Linear multifrequency-grey acceleration recast for preconditioned Krylov iterations

Acceleration of Preconditioned Krylov Solvers for Bubbly Flow Problems

We consider the linear system arising from discretization of the pressure Poisson equation with Neumann boundary conditions, derived from bubbly flow problems. In the literature, preconditioned Krylov iterative solvers are proposed, but they often suffer from slow convergence for relatively large and complex problems. We extend these traditional solvers with the so-called deflation technique, t...

Preconditioned Krylov solvers for kernel regression

A primary computational problem in kernel regression is solution of a dense linear system with the N × N kernel matrix. Because a direct solution has an O(N) cost, iterative Krylov methods are often used with fast matrix-vector products. For poorly conditioned problems, convergence of the iteration is slow and preconditioning becomes necessary. We investigate preconditioning from the viewpoint ...

Preconditioned Krylov Subspace Methods for Eigenvalue Problems

Preconditioned Krylov solvers on GPUs

In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR( s ) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers’ numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner imp...

Preconditioned Krylov Subspace Methods for Transport Equations

Transport equations have many important applications. Because the equations are based on highly non-normal operators, they present diiculties in numerical computations. The iterative methods have been shown to be one of eecient numerical methods to solve transport equations. However, because of the nature of transport problems, convergence of iterative methods tends to slow for many important p...