DOMAIN DECOMPOSITION PRECONDITIONERS FOR SECOND-ORDER HYPERBOLIC EQUATIONS ON L-SHAPED REGIONS  

作　　者：金小庆 王朝光 

机构地区：[1]Faculty of Science and Technology,University of Macao,Macao. [2]Department of Mathematics,University of Hong Kong,Hong Kong.

出　　处：《Numerical Mathematics A Journal of Chinese Universities(English Series)》1995年第1期54-62,共9页

摘　　要：Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjugate gradient method. For the constant-coefficient second-order hyperbolic equaions with initial and Dirichlet boundary conditions,we prove that the conditionnumber of the preconditioned interface system is bounded by 2+x2 2+0.46x2 where x is the quo-tient between the lime and space steps. Such condition number produces a convergence rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equations.Linear systems arising from implicit time discretizations and finite difference space discretizations of second-order hyperbolic equations on L-shaped region are considered. We analyse the use of domain deocmposilion preconditioner.s for the solution of linear systems via the preconditioned conjugate gradient method. For the constant-coefficient second-order hyperbolic equaions with initial and Dirichlet boundary conditions,we prove that the conditionnumber of the preconditioned interface system is bounded by 2+x2 2+0.46x2 where x is the quo-tient between the lime and space steps. Such condition number produces a convergence rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equations.

关 键 词：Domain decomposition hyperbolie equation CAPACITANCE matrix condition number preconditioned CONJUGATE gradient method 

分 类 号：O175.26[理学—数学]