The study of nonlinear problems related to the process of heat transfer in the substance is very important for practice. One of the problems that arise when studying the characteristics of new materials is the problem of simultaneous identification of temperature-dependent thermal conductivity and volumetric heat capacity of substance based on the results of experimental observations of the dynamics of the temperature field in an object. Previously, this problem was considered only in the one-dimensional case. It is desirable that these studies be carried out for a three-dimensional case, since experimental data are collected from three-dimensional objects. In this work, the above-mentioned problem is considered in the three-dimensional case. The consideration is based on the first boundary value problem for a three-dimensional unsteady heat equation. The inverse coefficients problem is reduced to a variational problem. The standard deviation of the calculated temperature field in the sample from its experimental value was chosen as the cost functional. Formulas for calculating the gradient of the cost functional are obtained. The results of the solution of the formulated problem are presented and discussed.

The study of nonlinear problems associated with the process of heat transfer in material is very important for practice. Previously, the authors proposed an effective algorithm for determining the volumetric heat capacity and thermal conductivity of a substance based on the results of experimental observations of the dynamics of the temperature field in an object or the dynamics of heat flows at the boundary of the domain. In this work, a new cost functional is used to determine temperature-dependent thermodynamic parameters, which is a weighted sum of the deviation of temperature in the domain and heat fluxes at the boundary of the domain from the experimental values. The use of the new functional showed a noticeable increase in the efficiency of the proposed algorithm and the reliability of the results obtained. The consideration is carried out on the basis of the first boundary value problem for a one-dimensional non-stationary heat equation. The inverse coefficient problem under consideration is reduced to a variational problem, which is solved by gradient methods based on the application of the Fast Automatic Differentiation technique. The question of the uniqueness of the solution to the inverse problem is investigated.

The study of nonlinear problems related to heat transfer in a substance is of great practical important. Earlier, this paper’s authors proposed an effective algorithm for determining the volumetric heat capacity and thermal conductivity of a substance based on experimental observations of the dynamics of the temperature field in the object. In this paper, the problem of simultaneous identification of temperature-dependent volumetric heat capacity and thermal conductivity of the substance under study from the heat flux at the boundary of the domain is investigated. The consideration is based on the first (Dirichlet) boundary value problem for a one-dimensional unsteady heat equation. The coefficient inverse problem under consideration is reduced to a variational problem, which is solved by gradient methods based on the application of fast automatic differentiation. The uniqueness of the solution of the inverse problem is investigated.

The study of nonlinear problems associated with heat transfer in the substance is very important for practice. Previously, we proposed an efficient algorithm for identifying the thermal conductivity of a substance based on the results of experimental observation of the dynamics of the temperature field in an object. In this paper, we investigate the possibility of extending the application of the proposed algorithm to obtain a numerical solution to the problem of simultaneous identification of the temperature-dependent the thermal conductivity and the volumetric heat capacity of the substance under study. The consideration is carried out on the basis of the first initial-boundary value problem for the one-dimensional non-stationary heat equation. The considered inverse coefficient problem is reduced to a variational problem, which is solved by gradient methods based on the application of the Fast Automatic Differentiation technique.

Different approaches to the calculation of the gradient of a composite function of several variables are compared, namely, exact analytically derived formulas, formulas based on the fast automatic differentiation (FAD) technique, and standard software packages implementing the ideas of the FAD technique. The approaches are compared as applied to a composite function representing the energy of a system of atoms with the Tersoff interatomic potential. The comparison criterion is the computer time required for computing the gradient of the function. The results show that the FAD technique is superior to the analytical formulas. The standard packages take nearly the same time to compute the function gradient as the FAD technique formulas.

Four parallel algorithms are considered that implement the branch-and-bound method (BnB) for solving problems of finding a global minimum. The algorithms are designed for computing systems with shared memory. The BnB is based on two basic operations: branching and eliminating. To implement the elimination operation, interval arithmetic is used, which for real intervals defines operations similar to ordinary arithmetic. The main difference between the algorithms lies in the different implementation of storing the list of subproblems. In the process of testing on a representative set of test problems, the speed of the algorithms, their scalability, and their resistance to search anomalies are investigated.

The study of nonlinear problems associated with heat transfer in substance is important for practice. Earlier, the authors proposed an efficient algorithm for determining the thermal conductivity from experimental observations of the dynamics of the temperature field in an object. In this work, we explore the possibility of extending the algorithm to the numerical solution of the problem of simultaneous identification of the temperature-dependent volume heat capacity and the thermal conductivity of the substance under study. The consideration is based on the Dirichlet boundary value problem for the one-dimensional nonstationary heat equation. The coefficient inverse problem in question is reduced to a variational problem, which is solved by applying gradient methods based on the fast automatic differentiation technique. The uniqueness of the solution to the inverse problem is analyzed.

