The multifrontal method is a well-established approach to parallel sparse direct solvers of linear algebraic equations systems with sparse symmetric positive-definite matrices. This paper discusses the approaches and challenges of scalable parallel implementation of the numerical phase of the multifrontal method for shared memory systems based on high-end server CPUs with dozens of cores. The commonly used parallelization schemes are often guided by an elimination tree, containing information about dependencies between logical tasks in a computational loop of the method. We consider a dynamic two-level scheme for the organization of parallel computations. This scheme employs the task-based model with dynamic switching between solving relatively small tasks in parallel and using parallel functions of BLAS for relatively large tasks. There are several problems with the implementation of this scheme, including time-consuming synchronizations and the need for smart memory management. We found a way to improve performance and scaling efficiency using the model of parallelism and memory management tools from the Threading Building Blocks library. Experiments on large symmetric matrices from the SuiteSparse Matrix Collection show that our implementation is competitive with the commercial direct sparse solver Intel MKL PARDISO.

The rise of supercomputing technologies during the last decade has enabled significant progress towards the invention of a personal biologically relevant computer model of a human heart. In this paper we present a new code for numerical simulation of cardiac electrophysiology on supercomputers. Having constructed a personal segmented tetrahedral grid of the human heart based on a tomogram, we solve the bidomain equations of cardiac electrophysiology using the finite element method thus achieving the goal of modeling of the action potential propagation in heart. Flexible object-oriented architecture of the software allows us to expand its capabilities by using relevant cell models, preconditioners and numerical methods for solving SLAEs. The results of numerical modeling of heart under normal conditions as well as a number of simulated pathologies are in a good agreement with theoretical expectations. The software achieves at least 75% scaling efficiency on the 120 ranks on the Lobachevsky supercomputer.

In this paper we present PMORSy—a new parallel software package for symmetric sparse matrix ordering on shared memory systems. The NP-complete fill-in minimization problem is solved by means of multilevel nested dissection algorithm with modifications for vertex separators. Parallel processing is done in a task-based fashion with the granularity tuning. We employ threading techniques on shared memory using OpenMP 3.0 technology as opposed to the Message Passing Interface-based approach widely used for parallel sparse matrix ordering. Experimental results on symmetric matrices from the University of Florida Sparse Matrix Collection and matrices from finite-element analysis of three-dimensional strength problems show that our implementation is competitive to the ParMETIS and PT-Scotch libraries both in ordering quality and performance. The PMORSy library is publicly available from the Lobachevsky State University Supercomputing Center web-site.

The article considers the role of the state in the Eurasian doctrine, one of the most distinctive and significant movements of the Russian sociological and political-philosophical thought abroad in the 1920-1930’s. The issues addressed by the Eurasians are still relevant under the current epoch of the new Russian statehood construction and to a certain extent are implemented in the contemporary political practice. According to the classical Eurasian doctrine, all nations of “Russia-Eurasia” are united by the “place of development” and constitute a single historical and socio-cultural world, which organically combines elements of the East and the West. The Eurasian doctrine of the state proclaims the idea of strong government and powerful state, which represents the interests of the people and maintains direct connections with its citizens by combining the law and justice principles with the norms of morality, welfare and conscience. The article examines the key Eurasian concept “ideocratic state” and the essential characteristics of the Eurasian concept of the state system, such as ideocracy, autarchy, idea-ruler, and ruling selection. The key state-forming concept is “Pan-Eurasian nationalism” interpreted by the Eurasians as an archetype of ideology, a basis of the national idea. The authors consider basic principles of the socio-economic structure of the Eurasian state, including active participation of the state in the economic life of the country, the coexistence of public and private properties. According to the Eurasian doctrine, the state-planned economy and the state regulation of culture form the foundations of autarchic states that protect the country from economic and humanitarian intervention. The authors come to the conclusion that Eurasian theory of the state can significantly enrich nowadays scientific theory and help to solve the tasks of modernization of the Russian society at the present stage for it takes into account specific national, geopolitical, historical, and cultural characteristics of our state and allows to preserve the identity and diversity of the Eurasian world.

In this paper we consider the problem of parallelization of Cholesky factorization numerical phase for sparse symmetric positive definite matrices. A new strategy for parallelization of the multifrontal method for shared-memory systems is suggested. This strategy combines two approaches to parallelism organization depending on the elimination tree level. At the bottom of the tree, parallel computing of nodes from a priority queue takes place. At the top levels of the tree, nodes are calculated sequentially, employing multithreaded BLAS procedures. Experimental results show that the implementation of the scheme described is commensurable with MUMPS and MKL PARDISO solvers.

The amplification of high energy chirped pulses in Large Mode Area tapered fiber amplifiers and their coherent combining have been investigated numerically. We have developed a three-dimensional model of strongly chirped nanosecond pulse amplification and compression back to femtosecond duration fully taking into account transverse and longitudinal variations of refractive index profile and distribution of active ions in the fiber, wavelength dependence of emission and absorption cross sections, gain saturation and Kerr nonlinearity. Modeling of Yb-doped fiber amplifier shows that up to 3 mJ of output energy can be extracted in 1 ns pulse with single-mode beam quality. Finally, we have investigated numerically the capabilities of compression and coherent combining of up to 36 perturbed amplifying channels in which high-order modes were excited and have obtained more than 70% combining efficiency and 380 fs compressed pulse duration.

