Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
Fast Fourier transforms for direct solution of Poisson's equation with staggered boundary conditions
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
Efficient Tridiagonal Solvers on Multicomputers
IEEE Transactions on Computers
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
Parallel Tridiagonal Equation Solvers
ACM Transactions on Mathematical Software (TOMS)
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Parallel Computers Two: Architecture, Programming and Algorithms
Parallel Computers Two: Architecture, Programming and Algorithms
Parallel ADI solver based on processor scheduling
Applied Mathematics and Computation
Sourcebook of parallel computing
Sourcebook of parallel computing
IEEE Transactions on Parallel and Distributed Systems
A parallel/recursive algorithm
Journal of Computational Physics
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Numerical Solution of Partial Differential Equations: An Introduction
Numerical Solution of Partial Differential Equations: An Introduction
Parallel Processing for Scientific Computing (Software, Environments and Tools)
Parallel Processing for Scientific Computing (Software, Environments and Tools)
Validity of the single processor approach to achieving large scale computing capabilities
AFIPS '67 (Spring) Proceedings of the April 18-20, 1967, spring joint computer conference
High-performance modeling acoustic and elastic waves using the parallel Dichotomy Algorithm
Journal of Computational Physics
The LuNA library of parallel numerical fragmented subroutines
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
Journal of Computational Physics
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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 problem is represented in two steps. The first preliminary step is calculating some rows of the inverse matrix of system of linear algebraic equations. The second step consists in calculating solutions for all right-hand sides. For reducing the communication interactions, based on the formulated and proved the main Gaussian Parallel Elimination Theorem for tridiagonal system of equations, we propose an original algorithm for calculating share components of the solution vector. Theoretical estimates validating the efficiency of the approach for both the common- and distributed-memory supercomputers are obtained. Direct and iterative methods of solving a 2D Poisson equation, which include procedures of tridiagonal matrix inversion, are realized using the MPI paradigm. Results of computational experiments on a multicomputer demonstrate a high efficiency and scalability of the parallel Dichotomy Algorithm.