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Volume 36, Issue 4
Quasi-Newton Waveform Relaxation Based on Energy Method

Yaolin Jiang & Zhen Miao

DOI: 10.4208/jcm.1702-m2016-0700

J. Comp. Math., 36 (2018), pp. 542-562.

Published online: 2018-06

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  • 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.

  • Keywords

Waveform relaxation, quasi-Newton, Energy method, Superlinear, Parallelism.

  • AMS Subject Headings

65L20, 65L70

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yljiang@xjtu.edu.cn (Yaolin Jiang)

mz91127@126.com (Zhen Miao)

  • BibTex
  • RIS
  • TXT
@Article{JCM-36-542, author = {Jiang , Yaolin and Miao , Zhen}, title = {Quasi-Newton Waveform Relaxation Based on Energy Method}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {36}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1702-m2016-0700}, url = {http://global-sci.org/intro/article_detail/jcm/12304.html} }
TY - JOUR T1 - Quasi-Newton Waveform Relaxation Based on Energy Method AU - Jiang , Yaolin AU - Miao , Zhen JO - Journal of Computational Mathematics VL - 4 SP - 542 EP - 562 PY - 2018 DA - 2018/06 SN - 36 DO - http://doi.org/10.4208/jcm.1702-m2016-0700 UR - https://global-sci.org/intro/article_detail/jcm/12304.html KW - Waveform relaxation, quasi-Newton, Energy method, Superlinear, Parallelism. AB -

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.

Jiang , Yaolin and Miao , Zhen. (2018). Quasi-Newton Waveform Relaxation Based on Energy Method. Journal of Computational Mathematics. 36 (4). 542-562. doi:10.4208/jcm.1702-m2016-0700
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