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 - <p style="text-align: justify;">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.</p>