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.     

Wound healing improvement by curcumin‐loaded electrospun nanofibers and BFP‐MSCs as a bioactive dressing

Wound healing, one of the most complex processes of the body involving the cooperation of several important biomolecules and pathways, is one of the major therapeutic and economic issues in regenerative medicine. The present study aimed to introduce a novel electrospun curcumin (Cur)‐incorporated chitosan/polyvinyl alcohol/carbopol/polycaprolactone nanofibrous composite for concurrent delivery of the buccal fat pad‐derived mesenchymal stem cells (BFP‐MSCs) and Cur to a full‐thickness wound on the mouse model. Scaffolds were characterized structurally using scanning electron microscopy (SEM), fluorescence microscopy imaging and Fourier‐transform infrared spectroscopy, and toxicity of the scaffolds was also evaluated after BFP‐MSC seeding by SEM imaging and 3‐(4,5 dimethyiazol‐2‐1)‐2‐5‐diphenyl tetrazolium bromide (MTT) assay. Then, its influence on the wound‐healing process was investigated as a wound dressing for a full‐thickness skin defect in mouse model. Results demonstrated that the designed composite scaffolds have the capability for cell seeding and support their growth and proliferation. Macroscopic and histopathological characteristics were evaluated at the end of the 7 and 14 days after surgery, and their results showed that our designed scaffold groups accelerated the wound‐healing process compared with the control group. Among those, scaffold/Cur, scaffold/Cur/BFP‐MSC and scaffold/BFP‐MSC groups demonstrated more wound repair efficacy. These results indicated that the combined grafts can be used to improve the wound‐healing process, and therefore, the electrospun nanofibers presented in this study, Cur and BFP‐MSC together, were demonstrated to have promising potential for wound‐dressing applications.     

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.     

Three-dimensional dynamic Green’s functions for a multilayered transversely isotropic half-space

With the aid of a method of displacement potentials, an efficient and accurate analytical derivation of the three-dimensional dynamic Green’s functions for a transversely isotropic multilayered half-space is presented. Constituted by proper algebraic factorizations, a set of generalized transmission–reflection matrices and internal source fields that are free of any numerically unstable exponential terms are proposed for effective computations of the potential solution. Three-dimensional point-load Green’s functions for stresses and displacements are given, for the first time, in the complex-plane line-integral representations. The present formulations and solutions are analytically in exact agreement with the existing solutions given by Pak and Guzina (2002) for the isotropic case. For the numerical computation of the integrals, a robust and effective methodology which gives the necessary account of the presence of singularities including branch points and poles on the path of integration is laid out. A comparison with the existing numerical solutions for multilayered isotropic half-space is made to confirm the accuracy of the numerical solutions.     

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.     

Three-dimensional dynamic Green’s functions in transversely isotropic tri-materials

An analytical derivation of the elastodynamic fundamental solutions for a transversely isotropic tri-material full-space is presented by means of a complete representation using two displacement potentials. The complete set of three-dimensional point-load, patch-load, and ring-load Green’s functions for stresses and displacements are given, for the first time, in the complex-plane line-integral representations. The formulation includes a complete set of transformed stress-potential and displacement-potential relations in the framework of Fourier expansions and Hankel integral transforms, that is useful in a variety of elastodynamic as well as elastostatic problems. For the numerical computation of the integrals, a robust and effective methodology is laid out. Selected numerical results for point-load and patch-load Green’s functions are presented to portray the dependence of the response on layering, the frequency of excitation, and type of loading.     

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...     

Chemical composition of the essential oil of Pelargonium quercetorum Agnew. of Iran

The volatile constituents in the essential oil of Pelargonium quercetorum Agnew., growing wild in Kurdistan, Iran were investigated through GC and GC/MS technique. Twenty-six compounds, representing 21 (80.77%) of the total oil were identified. The main components were: alpha-pinene (25.28%), alpha-fenchyl acetate (20.63%), limonene (9.94%), beta-caryophyllene (8.20%), camphene (4.31%), delta-cadinene (3.32%), beta-pinene (3.21%), alpha-amorphene (2.80%), valencene (2.73%), ledene (2.25%) and p-cymene (1.63%).