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.

In this paper we consider the problem of preconditioning symmetric positive definite matrices of the form Aα = A+αI where α > 0. We discuss how to cheaply modify an existing sparse approximate inverse preconditioner for A in order to obtain a preconditioner for Aα. Numerical experiments illustrating the performance of the proposed approaches are presented. AMS subject classification (2000): 65F...

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.

We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization distributed optimal control problem together with time-periodic parabolic equations. An upper bound spectral radius method is given which always less than 1. So conv...

A linear-solver preconditioner for the pressure systems in reservoir simulation based on Proper Orthogonal Decomposition (POD) is developed and investigated. The POD approach entails the use of a lower-dimensional space to approximate the original high-dimensional space. Essentially, POD can be considered as a Singular Value Decomposition (SVD) approach. The POD approximation error can be estim...