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Quasi-Newton Waveform Relaxation Based on Energy Method

Quasi-Newton Waveform Relaxation Based on Energy Method
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Year:    2018

Author:    Yaolin Jiang, Zhen Miao

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 542–562

Abstract

A quasi-Newton waveform relaxation (WR) algorithm for semi-linear reaction-diffusion equations is presented at first in this paper. Using the idea of energy estimate, a general proof method for convergence of the continuous case and the discrete case of quasi-Newton WR is given, which appears to be the superlinear rate. The semi-linear wave equation and semi-linear coupled equations can similarly be solved by quasi-Newton WR algorithm and be proved as convergent with the energy inequalities. Finally several parallel numerical experiments are implemented to confirm the effectiveness of the above theories.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1702-m2016-0700

Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 542–562

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Waveform relaxation quasi-Newton Energy method Superlinear Parallelism.

Author Details

Yaolin Jiang

Zhen Miao

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