Block stationary methods for nonsymmetric cyclically reduced systems arising from three-dimensional elliptic equations

被引:27
作者
Greif, C
Varah, J
机构
[1] Stanford Univ, SCCM Program, Stanford, CA 94305 USA
[2] Univ British Columbia, Dept Comp Sci, Vancouver, BC V6T 1Z4, Canada
关键词
cyclic reduction; stationary methods; three-dimensional problems; convection-diffusion;
D O I
10.1137/S0895479897317715
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a three-dimensional convection-diffusion model problem and examine systems of equations arising from performing one step of cyclic reduction on an equally spaced mesh, discretized using the seven-point operator. We present two ordering strategies and analyze block splittings of the resulting matrices. If the matrices are consistently ordered relative to a given partitioning, Young's analysis for the block Gauss-Seidel and block SOR methods can be applied. We compare partitionings for which this property holds with ones where the matrices do not have Property A yet still give rise to an efficient solution process. Bounds on convergence rates are derived and the work involved in solving the systems is estimated.
引用
收藏
页码:1038 / 1059
页数:22
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