Topic
Tridiagonal matrix algorithm
About: Tridiagonal matrix algorithm is a research topic. Over the lifetime, 1070 publications have been published within this topic receiving 21084 citations.
Papers published on a yearly basis
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Papers
TL;DR: A novel two-dimensional real-time modeling approach for a proton exchange membrane fuel cell (PEMFC) based on a tridiagonal matrix algorithm (Thomas algorithm) and a three-level bisection algorithm has been developed to solve spatial physical quantities distribution for electrochemical domain.
Abstract: This paper presents a novel two-dimensional real-time modeling approach for a proton exchange membrane fuel cell (PEMFC) based on a tridiagonal matrix algorithm (Thomas algorithm). The Thomas algorithm consists of a forward elimination and a backward substitution, its arithmetic complexity of computations being much lower than the Gaussian elimination. In order to use this advanced numerical solver, the differential equations of reactant gas convection and diffusion phenomena in serpentine channels are transformed into a tridiagonal equations system. In addition, a three-level bisection algorithm has been developed to solve spatial physical quantities distribution for electrochemical domain. The real-time computing methods developed in this paper are then implemented in C language for a fast execution time in a real-time processor. The proposed real-time model is experimentally validated using a 1.2 kW Ballard NEXA fuel cell system, and its practical feasibilities in advanced real-time control for PEMFC systems have been experimentally demonstrated in an RT-LAB real-time simulator.
27 citations
22 Dec 2011
TL;DR: Parallel implementation of algorithm of numerical solution of Navier-Stokes equations for large eddy simulation (LES) of turbulence is presented in this paper, where the dynamic Smagorinsky model is applied for sub-grid simulation of turbulence.
Abstract: Parallel implementation of algorithm of numerical solution of Navier-Stokes equations for large eddy simulation (LES) of turbulence is presented in this research. The dynamic Smagorinsky model is applied for sub-grid simulation of turbulence. The numerical algorithm was worked out using a scheme of splitting on physical parameters. At the first stage it is supposed that carrying over of movement amount takes place only due to convection and diffusion. Intermediate field of velocity is determined by method of fractional steps by using Thomas algorithm (tridiagonal matrix algorithm). At the second stage the determined intermediate field of velocity is used for determination of the field of pressure. Three dimensional Poisson equation for the field of pressure is solved using over relaxation method.
27 citations
TL;DR: Five extensions of tridiagonal, pentadiagonal, and cyclic triagonal matrix algorithms for the solution of algebraic decretized equations yielded by finite-difference, finite-volumes, finate-element, and controt-volume finite-element methods for fluid flow and heat transfer are presented.
Abstract: Tridiagonal, pentadiagonal, and cyclic triagonal matrix algorithms are well-eestablished elements of line-by-line iterative procedures for the solution of algebraic decretized equations yielded by finite-difference, finite-volumes, finate-element, and controt-volume finite-element methods for fluid flow and heat transfer In this article, five extensions of these algorithms are presented: a coupled tridiagonal matrix algorithm, a coupled cyclic tridiagonal matrix algorithm, the cyclic pentadiagonal matrix algorithm, a coupled pentadiagonal matrix algorithm, and a coupled cyclic pentadiagonal matrix algorithm
27 citations
TL;DR: An exponentially fitted finite difference method for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point approximates the exact solution very well.
26 citations
1 Aug 2010
TL;DR: A parallel algorithm for solving a series of matrix equations with a constant tridiagonal matrix and different right-hand sides and an original algorithm for calculating share components of the solution vector is proposed and studied.
Abstract: 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.
26 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 3 |
| 2024 | 7 |
| 2023 | 11 |
| 2022 | 22 |
| 2021 | 14 |
| 2020 | 11 |