Russian Journal of Numerical Analysis and Mathematical Modelling

Published by De Gruyter

Volume 28 Issue 2

April 2013

Issue of Russian Journal of Numerical Analysis and Mathematical Modelling

Contents
Journal Overview

Publicly Available April 5, 2013

Masthead

Page range: i-iv

Download PDF

April 5, 2013

Non-degenerate Eulerian finite element method for solving PDEs on surfaces

A. Y. Chernyshenko, M. A. Olshanskii

Page range: 101-124

Abstract

The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in ℝN, N = 2; 3. The method builds upon the formulation introduced in [7], where a surface equation is extended to a neighbourhood of the surface. The resulting degenerate PDE is then solved in one dimension higher, but can be solved on a mesh that is unaligned to the surface. We introduce another extended formulation, which leads to uniformly elliptic (non-degenerate) equations in a bulk domain containing the surface.We apply a finite element method to solve this extended PDE and prove the convergence of the finite element solutions restricted to the surface to the solution of the original surface problem. Several numerical examples illustrate the properties of the method.

April 5, 2013

Linear stability analysis of Poiseuille flow in a rectangular duct

K. V. Demyanko, Yu. M. Nechepurenko

Page range: 125-148

Abstract

A laminar flow of a viscous incompressible fluid with a constant pressure gradient (Poiseuille flow) is considered in a rectangular duct for different values of cross-sectional aspect ratio. A new method, significantly more efficient than the known ones, is proposed and justified for computing the critical Reynolds number of such a flow. The dependence of the critical Reynolds number on the cross-sectional aspect ratio is numerically studied. A theoretical justification of the obtained dependence is proposed

April 5, 2013

TT-GMRES: solution to a linear system in the structured tensor format

S. V. Dolgov

Page range: 149-172

Abstract

An adapted tensor-structured GMRES method for the TT format is proposed and investigated. The Tensor Train (TT) approximation is a robust approach to highdimensional problems. One class of such problems involves the solution of a linear system. In this work we study the convergence of the GMRES method in the presence of tensor approximations and provide relaxation techniques to improve its performance. Several numerical examples are presented. The method is also compared with a projection TT linear solver based on the ALS and DMRG methods. On a particular SPDE (high-dimensional parametric) problem these methods manifest comparable performance, with a good preconditioner the TT-GMRES overcomes the ALS solver.

April 5, 2013

Asymptotic estimates of radiation transfer through a stochastic medium and reconstruction of parameters of averaged radiation model

G. A. Mikhailov

Page range: 173-186

Abstract

Various models of exponentially correlated random media related to Poisson point ensembles are considered in the paper. Asymptotic estimates of the mean probability of a particle (radiation quantum) passing through media of such type are constructed on the base of the Poisson property of the flow of the trajectory intersections with constancy domains of random density and with the help of the central limit theorem for the corresponding‘optical’ length. The possibility to reconstruct the parameters of a radiation model from the averaged passage probability is also studied.

April 5, 2013

Numerical stochastic model of spatial fields of daily sums of liquid precipitation

V. A. Ogorodnikov, N. A. Kargopolova, O. V. Sereseva

Page range: 187-200

Abstract

A numerical stochastic model of spatial fields of daily sums of liquid precipitation constructed with the use of real observation data is proposed in the paper. Based on this model, simulation algorithms for conditionally distributed fields are constructed and certain examples of the use of this model in studying extreme properties of liquid precipitation fields are considered.

April 5, 2013

Minimax parametric optimization of numerical-statistical ‘method of similar trajectories’ for solution of radiation transfer theory problems

S. A. Rozhenko, G. A. Mikhailov

Page range: 201-212

Abstract

Algorithms of the ‘method of similar trajectories’ (MST) are implemented by a numerical-statistical simulation of the trajectories of particles, which are radiation ‘quanta’, according to an auxiliary radiation model and construction of weighted estimates of the functionals simultaneously for different values of ‘physical’ parameters. This paper is focused on the theoretical and numerical solution of the problem of choosing this auxiliary model with the aim to minimize the parametric maximum of the mean-square error of weighted estimates. We formulate new assertions concerning minimax MST algorithms and refine some previously known statements.

About this journal

Objective
The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest.

Topics

numerical analysis
numerical linear algebra
finite element methods for PDEs
iterative methods
Monte-Carlo methods
mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences

Article formats
Research articles

> Information on submission process