This paper discusses parallelization of the computationally intensive numerical factorization phase of sparse Cholesky factorization on shared memory systems. We propose and compare two parallel algorithms based on the multifrontal method. Both algorithms are implemented in a task-based fashion employing dynamic load balance. The first algorithm associates OpenMP tasks with the nodes of an elimination tree and relies on the OpenMP scheduler. The second algorithm employs a concurrent priority queue to implement balancing. Experimental results on symmetric positive definite matrices from the University of Florida Sparse Matrix Collection show that our implementation is comparable to MUMPS and Intel MKL PARDISO in terms of performance and scaling efficiency on shared memory systems.

Рассматривается задача переупорядочения строк и столбцов симметричной положительно определенной разреженной матрицы с целью уменьшения числа ненулевых элементов в факторе Холецкого. Данная задача является NP-полной. Для ее решения используются эвристические алгоритмы, основанные на применении методов теории графов. Предлагается параллельный алгоритм переупорядочения для вычислительных систем с общей памятью. В качестве базы для распараллеливания используется модификация многоуровневого метода вложенных сечений, ранее реализованная авторами в виде библиотеки с открытым исходным кодом MORSy. Основная идея распараллеливания заключается в организации и параллельной обработке очереди задач, которые могут быть решены независимо. В отличие от широко распространенных аналогов, применяющих MPI для организации параллелизма как на распределенной, так и на общей памяти, предложенный алгоритм использует возможности стандарта OpenMP 3.0. Вычислительные эксперименты выполнены на симметричных положительно определенных матрицах из коллекции университета Флориды. Показано, что параллельный код MORSy дает сходные или лучшие перестановки в сравнении с библиотекой ParMETIS для всех тестовых матриц, кроме одной, в большинстве случаев опережая ParMETIS по времени работы. Программная реализация выполнена в виде библиотеки с открытым исходным кодом и доступна для скачивания на сайте Приволжского научно-образовательного центра суперкомпьютерных технологий. This paper deals with the NP-complete problem of finding a symmetric positive definite sparse matrix ordering that minimizes the Cholesky factor fill-in. For this purpose, heuristic approaches based on graph algorithms are applied. A new parallel ordering algorithm for shared-memory computing systems is proposed. The modified multilevel nested dissection algorithm from the recently presented MORSy library is used as a basis for ordering. The parallel processing is done in a task-based fashion. It uses the OpenMP 3.0 task parallelism relying on the dynamic load balancing implemented during the OpenMP runtime. The numerical experiments were performed using a number of symmetric positive definite matrices from the University of Florida Sparse Matrix Collection. The experimental results show the competitiveness of the proposed implementation on shared memory systems compared to the widely used ParMETIS library. In our experiments, the parallel MORSy version provides a better ordering than ParMETIS on all but one matrix in terms of the Cholesky factor fill-in and outperforms ParMETIS in most cases. The parallel MORSy version is publicly available from the Supercomputing Center of Lobachevsky State University of Nizhni Novgorod.

The article is based on the detailed analysis of the intellectual labor and takes into account theoretical and practical aspects of the intellectual labor economics in the transition to the information society. The author describes the nature, specific features, content, structure and the bases for classification of the intellectual labor.

We developed a three-dimensional numerical model of Large-Mode-Area chirped pulse fiber amplifiers which includes nonlinear beam propagation in nonuniform multimode waveguides as well as gain spectrum dynamics in quasi-three-level active ions. We used our model in tapered Yb-doped fiber amplifiers and showed that single-mode propagation is maintained along the taper even in the presence of strong Kerr nonlinearity and saturated gain, allowing extraction of up to 3 mJ of output energy in 1 ns pulse. Energy scaling and its limitation as well as the influence of fiber taper bending and core irregularities on the amplifier performance were studied. We also investigated numerically the capabilities for compression and coherent combining of up to 36 perturbed amplifying channels and showed more than 70% combining efficiency, even with up to 11% of high-order modes in individual channels.

The article deals with important economic and sociological problems taking into account their relevance to economics and sociology of labor as two independent sciences. The author suggests some demarcation boundaries of the concepts relevant to contemporary life within these two disciplines.

The article is devoted to the clarification of the conceptual content of the most important scientific categories - government, management and administration - which is of considerable significance both for the substantiation of scientific theories, and for the determination of research tools for applied and empirical studies.

2D calculations of the promising laser hohlraums were performed with using of the Sinara computer code. These hohlraums are intended for achievement of indirectly-driven thermonuclear ignition at laser energy above 1 MJ. Two calculation variants of the laser assembly with the form close to a rugby ball were carried out: with laser entrance hole shields and without shields. Time dependent hohlraum radiation temperature and x-ray flux asymmetry on a target were obtained.