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

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 deocmposition preconditioners far 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 condition number of the preconditioned interface system is bounded by (2+α~2)/(2+0.46α~2) where α it the quo- tient between the time and space steps. Such condition number produces a convergnce rale that is independent of gridsize and aspect ratios. The results could be extended to parabolic equa- tions.