引用本文:李明, 郑洲顺, 赵金娥.求解带间断系数非线性椭圆问题的两重网格法[J].西南大学学报(自然科学版),2019,41(5):48~52
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求解带间断系数非线性椭圆问题的两重网格法
李明, 郑洲顺, 赵金娥1,2
1. 中南大学 数学与统计学院, 长沙 410083;2. 红河学院 数学学院, 云南 蒙自 661199
摘要:
利用有限差分法离散带间断系数的非线性椭圆问题,针对离散后所得到的非线性方程组,从减少计算量的角度出发,只使用一个辅助的粗层网格空间,并在最细层网格上求解线性校正方程组,构造了两重网格(NETG)法.数值结果表明,新算法在计算量和计算时间方面优于以往的算法.
关键词:  非线性椭圆问题|两重网格法|有限差分法|线性校正方程组
DOI:10.13718/j.cnki.xdzk.2019.05.008
分类号:O241.6
基金项目:国家重点研发计划项目(2017YFB0305601;2017YFB0701700);云南省科技厅项目(2017FH001-012,2017FH001-015);红河学院中青年学术带头人后备人才项目(2015HB0304);红河学院科研项目(XJ15Y19).
A Two-Level Method for Solving Nonlinear Elliptic Problems with a Jumping Coefficient
LI Ming, ZHENG Zhou-shun, ZHAO Jin-e1,2
1. School of Mathematics and Statistics, Central South University, Changsha 410083, China;2. Department of Mathematics, Honghe University, Mengzi Yunnan 661199, China
Abstract:
An efficient two-level method is studied to solve the nonlinear systems which arise from a nonlinear elliptic problem with a jumping coefficient by a finite difference method. Only one auxiliary coarse grid space is needed with a suitable mesh size discretization, and linear correction equations are applied instead of the nonlinear systems on the finest grid space. Numerical results are given to verify the computational cost and efficiency of the proposed approach and the results are compared with the existing numerical methods for solving nonlinear elliptic problems with a jumping coefficient.
Key words:  nonlinear elliptic problem|two-grid method|finite different method|linear correcting equations
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