The work is devoted to the development and study of a method for solving global optimization problems with interval constraints. The paper proposes a global optimization algorithm based on a deterministic method of selecting starting points for local search methods. The starting points are the extremum points of functions of one variable, obtained by restricting the objective function to straight, collinear coordinate vectors. The effectiveness of the proposed algorithm is demonstrated by the example of the problem of minimizing the energy of a fragment of a flat crystal lattice. The energy of interatomic interaction is calculated using the Tersoff potential. An experimental comparison is made of the developed algorithm with the classical version of the multi-start method, in which pseudo-random points uniformly distributed in the parallelepiped are used to select starting points. As a local search method, in both cases, one of the modifications of the coordinate wise descent method is used. The developed method can be applied to problems with an unknown analytical expression for an objective function that is often encountered in practice.

В работе предлагается и экспериментально проверяется один из подходов к гибридизации и подбору параметров методов минимизации используемых в методе мульти-старта. Подход заключается в комбинации методов одномерного поиска в зависимости от значений минимизируемой функции получаемых в процессе расчетов. Метод мульти-старта заключается в многократном запуске методов поиска локального минимума из различных стартовых точек. Поэтому можно предположить, что возникающие на каждой итерации метода задачи локальной минимизации, имеют сходные характеристики. За счет использования этой особенности метода мульти-старта удалось обеспечить подбор параметров в процессе работы. Проведены численные эксперименты по определению зависимости быстродействия методов локального спуска в зависимости от параметров и предложен алгоритм выбора оптимального значения параметров. Экпериментально показано, что интервал оптимальности параметров имеет достаточно широкие границы. Численные эксперименты проводились на задаче поиска глобального минимума энергии совокупности атомов фрагмента плоской кристаллической решетки. Для расчетов энергии межатомного взаимодействия применялся потенциал Терсоффа.

The paper describes a simulator of parallel Branch and Bound (BnB) method. Several subdomain trees for benchmark functions are analyzed, a characteristic Gaussian-like distribution is discovered. An algorithm of artificial tree generation is formulated according to this criterion. The process of simulator modeling is described, several computational experiments are conducted. Their results show a hyperbolic decrease trend for modeled time as the number of computational units grows, which is concluded to be similar to real systems.

Any real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first's layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.

The paper considers the implementation of a direct kinematics problem solver using one of the options for the numerical implementation of Kolmogorov's superposition, proposed by Sprecher and modified by Coppen. The idea of the solver is to create a dataset by solving the inverse kinematics problem, training a specific neural network on a high-performance computing cluster, and embedding the trained neural network into a low-power microprocessor that controls the manipulator. Implementation on a heterogeneous system made it possible to reduce the process of collecting a dataset with 2.108 records of to several minutes.

Kolmogorov and Arnold proved that any real continuous bounded function of many variables can be represented as a superposition of functions of one variable and addition. In subsequent works by Neht-Nielsen, it was shown that such a specific type of superposition can be interpreted as a two-layer forward neural network. Such a superposition can also be used as a universal approximation of the function of many variables. In the work, one of the variants of numerical implementation of Kolmogorov's superposition, proposed by Sprecher and modified by Koppen, was investigated. In addition, the functions of the first layer were considered as a generator of space-filling curves (Peano curves). Numerical experiments were conducted to study the accuracy of the approximation of the function of many variables for the numerical implementation of Kolmogorov's superposition, proposed by Sprecher and modified by Koppen, for a simplified version of this superposition and for an approach using filling curves. A comparative analysis showed that the best results are obtained using space-filling curves.

This paper proposes a parallel implementation of the method of non-uniform coverings, designed for computing systems with shared memory. The method of non-uniform coverings is one of the most well-known deterministic methods for solving global optimization problems, based on the scheme of branches and boundaries. Due to the high computational complexity of the method and the wide availability of high-performance multi-core systems with shared memory, the development of parallel implementations of this method is of particular relevance. There are various approaches to parallelizing the method of non-uniform coverings. First, there are several standards for creating multi-threaded applications such as OpenMP, MPI, C ++ 17 functionality. Secondly, there are different approaches to the organization of storage and access to lists of subtasks and synchronization between threads. Thirdly, the branching procedures and evaluation estimates differ. Earlier, a comparison was made of the indicated approaches to the parallelization of the method of non-uniform coverings. One of the most effective methods is the frontal method of non-uniform coverings, it uses a branching strategy wide, OpenMP technology is used for parallelization, and the data storage structure consists of two arrays of pools / subtasks. This approach has the following advantages - ease of implementation, sufficient speed and stability. As disadvantages of the method, you can specify the high requirements for RAM. To eliminate this drawback, this article proposes a parallel implementation of the K-frontal method of non-uniform coverings. The method was tested using a library of test functions on a hybrid high-performance computing cluster of FRC CS RAS.

In this paper, we consider the problem of finding the energy minimum of the aggregate of atoms of a fragment of a planar crystal lattice. To calculate the energy, the Brennor or REBO (reactive empirical bond order) method is used. The REBO potential is calculated using the LAMMPS package (Large-scale Atomic / Molecular Massively Parallel Simulator). As optimization methods, both the gradientless methods and the methods using the first derivatives of the functional are used. To calculate the derivatives, the combined differentiation method, implemented in the LAMMPS package, is used, using sequentially forward and reverse methods of fast automatic differentiation.

