Parallel Thomas approach development for solving tridiagonal systems in GPU programming − steady and unsteady flow simulation

Abstract

The solution of tridiagonal system of equations using graphic processing units (GPU) is assessed. The parallel-Thomas-algorithm (PTA) is developed and the solution of PTA is compared to two known parallel algorithms, i.e. cyclic-reduction (CR) and parallel-cyclic-reduction (PCR). Lid-driven cavity problem is considered to assess these parallel approaches. This problem is also simulated using the classic Thomas algorithm that runs on a central processing unit (CPU). Runtimes and physical parameters of the mentioned GPU and CPU algorithms are compared. The results show that the speedup of CR, PCR and PTA against the CPU runtime is 4.4x,5.2x and 38.5x, respectively. Furthermore, the effect of coalesced and uncoalesced memory access to GPU global memory is examined for PTA, and a 2x-speedup is achieved for the coalesced memory access. Additionally, the PTA performance in a time dependent problem, the unsteady flow over a square, is assessed and a 9x-speedup is obtained against the CPU.

Efficient graphic processing unit implementation of the chemical-potential multiphase lattice Boltzmann method

“…There are two differences between PCR and CR: PCR has only a forward reduction stage and utilizes all threads in all levels of the procedure. An important problem is that in order to use CR and PCR algorithms for solving tridiagonal systems, the size of matrices must be 2 n (Souri et al, 2020). This is a major obstacle preventing these methods application in CP-LBM simulation.…”