26 citations · 141 across the 20 of their papers we have counts for
10 papers · 1 filter
A three-dimensional Laguerre one-way wave equation solver
Andrew V. Terekhov
A finite difference algorithm based on the integral Laguerre transform in time for solving a three-dimensional one-way wave equation is proposed. This allows achieving high accurac…
An extra-components method for evaluating fast matrix-vector multiplication with special functions
Andrew V. Terekhov
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshe…
Generating Laguerre expansion coefficients by solving a one-dimensional transport equation
Andrew V. Terekhov
Spectral methods based on integral transforms may be efficiently used to solve differential equations in some special cases. This paper considers a different approach in which algo…
The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver
Andrew V. Terekhov
This paper considers spectral-difference methods of a high-order of accuracy for solving the one-way wave equation using the Laguerre integral transform with respect to time as the…
The Laguerre finite difference one-way equation solver
Andrew V. Terekhov
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of par…
A fast parallel algorithm for solving block-tridiagonal systems of linear equations including the domain decomposition method
Andrew V. Terekhov
In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The…
High-performance modeling acoustic and elastic waves using the Parallel Dichotomy Algorithm
Alexey G. Fatyanov, Andrew V. Terekhov
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced b…
High performance parallel algorithm for solving elliptic equations with non-separable variables
Andrew V. Terekhov
A parallel algorithm for computing the finite difference solution to the elliptic equations with non-separable variables is presented. The resultant matrix is symmetric positive de…
Application of the Parallel Dichotomy Algorithm for solving Toeplitz tridiagonal systems of linear equations with one right-hand side
Andrew V. Terekhov
Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we propose a parallel procedure for solving tridiagonal systems of equations with Toeplitz matrices. Taking…
Parallel dichotomy algorithm for solving tridiagonal SLAEs
Andrew Terekhov
A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides is proposed and studied. The process of solving the…