A parareal approach of semi-linear parabolic equations based on general waveform relaxation

被引：8

作者：

Li, Jun ^{[1
]}

Jiang, Yao-Lin ^{[1
]}

Miao, Zhen ^{[1
]}

机构：

[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 35卷 / 06期

基金：

中国国家自然科学基金;

关键词：

convergence analysis; general waveform relaxation; parareal approach; semi-linear parabolic equations; PDE level; CONVERGENCE ANALYSIS; ALGORITHM;

D O I：

10.1002/num.22390

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a parareal approach of semi-linear parabolic equations based on general waveform relaxation (WR) at the partial differential equation (PDE) level. An algorithm for initial-boundary value problem and two algorithms for time-periodic boundary value problem are constructed. The convergence analysis of three algorithms are provided. The results show that the algorithm for initial-boundary value problem is superlinearly convergent while both algorithms for the time-periodic boundary value problem linearly converge to the exact solutions at most. Numerical experiments show that the parareal algorithms based on general WR at the PDE level, compared with the parareal algorithm based on the classical WR at the ordinary differential equations (ODEs) level (the PDEs is discretized into ODEs), require much fewer number of iterations to converge.

引用

页码：2017 / 2043

页数：27

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