Performance Comparison of GPU-Based Jacobi Solvers Using CUDA Provided Synchronization Methods

Abstract

In this manuscript, variants of Jacobi solver implementation on general purpose graphical processing units (GPGPU) have been purposed and compared. During this work, parallel implementation of finite element method (FEM) using Poisson's equation on shared memory architecture as well as on GPGPUs has been observed to identify computationally most expensive part of FEM software, which is linear algebra Jacobi solver. Sparse matrices were used for system of linear equations. Nine implementations of Jacobi solver have been developed and compared using various synchronization and computation methods like atomicAdd, atomicAdd_block, butterfly communication, grid synchronization, hybrid and whole GPU based computation methods, respectively. Experiments have showed that Jacobi implementations based on our implemented Butterfly communication method have outperformed CUDA 10.0 provided critical execution methods like atomicAdd, atomicAdd_block and grid methods. The GPU has achieved a max speedup of 46 times using GTX 1060 and 60 times using Quadro P4000 with double precision computations when compared with sequential implementation on Core-i7 8750H. All the developments were performed using C/C++ GNU compiler 7.3.0 on Ubuntu 18.04 and CUDA 10.0.

GPU Accelerated Nonlinear Electronic Circuits Solver for Transient Simulation of Systems with Large Number of Components

“…Several articles have recently been published CUDA parallelization [3][4][5][6]. This article focuses on simulation of electric circuits whose published articles can be divided into several groups: individual problems that can be encountered when solving simulations of electrical circuits, such as the parallel solution of sparse matrices [7][8][9] , accelerated algorithms for calculations of preconditioning of matrices [10][11][12][13], or general acceleration of simulation of electric circuits [14,15]. There is even a special parallelized version of the SPICE simulator, CUSpice.…”

“…A very similar article, but GPU-oriented parallelization Jacob's iterative algorithm is [10]. The authors again present several modifications of the algorithm for accelerating the GPU calculation method.…”