求解二阶椭圆型方程Dirichlet问题的几种算法  

Several Algorithms for Solving Dirichlet Problem of Second Elliptic Equations

作　　者：闵涛[1] 高青青 

机构地区：[1]西安理工大学理学院

出　　处：《科技通报》2017年第12期44-49,共6页Bulletin of Science and Technology

基　　金：国家自然科学基金重大项目基金资助(51190093);国家自然科学基金(50979088);国家自然科学基金(51179151)

摘　　要：利用有限差分法将椭圆型方程离散为线性方程组,分别用BICGSTAB算法、CG算法、GMRES算法和LSQR算法对其求解,并对这四种算法的求解精度,计算时间及收敛效果进行了比较分析,结果表明:这四种算法对求解此类问题各有优点和不足,相对来说BICGSTAB算法效果最好,LSQR算法效果最差。By using the finite difference method to discrete elliptic equations into equations. BICGSTAB algorithm, CG algorithm, GMRES algorithm and LSQR algorithm are used to solve the problem, And the accuracy, the time of calculation and the effect of convergence of the four algorithms are compared and analyzed. The results show that these four algoithms have advantages and disadvantages in solving these problems, Relatively speaking, the BICGSTAB algorithm is the best, and the LSQR algorithm is the worst.

关 键 词：椭圆型方程 有限差分法 线性方程组 算法 

分 类 号：O241.6[理学—计算数学]