Рабочей областью робота называется множество положений, которые может принимать его рабочий инструмент. Знание рабочей области необходимо при проектировании роботов, их размещении, оценке их функциональных возможностей, прокладке траектории движения робота. К настоящему времени разработано много методов для определения рабочей области. Следует заметить, что наибольшим потенциалом обладают детерминированные методы, позволяющие в автоматическом режиме получать аппроксимации с заданной точностью. Известным недостатком детерминированных методов является их высокая вычислительная сложность, которая препятствует эффективному широкому применению этих методов на практике. В работе предлагается параллельный алгоритм построения аппроксимации рабочей области с гарантированной точностью. Для создания многопоточного приложения применен пакет OpenMP. Разработана оригинальная техника, позволяющая равномерно распределять нагрузку по потокам без явной балансировки. Приводятся результаты экспериментов, показывающие высокую эффективность распараллеливания для многоядерных систем. Не менее важной задачей является визуализация построенных аппроксимаций. Рабочая область зачастую имеет сложную структуру с внутренними полостями. В данной работе предлагаются подходы для эффективной визуализации рабочей области робота, основанные на технологии дополненной реальности, позволяющие не только изучать строение объекта, но и помещать его в требуемый контекст.

The experience of using Cuda Unified Memory technology to develop Multi-GPU applications is described. The paper deals with the method of transferring computations on the MGDS-GPU model two-dimensional problem described by the equations of single-layer shallow water with variable density over an uneven bottom. To solve the problem was applied balance - characteristic scheme “CABARET”. The minimum steps necessary to go from computing on the GPU to computing on the MULTI-GPU are given. The computational efficiency is investigated depending on the size of the grid.

In this paper, we compare the three approaches for calculating the gradient of a complex function of many variables. The compared approaches are: the use of precise, analytically derived formulas; the usage of formulas derived with the aid of the Fast Automatic Differentiation methodology; the use of standard software packages that implement the ideas of Fast Automatic Differentiation methodology. Comparison of approaches is carried out with the help of a complex function that represents the energy of atoms system whose interaction potential is the Tersoff potential. As a comparison criterion, the computer time required to calculate the gradient of the function is used. The results show the superiority of the Fast Automatic Differentiation methodology in comparison with the approach using analytical formulas. Standard packages compute the function gradient around the same time as using the formula of the Fast Automatic Differentiation methodology.

В данной работе проводится сравнительный анализ четырех типов процессоров на примере задачи восстановления начальных данных для уравнения переноса. Задача решается методом Левенберга-Марквардта, который декомпозирован на четыре подзадачи – вычисление вектор-функции, вычисление матрицы первых производных вектор-функции (матрицы Якоби), матричное умножение и решение системы линейных уравнений. Вычисление матрицы Якоби производится с помощью методологии быстрого автоматического дифференцирования, при этом применяется пакет прикладного программного обеспечения Adept версии 1.1. Для ускорения расчетов использовано директивное многопоточное программирование c динамическим распределением вычислений между потоками и технология SIMD (Single Instruction Multiple Data) – принцип компьютерных вычислений, позволяющий обеспечить параллелизм на уровне данных. Вышеупомянутые технологии позволили в полной мере задействовать особенности архитектуры современных процессоров Intel, такие как многоядерность/многопоточность, расширение системы команд микропроцессоров Intel/AMD – Advanced Vector Extensions (AVX/AVX2), обрабатывающее данные в формате с плавающей запятой в группах длиной 256 бит, и FMA (Fused Multiply-Add) – технологию, предназначенную для выполнения совмещенной операции умножения-сложения. В сравнении участвуют процессоры Intel Core i7 4770 (Haswell), Intel Xeon E5-2683V4 (Broadwell), Intel Xeon Phi coprocessor SE10/7120 и IBM Power 8. Даны рекомендации по выбору типа процессора в зависимости от решаемой задачи.

В данной работе рассматриваются три эффективные параллельные реализации метода неравномерных покрытий, предназначенные для вычислительных систем с общей памятью. Метод неравномерных покрытий является одним из наиболее известных детерминированных методов решения задач глобальной оптимизации, основанных на схеме ветвей и границ. Учитывая вычислительную сложность метода и широкое распространение высокопроизводительных многоядерных систем с общей памятью, особую актуальность приобретает разработка параллельных реализаций данного метода. В статье предлагается несколько подходов к распараллеливанию метода неравномерных покрытий. В настоящее время существует несколько стандартов создания многопоточных приложений. В работе рассматривается два таких стандарта: OpenMP 4.0 и C++ 17. Для синхронизации между потоками используется несколько режимов. В работе приводится описание алгоритмов и их программных реализаций. Экспериментальное исследование проводилось на тестовой задаче, приближенной к реальной – поиск минимума энергии молекулярного кластера. В качестве вычислительных платформ для проведения экспериментов использовались современные высокопроизводительные системы. Исследование показало, что для данного типа задач, производительность методов (по количеству итераций) находится примерно на одном уровне. Кроме этого было показано экспериментально, что усложнение алгоритма не всегда приводит к увеличению его эффективности.