interpolation of the approximate solution from the preceding coarser grid is taken as the initial guess. It is proved that the convergence rate of this algorithm does not depend on the number of unknowns and grids

World War I and Identity Crisis of Russian Germans

The authors consider the position of Russian Germans in the empire, who during World War I became victims of the foreign policy circumstance. There is analyzed the process of the transformation of the state-ethnic identity of the Germans through the identification of factors that had a psychological impact on them and contributed to the formation of a “negative” identity in their environment. The sources for the study are the letters of military doctor F.O. Krause and Russian Germans who served on the Caucasian front, as well as German colonists from various provinces of the Russian Empire; decrees and orders of the military and civil administration, periodical materials; office correspon- dence between ministries and other materials stored in the central and regional archives of the Russian Federation. The study shows that the rise in nationalist sentiments in Russian society and the implementation of anti-German policy in the country exerted significant psychological pressure on Russian Germans. Due to this, during World War I they found themselves in a “new reality.” The authors come to the conclusions that influenced by numerous factors, Russian Germans had to choose various ways to preserve their identity: changing the name, emigrating, completely immersing themselves in their professional activities

“Mean Field Games” as Mathematical Models for Control and Optimization of Business Activity

The article is a review of modern mathematical economic models with the “Mean Field Games” structure. They are currently used for the predictive modelling under given control conditions or for optimizing control actions to achieve the desired result. The mathematical model is a pair of parabolic partial differential equations with a set of initial and boundary conditions for optimizing a given target functional. For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. This mathematical apparatus is used for the quantitative modelling of the distribution or the use of alternative resources, environmental problems, optimization of wages and insurance, network sales, and other economic activities to predict the aggregate behavior of the great mass of agents looking for instant personal benefit

A Cascadic Algorithm for the Solution of Nonlinear Sign-indefinite Problems

. In this paper we propose a cascadic algorithm for a weakly nonlinear sign-indefinite elliptic Dirichlet problem. The standard finite element discretization with piecewise linear finite elements leads to a system of nonlinear equations. We solve these nonlinear equations by a cascadic organization of Newton's method with "frozen derivatives" on a sequence of nested grids. This gives a simple version of a multigrid method without projections on coarser grids. The cascadic algorithm starts on a comparatively coarse grid where the number of unknowns is small enough to obtain an approximate solution within sufficiently high precision without substantial computational effort. On each finer grid we perform exactly one Newton step taking the approximate solution from the coarsest grid as initial guess. The arising linear systems are solved iteratively by Jacobi-type iterations with special parameters. As initial guess for the iterations we use the approximate solution from the previous grid...

«Игры среднего поля» как математические модели управления и оптимизации экономической активности

The article is a review of modern mathematical economic models with the “Mean Field Games” structure. They are currently used for the predictive modelling under given control conditions or for optimizing control actions to achieve the desired result. The mathematical model is a pair of parabolic partial differential equations with a set of initial and boundary conditions for optimizing a given target functional. For them, the discretization is applied to obtain systems of nonlinear algebraic equations which are solved by computer in an iterative way to get the best instant benefit for each agent. This mathematical apparatus is used for the quantitative modelling of the distribution or the use of alternative resources, environmental problems, optimization of wages and insurance, network sales, and other economic activities to predict the aggregate behavior of the great mass of agents looking for instant personal benefitСтатья посвящена обзору современных математических экономических моделей в терминах теории “Mean Field Game”. В настоящее время такие модели используются для прогностического моделирования при заданных условиях управления или для поиска оптимального управления динамической системой для достижения желаемого результата. Математическая модель представляет собой пару параболических уравнений в частных производных с начальными и граничными условиями для оптимизации заданного целевого функционала. Для них применяется дискретизация с целью формирования системы нелинейных алгебраических уравнений, которые решаются на компьютере итерационным образом для получения наибольшего текущего выигрыша каждым агентом. Данный математический аппарат используется для количественного моделирования распределения или формирования альтернативных ресурсов, решения экологических проблем, оптимизации заработной платы и страхования, сетевых продаж и других видов экономической деятельности для предсказания агрегатного поведения огромной массы агентов, ищущих собственную выгод

