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 ...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.展开更多
文摘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.
