An Investigation into Preconditioning Iterative Solvers for Hydrodynamic Problems
نویسندگان
چکیده
Two Krylov subspace iterative methods, GMRES and QMR, were studied in conjunction with several preconditioning techniques for solving the linear system raised from the finite element discretisation of incompressible Navier-Stokes equations for hydrodynamic problems. The preconditioning methods under investigation were the incomplete factorisation methods such as ILU(0) and MILU, the Stokes preconditioner, and the Elman-Silvester block triangular preconditioner. It is observed that the GMRES solver with the Elman-Silvester preconditioner provides faster convergence than the other methods studied here. Keywords– Krylov subspace, Navier-Stokes, preconditioned iterative methods, finite element
منابع مشابه
ACCELERATION OF GMRES CONVERGENCE FOR SOME CFD PROBLEMS: preconditioning and stabilization techniques
Large CFD problems are often solved using iterative methods. Preconditioning is mandatory to accelerate the convergence of iterative methods. This paper presents new results using several preconditioning techniques. These preconditoners are non-standard in the CFD community. Several numerical tests were carried out for solving three-dimensional incompressible, compressible and magneto-hydrodyna...
متن کاملPreconditioned Iterative Methods for Solving Linear Least Squares Problems
New preconditioning strategies for solving m × n overdetermined large and sparse linear least squares problems using the CGLS method are described. First, direct preconditioning of the normal equations by the Balanced Incomplete Factorization (BIF) for symmetric and positive definite matrices is studied and a new breakdown-free strategy is proposed. Preconditioning based on the incomplete LU fa...
متن کاملIterative Solvers for the Stochastic Finite Element Method
This paper presents an overview and comparison of iterative solvers for linear stochastic partial differential equations (PDEs). A stochastic Galerkin finite element discretization is applied to transform the PDE into a coupled set of deterministic PDEs. Specialized solvers are required to solve the very high-dimensional systems that result after a finite element discretization of the resulting...
متن کاملParallel Iterative Solvers for Ill-Conditioned Problems with Reordering
1. Preconditioned Iterative Solvers with Multicoloring In the previous work [1], author developed an efficient parallel iterative solver for finite-element applications on the Earth Simulator (ES) [2] using multi-level hybrid parallel programming model with MPI and OpenMP. The method employs three-level hybrid parallel programming model for SMP cluster architectures, consisting of MPI, OpenMP a...
متن کاملIterative Solution of Dense Linear Systems
Integral equation methods have been used with great success in electromagnetic scattering calculations and in other problems involving unbounded computational domains. Their application is in many cases limited by the storage requirements of dense matrices and also by the rapidly increasing computational time. However, the use of iterative solvers and special methods for computing the matrix-ve...
متن کامل