Multigrid Waveform Relaxation of Spatial Finite Element Meshes: The Continuous-Time Case

Abstract

The waveform relaxation method and its multigrid acceleration are studied as solution procedures for the system of ordinary differential equations obtained by finite element discretisation of a linear parabolic initial boundary value problem. The convergence properties of the continuous-time algorithm are theoretically investigated on finite-length and infinite-length time-intervals. In addition, quantitative convergence estimates and numerical results are presented for one-dimensional and two-dimensional model problems.

Additional Information

©1996 Society for Industrial and Applied Mathematics. Reprinted with permission. Received by the editors November 23, 1993; accepted for publication (in revised form) May 11, 1994. This text presents research results of the Belgian Incentive Programme "Information Technology", Computer Science of the Future (IT/IF/5), initiated by the Belgian State--Prime Minister's Service--Federal Office for Scientific, Technical and Cultural Affairs. The scientific responsibility is assumed by its authors. This work was supported in part by NSF Cooperative Agreement CCR-9120008. The authors would like to thank Prof. Walter Van Assche for his valuable comments on the use of Laguerre polynomials in the proof of Lemma 2.1 (Appendix) and an anonymous referee for suggesting the proof of Lemma 2.1 based on perturbation theory.

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