红黑排序混合算法收敛速度分析

The algorithm of applying the block Gauss elimination to the Red-Black or-dering matrix to reduce the order of the system then solve the reduced system byiterative methods is called Hybrid Red-Black Ordering algorithm.In this paper,we discuss the convergence rate of the hybrid methods combined with JACOBI,CG,GMRES(m).Theoretical analysis shows that without preconditioner thesethree hybrid methods converge about 2 times as fast as the corresponding natural ordering methods.For the case that all the eigenvalues is near the real axis, the GMRES(m) algorithm converges about 3 times faster than the natural ordering GMRES(m).Various numerical experiments are presented.For large scale prob-lem with preconditioners, numerical experiments show that the GMRES(m) hybrid methods converge from about 3 times to even 5 times as fast as the natural order-ing methods and the computing time is reduced to about 1/3 even 1/6 of that of the natural ordering methods.     

结合气体分子动力学方法的RKDG有限元格式求解一维Euler可压方程组

In this paper, two numerical methods are developed for solving one-dimensionl compressible ELder equations by the RKDG finite element method.The schemesare obtained based on an important relation between the Boltzmann equation andthe ELder equations.The schemes have the TVD-like property under the uniform meshes.Several numerical results also present the performance of the schemes.