三维对流扩散方程的多重网格算法研究_葛永斌.pdf

54 ， （ ） 2009 45 13 Computer Engineering and Applications 计算机工程与应用 三维对流扩散方程的多重网格算法研究 葛永斌，曹富军，马廷福，郝庆一 ， ， ， GE Yong-bin CAO Fu-jun MA Ting-fu HAO Qing-yi 宁夏大学数学计算机学院，银川 750021 ， ， ， School of Mathematics and Computer Science Ningxia University Yinchuan 750021 China ： E-mail ge_y_b@163.com ， ， ， GE Yong -bin CAO Fu -jun MA Ting -fu et al.Research on multigrid algorithm for 3D convection -diffusion equation. ， ， （）： Computer Engineering and Applications 2009 45 13 54-58. ： （ ） Abstract Multigrid algorithms based on the finite difference method of three dimensional 3D convection diffusion equation are studied.The second order central difference and the fourth order compact difference schemes in general meth-size are presented.A partial semi-coarsening multigrid strategy is designed to solve the resulting sparse linear systems and the corresponding restriction ， and interpolation operators are also constructed.Finally the computational results are compared with those computed by traditional multigrid method under full -coarsening strategy in equal mesh -size.The numerical experiments verify that the present partial semicoarsening multigrid method with general mesh-size is more accurate and efficient than the traditional multigrid method with equal mesh-size discretization for anisotropic problems. ： ； ； ； Key words 3D convection diffusion equation general mesh-size fourth-order compact difference scheme multigrid method 摘 要：研究了三维对流扩散方程基于有限差分法的多重网格算法。差分格式采用一般网格步长下的二阶中心差分格式和四阶紧 致差分格式，建立了与两种格式相适应的部分半粗化的多重网格算法，构造了相应的限制算子和插值算子，并与传统的等距网格 下的完全粗化的多重网格算法进行了比较。数值研究结果表明，对于各向异性问题