Для сигма-модели гидротермодинамики Черного и Азовского морей, разработанной в ИВМ РАН, реализован алгоритм решения задачи совместного усвоения мгновенных данных температуры поверхности моря со спутников и профилей температуры по глубине с недельным осреднением. Сравнение результатов расчетов численной модели с усвоением данных наблюдений и без усвоения доказывает эффективность процедур усвоения данных. Показано, что совместное усвоение данных по температуре поверхности моря и вертикальных профилей температуры воды не ухудшает точность расчетов приповерхностной температуры воды, но в то же время повышает точность расчетов ее вертикальной структуры. Purpose. This study addresses simulation for sea hydrothermodynamics by solving the problem of joint variational data assimilation of sea surface temperature and vertical temperature profiles. Data assimilation allows correcting the calculations for the numerical model using measurement of the environmental data. Methods and Results. Mathematical model of the hydrothermodynamics of the Black and Azov Seas, developed at the Marchuk Institute of Numerical Mathematics of the RAS with a sigma- coordinate system is considered. A problem that combines variational data assimilation of sea surface temperature data and three-dimensional temperature fields with weekly averaging is formulated. A cost functional is introduced, incorporating satellite-derived sea surface temperature observations and vertical temperature profiles. The necessary condition for the minimum of this functional is recast as an optimality system, comprising the direct problem, the adjoint problem, and a control condition. The results of solving the stated problem are presented for the water areas of the Black and Azov Seas. Conclusions. A comparison of numerical model results with and without assimilation was performed, demonstrating the efficiency of the assimilation procedures. It is shown that the combined variational assimilation of sea surface temperature data from the SNPP satellite and vertical profiles averaged over a week allows reproducing sea surface temperature with sufficient accuracy when comparing the simulation results with data from the Aqua and Terra satellites, which were not used in the assimilation process. Numerical experiments established that temperature profile assimilation can be performed once a week without loss of accuracy. Furthermore, the additional assimilation of profiles enables the generation of three-dimensional reanalysis fields for the studied region, which describe the thermohaline structure throughout the water column.
This study investigates a state-dependent Chandrasekhar integral equation and establishes the existence and uniqueness of a continuous solution via the Banach fixed- point theorem in an appropriate Lipschitz space. Building upon this analytical foundation, we propose a robust numerical scheme that integrates successive approximation techniques with suitable quadrature rules. A comprehensive convergence analysis is carried out, including an implicit power-series representation of the solution and explicit bounds on both iteration and quadrature errors. The effectiveness of the proposed method is illustrated through several representative examples, encompassing linear, nonlinear, and strongly nonlinear models. The numerical results demonstrate rapid convergence, strong stability, and high accuracy, underscoring the approach’s capability for the efficient computation of state-dependent integral equations arising inradiative transfer and related applications. В данной работе исследуется интегральное уравнение Чандрасекара с зависимостью от состояния, а также устанавливается существование и единственность его непрерывного решения с помощью теоремы Банаха о неподвижной точке в соответствующем пространстве Липшица. На основе этого аналитического подхода предлагается устойчивая численная схема, сочетающая методы последовательных приближений с подходящими квадратурными формулами. Проведен всесторонний анализ сходимости, включающий неявное представление решения в виде степенного ряда, а также получение явных оценок погрешностей как итераций, так и квадратур. Эффективность предложенного метода демонстрируется на ряде показательных примеров, охватывающих линейные, нелинейные и сильно нелинейные модели. Полученные численные результаты свидетельствуют о быстрой сходимости, высокой устойчивости и точности метода, что подтверждает его эффективность при решении интегральных уравнений, зависящих от состояния и возникающих в задачах переноса излучения и смежных областях.
