Factorization of the incompressible Stokes operator linking pressure and velocity is revisited.The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Ar...Factorization of the incompressible Stokes operator linking pressure and velocity is revisited.The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability.It is shown that the Stokes operator can be inversed within an acceptable computational effort.This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix.It is shown,additionally,that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers,as well as for other problems where convergence of iterative methods slows down.Implementation of the Stokes operator inverse to time-steppingbased formulation of the Newton and Arnoldi iterations is discussed.展开更多
We present simultaneous reduction algorithms for two(nonsymmetric)matrices A and B to upper Hessenberg and lower Hessenberg forms,respectively.One is through the simultaneous similarity reduction and the other is thro...We present simultaneous reduction algorithms for two(nonsymmetric)matrices A and B to upper Hessenberg and lower Hessenberg forms,respectively.One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration.The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm.We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system.It is proved that the model reduction has the desirable moment matching property.展开更多
文摘Factorization of the incompressible Stokes operator linking pressure and velocity is revisited.The main purpose is to use the inverse of the Stokes operator with a large time step as a preconditioner for Newton and Arnoldi iterations applied to computation of steady three-dimensional flows and study of their stability.It is shown that the Stokes operator can be inversed within an acceptable computational effort.This inverse includes fast direct inverses of several Helmholtz operators and iterative inverse of the pressure matrix.It is shown,additionally,that fast direct solvers can be attractive for the inverse of the Helmholtz and Laplace operators on fine grids and at large Reynolds numbers,as well as for other problems where convergence of iterative methods slows down.Implementation of the Stokes operator inverse to time-steppingbased formulation of the Newton and Arnoldi iterations is discussed.
基金Research of R.Li is supported in part by NSF grants DMS-1115834 and DMS-1317330and a Research Gift Grant from Intel Corporation.Research of Q.Ye is supported in part by NSF Grants DMS–1318633 and DMS-1317424.
文摘We present simultaneous reduction algorithms for two(nonsymmetric)matrices A and B to upper Hessenberg and lower Hessenberg forms,respectively.One is through the simultaneous similarity reduction and the other is through a Lanczos–Arnoldi-type iteration.The algorithm that uses the Lanczos–Arnoldi-type iteration can be considered as a generalization of both the nonsymmetric Lanczos algorithm and the standard Arnoldi algorithm.We shall also apply our reduction to construct a model reduction for certain kind second-order single-input single-output system.It is proved that the model reduction has the desirable moment matching property.
