Bilus: A block version of ilus factorization

ILUS factorization has many desirable properties such as its amenability to the skyline format, the ease with which stability may be monitored, and the possibility of constructing a preconditioner with symmetric structure. In this paper we introduce a new preconditioning technique for general sparse linear systems based on the ILUS factorization strategy. The resulting preconditioner has the same properties as the ILUS preconditioner. Some theoretical properties of the new preconditioner are discussed and numerical experiments on test matrices from the Harwell-Boeing collection are tested. Our results indicate that the new preconditioner is cheaper to construct than the ILUS preconditioner.     

Numerical implementation of the QMR algorithm by using discrete stochastic arithmetic

In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced byA, it is necessary to decide whether to construct the Lanczos vectorsv _n +1 andw _n +1 as regular or inner vectors. For a regular step it is necessary thatD _k =W _k ^T V _k is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix D_k,σ _min (D _k ), is computed and an inner step is performed ifσ _min (D _k )<∈, where ∈ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance ∈. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.     

On the preconditioning of the block tridiagonal linear system of equations

Two algorithms for computing the inverse factors of general tridiagonal and pentadiagonal matrices are obtained. Then, these algorithms are used for computing a block ILU preconditioner for the block tridiagonal linear system of equations. Some numerical results are given to show the robustness and efficiency of the preconditioner. The performance of the proposed preconditioner is compared with a recently proposed method.     

A new relaxed HSS preconditioner for saddle point problems

We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues distribution of the preconditioned matrix are presented. The preconditioned system is solved by a Krylov subspace method like restarted GMRES. Finally, some numerical experiments on test problems arisen from finite element discretization of the Stokes problem are given to show the effectiveness of the preconditioner.     

On the parameter selection in the transformed matrix iteration method

Numerical Algorithms - Recently, Axelsson and Salkuyeh in (BIT Numerical Mathematics, 59 (2019) 321–342) proposed the transformed matrix iteration (TMIT) method for solving a certain...     

First-time lidar measurement of water vapor flux in a volcanic plume

The CO₂ laser-based lidar ATLAS has been used to study the Stromboli volcano plume. ATLAS measured water vapor concentration in cross-sections of the plume and wind speed at the crater. Water vapor concentration and wind speed were retrieved by differential absorption lidar and correlation technique, respectively. Lidar returns were obtained up to a range of 3 km. The spatial resolution was 15 m and the temporal resolution was 20 s. By combining these measurements, the water vapor flux in the Stromboli volcano plume was found. To our knowledge, it is the first time that lidar retrieves water vapor concentrations in a volcanic plume.     

Investigation of Poly(ether-b-amide)/Nanosilica Membranes for CO2/CH4Separation

The results of molecular dynamics （MD） simulations on transport process of CO2 and CH4 gases in poly（ether-b- amide） （PEBAX）/nanosilica membranes are discussed. The diffusion coefficients for CH4 and CO2 gases at 6 cases with different amounts of nanosilica loading in the simulation boxes are presented. The results show that diffusion coefficients for CO2 gas in all cases are larger than those for the CH4 one. Moreover 10% nanosilica loading case shows maximum effects on diffusion coefficients and improves them by more than 68% and 157% for CO2 and CH4 gases, respectively. Additionally, the results of 3-D Cartesian trajectories and displacements curves are presented and the jumping attempt of CO2 is significantly more than that of CH4. Due to the rubbery state of PEBAX membranes in ambient temperature, the results confirm that channel lifetimes are very short and then back diffusion is not observed for this polymer.     

A new iterative method for solving a class of complex symmetric system of linear equations

We present a new stationary iterative method, called Scale-Splitting (SCSP) method, and investigate its convergence properties. The SCSP method naturally results in a simple matrix splitting preconditioner, called SCSP-preconditioner, for the original linear system. Some numerical comparisons are presented between the SCSP-preconditioner and several available block preconditioners, such as PGSOR (Hezari et al. Numer. Linear Algebra Appl. 22, 761–776, 2015) and rotate block triangular preconditioners (Bai Sci. China Math. 56, 2523–2538, 2013), when they are applied to expedite the convergence rate of Krylov subspace iteration methods for solving the original complex system and its block real formulation, respectively. Numerical experiments show that the SCSP-preconditioner can compete with PGSOR-preconditioner and even more effective than the rotate block triangular preconditioners.     

An efficient method to set up a Lanczos based preconditioner for discrete ill-posed problems

Rezghi and Hosseini [M. Rezghi, S.M. Hosseini, Lanczos based preconditioner for discrete ill-posed problems, Computing 88 (2010) 79–96] presented a Lanczos based preconditioner for discrete ill-posed problems. Their preconditioner is constructed by using few steps (e.g., k) of the Lanczos bidiagonalization and corresponding computed singular values and right Lanczos vectors. In this article, we propose an efficient method to set up such preconditioner. Some numerical examples are given to show the effectiveness of the method.