QUASI-NEWTON WAVEFORM RELAXATION BASED ON ENERGY METHOD  

作　　者：Yaolin Jiang Zhen Miao 

机构地区：[1]School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China

出　　处：《Journal of Computational Mathematics》2018年第4期542-562,共21页计算数学（英文）

基　　金：This work was supported by the Natural Science Foundation of China （NSFC） under grant （11371287, 61663043） and Natural Science Basis Research Plan in Shaanxi Province of China under grant 2016JM5077.

摘　　要：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.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.

关 键 词：Waveform relaxation QUASI-NEWTON Energy method SUPERLINEAR PARALLELISM 

分 类 号：O4-09[理学—物理] O345