A method of two-level parallelization of the Thomas algorithm for solving tridiagonal linear systems on hybrid computers with multicore coprocessors


  • A.N. Bykov Russian Federal Nuclear Center – All-Russian Scientific Research Institute of Experimental Physics




systems of linear algebraic equations, tridiagonal matrices, Thomas algorithm, parallelization of Thomas algorithm, parallel-pipeline method, Yanenko’s method, parallel computers, Intel Xeon Phi


A method of two-level parallelization of the Thomas algorithm for solving tridiagonal linear systems (the thread-level parallelism using OpenMP and the process-level parallelism using MPI) arising when modeling two-dimensional and three-dimensional physical processes is described. The features of its implementation for parallel multiprocessor systems and for hybrid multiprocessor systems with multicore coprocessors Intel Xeon Phi are analyzed. The arithmetic complexity of this method is estimated. Some numerical results obtained when studying its scalability are discussed.

Author Biography

A.N. Bykov


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How to Cite

Федоров А. A Method of Two-Level Parallelization of the Thomas Algorithm for Solving Tridiagonal Linear Systems on Hybrid Computers With Multicore Coprocessors // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2016. 17. 234-244. doi 10.26089/NumMet.v17r322



Section 1. Numerical methods and applications