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This study presents some new iterative algorithms based on the gradient method to solve general constrained systems of conjugate transpose matrix equations for both real and complex matrices. In addition, we analyze the convergence properties of these methods and provide numerical techniques to determine the solutions. The effectiveness of the proposed iterative methods is demonstrated through various numerical examples employed in this study. [ABSTRACT FROM AUTHOR]

The incompressible miscible displacement of two-dimensional Darcy–Forchheimer flow is discussed in this paper, and the mathematical model is formulated by two partial differential equations, a Darcy–Forchheimer flow equation for the pressure and a convection–diffusion equation for the concentration. The model is discretized using a fully mixed virtual element method (VEM), which employs mixed VEMs to solve both the Darcy–Forchheimer flow and concentration equations by introducing an auxiliary flux variable to ensure full mass conservation. By using fixed point theory, we proved the stability, existence and uniqueness of the associated mixed VEM solution under smallness data assumption. Furthermore, we obtain optimal error estimates for concentration and auxiliary flux variables in the |$\texttt {L}^{2}$| - and |$\textbf {L}^{2}$| -norms, as well as for the velocity in the |$\textbf {L}^{2}$| -norm. Finally, several numerical experiments are presented to support the theoretical analysis and to illustrate the applicability for solving actual problems. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann method (LBM) is a powerful fluid flow solver. Using this method to solve other PDEs might be a difficult task. The first challenge is to find a suitable local equilibrium distribution function (EDF) capable of recovering the desired PDE. The next difficulty arises from the explicit nature of LBM. The conditional stability of the LBM algorithm affects the numerical solution accuracy. Damped Kuramoto–Sivashinsky (DKS) equation is a fourth–order PDE that recently challenged many numerical methods' abilities. This equation is highly sensitive to a parameter that causes three states of solutions in a small interval of freedom. In this paper, we challenged LBM to solve the two–dimensional DKS equation by finding EDF using the Chapman–Enskog analysis up to the fourth–order. Also, the von Neumann analysis and a simple genetic algorithm are applied to find reliable values for the free parameters. Furthermore, a modification on image-based ghost node method is proposed for implementation of the boundary conditions in the complex geometries. [ABSTRACT FROM AUTHOR]

This study presents some new iterative algorithms based on the gradient method to solve general constrained systems of conjugate transpose matrix equations for both real and complex matrices. In addition, we analyze the convergence properties of these methods and provide numerical techniques to determine the solutions. Then we prove that the optimal parameters of the new algorithm satisfy a constrained optimization problem. The effectiveness of the proposed iterative methods is demonstrated through various numerical examples employed in this study and compared the results by some existing algorithms. [ABSTRACT FROM AUTHOR]

This paper introduces an extension of a fully discrete matrix–vector form (MVF) for the lattice Boltzmann method (LBM) to handle the multiple relaxation time parameter (MRT) LBM. The proposed approach offers a more efficient and practical framework for simulating fluid flows, with the added benefit of being able to handle complex geometries using the image-based ghost (IBG) method. The advantages and limitations of this approach are discussed, including its simplicity in linear algebraic extension, parallel computing capability, computational speed, and memory usage. The results of numerical experiments demonstrate the improved computational efficiency of the proposed method, highlighting its potential for future applications in various fields of computational fluid dynamics. [ABSTRACT FROM AUTHOR]

Purpose: The main aim of the current paper is to find a numerical plan for hydraulic fracturing problem with application in extracting natural gases and oil. Design/methodology/approach: First, time discretization is accomplished via Crank-Nicolson and semi-implicit techniques. At the second step, a high-order finite element method using quadratic triangular elements is proposed to derive the spatial discretization. The efficiency and time consuming of both obtained schemes will be investigated. In addition to the popular uniform mesh refinement strategy, an adaptive mesh refinement strategy will be employed to reduce computational costs. Findings: Numerical results show a good agreement between the two schemes as well as the efficiency of the employed techniques to capture acceptable patterns of the model. In central single-crack mode, the experimental results demonstrate that maximal values of displacements in x- and y- directions are 0.1 and 0.08, respectively. They occur around both ends of the line and sides directly next to the line where pressure takes impact. Moreover, the pressure of injected fluid almost gained its initial value, i.e. 3,000 inside and close to the notch. Further, the results for non-central single-crack mode and bifurcated crack mode are depicted. In central single-crack mode and square computational area with a uniform mesh, computational times corresponding to the numerical schemes based on the high order finite element method for spatial discretization and Crank-Nicolson as well as semi-implicit techniques for temporal discretizations are 207.19s and 97.47s, respectively, with 2,048 elements, final time T = 0.2 and time step size τ = 0.01. Also, the simulations effectively illustrate a further decrease in computational time when the method is equipped with an adaptive mesh refinement strategy. The computational cost is reduced to 4.23s when the governed model is solved with the numerical scheme based on the adaptive high order finite element method and semi-implicit technique for spatial and temporal discretizations, respectively. Similarly, in other samples, the reduction of computational cost has been shown. Originality/value: This is the first time that the high-order finite element method is employed to solve the model investigated in the current paper. [ABSTRACT FROM AUTHOR]

Verbal and oral apraxia are two possible consequences of stroke. It seems that there are not sufficient studies regarding the frequency of these disorders. This study aimed to evaluate the frequency of Verbal and oral apraxia. In addition, the relationship between apraxia and some variables such as age, gender, and education, as well as the relationship between types of apraxia with each other, and damaged areas of the brain in apraxia of the oral system in Persian-speaking patients with stroke were studied. In this descriptive-analytical study, 42 patients participated using the convenient sampling method. Verbal and oral apraxia were assessed using the oral and verbal apraxia tasks for adults test. Data were analyzed using independent t-test, Chi-square, and Fisher's exact test. The frequency of patients with oral apraxia was 35.7%, those with verbal apraxia was 2.3%, and the combination of both verbal and oral apraxia was 4.7%. People with apraxia were significantly older than those without apraxia. There was not any significant relationship between apraxia and gender, apraxia and education, and oral apraxia with verbal apraxia (p < 0.05). The present study's findings showed the high frequency of post-stroke apraxia and the high rate of its incidence with age. [ABSTRACT FROM AUTHOR]