The finite element method for modeling spherically symmetric pulsations of the earth

Рассматриваются вопросы математического и численного моделирования геодинамических про- цессов расширения, сжатия, разогревания и охлаждения Земли.Some problems of mathematical and numerical modeling of geodynamic processes of expansion, compression, heating and cooling of the Earth are considered

The finite element method for modeling spherically symmetric pulsations of the earth

Рассматриваются вопросы математического и численного моделирования геодинамических про- цессов расширения, сжатия, разогревания и охлаждения Земли.Some problems of mathematical and numerical modeling of geodynamic processes of expansion, compression, heating and cooling of the Earth are considered

A slow mode transition region adjoining the front boundary of a magnetic cloud as a relic of a convected solar wind feature: Observations and MHD simulation

We identify a planar, pressure-balanced structure bounded by sharp changes in the dynamic pressure plastered against the front boundary of the magnetic cloud which passed Earth on 20 November 2003. The front boundary of the magnetic cloud (MC) is particularly well-defined in this case, being located where the He++/H+ number density ratio jumps from 4 to 10% for the first time and the proton plasma beta decreases sharply from ∼1 to ∼0.001. The feature, estimated to have a length scale ∼50 RE in the Sun-Earth direction, bears close resemblance to a slow mode transition region in that the magnetic pressure decreases, the plasma pressure increases, and their temporal variations are anticorrelated. Using a 2-D MHD simulation, we hypothesize that a pressure-balanced structure was encountered by the MC en route to Earth. Our calculations reproduce qualitatively the major features of the observations. Using a simplified geometry suggested by the observations, we find that the lateral deflection speed of the plasma is less than the lateral expansion speed of the MC. We infer that the structure traversed the MC sheath in ∼20 h, consistent with its crossing of the MC\u27s shock at 0.6–0.7 AU. The finding is consistent with the recent paradigm according to which solar wind plasma and magnetic field tend to pile up in front of interplanetary ejecta because the expansion of the ejecta hinders the shocked solar wind plasma from deflecting effectively around the object. Also, the inferred “age” of the layer contiguous to the surface of the MC, the earliest relic of its passage through the inner heliosphere, is in agreement with general estimates

Функция распределения плотности вероятностей суммы квадратов случайных величин при ненулевых математических ожиданиях

The article concluded probability distribution functions sum of the squares of the random variables in the non-zero expectations. The resulting distribution function is possible to create an efficient single-step phase ambiguity resolution algorithm in determining the spatial orientation of the signals of satellite radio navigation systems. Obtained thresholds at rejecting false solutions, as well as statistical data of the algorithmВ статье произведен вывод функции распределения плотности вероятностей суммы квадратов случайных величин при ненулевых математических ожиданиях. Полученная функция распреде- ления позволила создать эффективный одномоментный алгоритм разрешения фазовой неодно- значности при измерении пространственной ориентации по сигналам спутниковых радионави- гационных систем. Получены пороговые значения при отбраковке ложных решений, а также статистические характеристики полученного алгоритм

The Possibility of Creation of Rotary-Type Source of Seismic Transverse Waves with Electromagnetic Excitation

Use of transverse waves in exploration seismology provides some additional information needed to improve prediction of hydrocarbon deposits. Traditional sources of transverse waves have a number of disadvantages associated with bad reproducibility of influence, and the predominant excitation of longitudinal waves. In this work a variant of a rotary-type source of transverse waves with electromagnetic excitation which free from these disadvantages has been considered. Assessment of the required design parameters of this source and comparison the characteristics of the developed source in comparison with other similar devices are presented.Использование поперечных волн в сейсморазведке дает ряд дополнительных сведений, необходимых для повышения качества прогнозирования месторождений углеводородов. Традиционно используемые источники поперечных волн обладают рядом недостатков, связанных как с плохой воспроизводимостью воздействия, так и с преимущественным возбуждением продольных волн. В статье рассмотрен вариант роторного источника поперечных волн с электромагнитным возбуждением, свободного от указанных недостатков. Приведены оценки необходимых конструктивных параметров этого источника и сопоставление характеристик разрабатываемого источника по сравнению с другими видами аналогичных устройств