The discretization of linear partial differential equations with random data by means of the stochastic Galerkin finite element method results in general in a large coupled linear of system of equations. Using the stochastic diffusion equation as a model problem, we introduce and study a symmetric positive definite Kronecker product preconditioner for the Galerkin matrix. We compare the popular...

The paper concerns with an iterative technique for solving discretized Stokes type equations with varying viscosity coefficient. We build a special block preconditioner for the discrete system of equations and perform an analysis revealing its properties. The subject of this paper is motivated by numerical solution of incompressible non-Newtonian fluid equations. In particular, the general anal...

Motivated by the paper [16], where the authors proposed a method to solve a symmetric positive definite (SPD) system Ax = b via a sparse-sparse iterative-based projection method, we extend this method to nonsymmetric linear systems and propose a modified method to construct a sparse approximate inverse preconditioner by using the Frobenius norm minimization technique in this paper. Numerical ex...

The JOREK extended magneto-hydrodynamic (MHD) code is a widely used simulation for studying the non-linear dynamics of large-scale instabilities in divertor tokamak plasmas. Due to large scale-separation intrinsic these phenomena both space and time, computational costs simulations realistic geometry with parameters can be very high, motivating investment considerable effort optimization. In th...

In this paper, we provide new preconditioner for saddle point linear systems with (1,1) blocks that have a high nullity. The preconditioner is block triangular diagonal with two variable relaxation paremeters and it is extension of results in [1] and [2]. Theoretical analysis shows that all eigenvalues of preconditioned matrix is strongly clustered. Finally, numerical tests confirm our analysis.

In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming CrouzeixRaviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality ...

Block lower triangular matrices and block upper triangular matrices are popular preconditioners for 2×2 block matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned matrices are related.

A relaxed splitting preconditioner based on matrix splitting is introduced in this paper for linear systems of saddle point problem arising from numerical solution of the incompressible NavierStokes equations. Spectral analysis of the preconditioned matrix is presented, and numerical experiments are carried out to illustrate the convergence behavior of the preconditioner for solving both steady...

We investigate the use of Hessian Free optimization for learning deep autoencoders. One of the critical components in that algorithm is the choice of the preconditioner. We argue in this paper that the Jacobi preconditioner leads to faster optimization and we show how it can be accurately and efficiently estimated using a randomized algorithm.