Представлена конечно-разностная схема на адаптивных подвижных сетках для расчета взаимодействия длинных поверхностных волн с неподвижным частично погруженным в воду телом в рамках полностью нелинейной 3D-модели потенциальных течений. Приведены результаты теоретического исследования свойств схемы, в частности, доказано выполнение свойства самосопряженности разностного оператора для потенциала вектора скорости. Purpose. Accounting for three-dimensional effects leads to more accurate estimation of wave forces on marine structures. The purpose of the present work, which consists of two parts, is a numerical study of the influence of diffraction effects on the main characteristics of interaction between long surface waves such as tsunami waves and large partially immersed structures. Methods. In the first part of the work, a mathematical formulation is developed within the framework of a 3D potential flow model with a free boundary. The problem of long surface wave interaction with partially immersed or gravity-based structures is formulated in a curvilinear moving coordinate system. A new finite-difference scheme on movable grids is described in detail. The grids adapt to the lateral faces of the fixed structure, to the curvilinear surfaces of its bottom and the basin bed, and to the moving water surface. The difference equations for the velocity potential are derived using a three-dimensional analogue of the integro-interpolation method. Results. Original second-order approximation formulas for the Neumann condition on impermeable surfaces are derived. These formulas are based on the application of the conservative form of the elliptic equation with variable coefficients for the velocity potential and use its values only at boundary nodes and nodes of the first internal adjacent layer. It is proved that with such approximations, the difference operator for the potential is self-adjoint and inherits this property of the differential operator. Conclusions. The properties of the finite-difference scheme, established theoretically, ensure that its application will not lead to known numerical effects that distort the values of the computed quantities. The practical significance of the obtained theoretical results will be demonstrated in the second part of this work. Therein, by comparing the results with calculations based on the two- dimensional potential flow model, the importance of accounting for the diffraction of long waves impacting large partially immersed structures will be shown.
В статье представлен инструмент для автоматического анализа неточностей динамической информации для оптимизаций подстановки функций и программной предподкачки данных с аппаратной поддержкой в компиляторе LCC для архитектуры “Эльбрус”. Разработанное решение сочетает статический и динамический анализ, выявляя места, где отсутствие либо ошибочность динамической информации приводит к построению неоптимального машинного кода и замедлению работы компилируемой программы. Инструмент формирует отчеты с рекомендациями по расстановке подсказок программистом, что позволяет ускорить анализируемую программу. При тестировании инструмента на наборах тестов SPEC CPU 2006 и 2017 среднее геометрическое ускорение составило до 87.9 %. This paper presents a tool for automatic analysis of inaccuracies in function in-lining and software data pre-fetching with hardware support optimizations in the LCC compiler for the “Elbrus” VLIW architecture. The proposed approach combines static and dynamic methods to identify cases where compiler heuristics fail due to the lack of profiling information. The tool automatically incorporates program code to collect statistical information, analyzes optimization behavior, and generates detailed reports with recomendations for the software developer. These reports indicate where compiler hints should be manually added to improve performance. The tool consists of two main components: a compiler module that incorporates a program and a runtime library that gathers and analyzes statistical data. It provides guidance on when to apply or disable optimizations. This approach mitigates typical drawbacks of profile-guided optimization (PGO), such as the need to recompile program after codebase update and distortion of profiling data during later compilation stages. Experimental evaluation was performed on the SPEC CPU 2006 and 2017 benchmarks using the Elbrus v5 processor. The results demonstrate that applying the recommended hints leads to measurable performance improvements of up to 87.9 % based on the geometric mean (gmean) for inline optimization and up to 3.8 % gmean for software pre-fetch optimization. The proposed tool significantly simplifies the tuning of compiler optimizations and contributes to more efficient software development for the Elbrus platform.
Представлена информационно-вычислительная система (ИВС) для оценки потоков парниковых газов с поверхности Земли. Разработка основана на методологии структурного анализа. Система интегрирует спутниковые данные, глобальную транспортную химическую модель и алгоритмы усвоения данных. Описана архитектура ИВС, включая модули для обработки данных, вычислений и визуализации. Приведены результаты тестовых расчетов по оценке потоков метана с поверхности Земли. Objective. This research aims to develop a model for an information and computing system (ICS) for assessing greenhouse gas fluxes from the Earth’s surface based on satellite data and global transport and diffusion models. The study addresses the critical need for accurate environmental monitoring tools capable of integrating observational data with mathematical modelling for compre- hensive greenhouse gas emission assessment. Methodology. The development of the functional model was performed using structural analysis methods, including IDEF0 methodology and data flow diagrams (DFD). The study employed process decomposition techniques to determine information links between system components. ER diagrams were implemented to formalize data structure, while the microservices principle was used for integration of computational modules, storage systems, data visualization tools, and user interfaces. Results. The developed ICS architecture includes three hierarchical levels: user interaction module (interface), main ICS module (server, API), and computational module. The system integra- tes three key subsystems: data collection and preprocessing, data assimilation (computational subsystem), and results analysis and reporting. An ICS prototype was successfully deployed using the MOZART-4 chemical transport model and AIRS satellite data, with numerical experiments conducted to assess methane emissions for 2016 in a selected territory. Originality/Value. The proposed system provides a comprehensive approach to assessment of greenhouse gas flux using modern data assimilation methods with geoinformation analysis capabiliti- es. The modular architecture ensures flexibility in parameter configuration and scalability for processing large data volumes. The ICS can be used by researchers and environmental monitoring specialists to conduct research, providing practical value for the scientific community.
