Chikitkin, A. Petrov, M. Titarev, V. Utyuzhnikov, S.
Published in
Lobachevskii Journal of Mathematics

Different parallel distributed-memory versions of Lower-Upper Symmetric Gaussâ€“Seidel (LU-SGS) method for solution of discrete equations in finite-volume framework are compared in terms of parallel structure of algorithms. New version based on multilevel recursive decomposition is proposed.

Aparinov, A. A. Setukha, A. V. Stavtsev, S. L.
Published in
Lobachevskii Journal of Mathematics

In this article authors analyse the specifics of parallel implementation of numericalmethods based on integral equations. The necessity to create original parallel subroutines implementing fast matrix algorithms for efficient work with big dense matrices is stressed out. Specifics of parallel algorithms and calculating capabilities of integral equa...

Levchenko, V. D. Perepelkina, A. Y.
Published in
Lobachevskii Journal of Mathematics

LRnLA algorithms provide many advantages for stencil computations. In contrast to the traditional stepwise approaches, the performance efficiency does not decrease with the problem data size and the parallel scaling is close to linear. This is achieved by tracing the data dependencies of the problem, taking into account the finite information propa...

Zamarashkin, N. L. Zheltkov, D. A.
Published in
Lobachevskii Journal of Mathematics

The block Lanczos method for huge sparse linear systems over large prime finite fields is accelerated on GPU. Calculations on GPU are used for the operations with the dense matrices and blocks. The achieved acceleration of block operations significantly increases the parallel resource of the entire method, expanding the scalability area close to li...

Bazulin, E. G. Goncharsky, A. V. Romanov, S. Y. Seryozhnikov, S. Y.
Published in
Lobachevskii Journal of Mathematics

This paper is concerned with developing efficient methods for solving inverse problems of ultrasonic nondestructive imaging in the framework of a scalar wave model, which describes the propagation, diffraction and refraction of longitudinal ultrasonic waves. The problem of recovering the velocity of a longitudinal wave in a solid is formulated as a...

Sokolinsky, L. B.
Published in
Lobachevskii Journal of Mathematics

This article presents a new high-level parallel computational model named BSF "â€” Bulk Synchronous Farm. The BSF model extends the BSP model to deal with the computeintensive iterative numericalmethods executed on distributed-memory multiprocessor systems. The BSF model is based on the master-worker paradigm and the SPMD programming model. The BSF m...

Danshin, A. A. Gurevich, M. I. Ilyin, V. A. Kovalishin, A. A. Velikhov, V. E.
Published in
Lobachevskii Journal of Mathematics

There are several methods of numerical solution of eigenvalue problems by the Monte Carlo method, which are used in the calculation of nuclear reactors. This paper is devoted to the investigation of the possibility of using such methods for solving the stationary Schrodinger equation. The latter equation can easily be transformed into the form of a...

Chernyavskiy, A. Yu. Voevodin, Vad. V. Voevodin, Vl. V.
Published in
Lobachevskii Journal of Mathematics

We present the detailed description of parallel computational structure of quantum circuits modeling. The deep theoretical and experimental analysis of corresponding algorithms and relations of their features to the nature of quantum computations are considered. Special attention is paid to the extension of modeling to the case of noisy circuits, w...

Strongin, R. G. Gergel, V. P. Barkalov, K. A. Sysoyev, A. V.
Published in
Lobachevskii Journal of Mathematics

This paper addresses computationally intensive global optimization problems, for solving of which the supercomputing systems with exaflops performance can be required. To overcome such computational complexity, the paper proposes the generalized parallel computational schemes, which may involve numerous efficient parallel algorithms of global optim...

Amosov, G. G.
Published in
Lobachevskii Journal of Mathematics

In this paper we study the general properties of non-commutative operator graphs. The problem of the existence of quantum anticliques is considered. The covariant property for the resolution of the identity which generates the graph is investigated.