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Preconditioning waveform relaxation iterations for differential systems |
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| Authors: | K Burrage Z Jackiewicz S P Nørsett R A Renaut |
| Institution: | (1) CIAMP, Department of Mathematics, University of Queensland, 4072 Brisbane, Australia;(2) Department of Mathematics, Arizona State University, 85287-1804 Tempe, AZ, USA;(3) Division of Mathematical Sciences, Norwegian Institute of Technology, N-7034 Trondheim-NTH, Norway |
| Abstract: | We discuss preconditioning and overlapping of waveform relaxation methods for sparse linear differential systems. It is demonstrated that these techniques significantly improve the speed of convergence of the waveform relaxation iterations resulting from application of various modes of block Gauss-Jacobi and block Gauss-Seidel methods to differential systems. Numerical results are presented for linear systems resulting from semi-discretization of the heat equation in one and two space variables. It turns out that overlapping is very effective for the system corresponding to the one-dimensional heat equation and preconditioning is very effective for the system corresponding to the two-dimensional case.The work of the second author was supported by the National Science Foundation under grant NSF DMS 92-08048. |
| Keywords: | Waveform relaxation splittings preconditioning overlapping error analysis parallel computing |
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