An efficient asynchronous approach for Gauss-Seidel iterative solver for FDM/FEM equations on multi-core processors

In this paper, we proposed a new parallel iterative asynchronous method for Gauss-Seidel and Successive Over-Relaxation (SOR) for finite difference method (FDM) and finite element method (FEM). The approach attempts to minimize the thread synchronization which incurs a lot of thread idle time due to the dependency of computation. Our proposed method maximizes the thread utilization on multi-core processors with some space requirement for storing current states. We implement our proposed method based on the Poisson's equation with FDM. It is found that our proposed algorithm runs 5.88 times faster than the original Gauss-Seidel and achieve speedup up to 1.25 compared with the parallel Sliding Window version.

[1]  David J. Evans,et al.  Parallel S.O.R. iterative methods , 1984, Parallel Comput..

[2]  Geoffrey C. Fox,et al.  A parallel Gauss-Seidel algorithm for sparse power system matrices , 1994, Proceedings of Supercomputing '94.

[3]  Michael J. Quinn,et al.  Parallel programming in C with MPI and OpenMP , 2003 .

[4]  Ronald H. Perrott,et al.  Parallel programming , 1988, International computer science series.

[5]  David A Lowther,et al.  The Solution of Electromagnetic Field Problems Using a Sliding Window Gauss-Seidel Algorithm on a Multicore Processor , 2010, IEEE Transactions on Magnetics.

[6]  Jens Breitbart.  Data structure design for GPU based heterogeneous systems , 2009, 2009 International Conference on High Performance Computing & Simulation.

[7]  C. Chantrapornchai,et al.  GPU-based total variation image restoration using Sliding Window Gauss-Seidel algorithm , 2011, 2011 International Symposium on Intelligent Signal Processing and Communications Systems (ISPACS).

[8]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[9]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[10]  Jérémie Allard,et al.  Parallel Dense Gauss-Seidel Algorithm on Many-Core Processors , 2009, 2009 11th IEEE International Conference on High Performance Computing and Communications.