Linda Alzaben - Academia.edu (original) (raw)

Papers by Linda Alzaben

Research paper thumbnail of On the stabilization of a virtual element method for an acoustic vibration problem

arXiv (Cornell University), Jan 8, 2024

In this paper we introduce an abstract setting for the convergence analysis of the virtual elemen... more In this paper we introduce an abstract setting for the convergence analysis of the virtual element approximation of an acoustic vibration problem. We discuss the effect of the stabilization parameters and remark that in some cases it is possible to achieve optimal convergence without the need of any stabilization. This statement is rigorously proved for lowest order triangular element and supported by several numerical experiments.

Research paper thumbnail of Prospective study of depression among dialysis patients in Saudi Arabia

International Urology and Nephrology, 2015

Research paper thumbnail of Multi-Step Preconditioned Newton Methods for Solving Systems of Nonlinear Equations

The study of different forms of preconditioners for solving a system of nonlinear equations, by u... more The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

Research paper thumbnail of On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity

Computational Methods in Applied Mathematics

In this paper we provide some more details on the numerical analysis and we present some enlighte... more In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lamé parameters and on the underlying mesh.

Research paper thumbnail of Assessment of local and non–local turbulent flow components on turbulence–flame interaction

Journal of Physics: Conference Series, 2021

In the framework of turbulence-flame interaction, the flame is characterized by the gradient of a... more In the framework of turbulence-flame interaction, the flame is characterized by the gradient of a reactive scalar such as the progress variable, whereas the turbulence is represented by the vorticity and the strain rate. Quantitative assessment of this interaction is performed trough the study of the coupled transport between these quantities that are subject to the effects of heat release and chemical reactions. The present analysis aims at improving the understanding of the small scale turbulence – flame interaction properties, through the introduction of an additive decomposition of the strain rate and vorticity fields into their local and non-local components. The respective role of the local and non-local effects is studied for a broad range of Karlovitz numbers, by virtue of direct numerical simulations (DNS) of turbulent, premixed, lean, and statistically planar flames of methane-air. In the conditions of the present study, the alignment between flame front normals and the st...

Research paper thumbnail of On the spectrum of the finite element approximation of a three field formulation for linear elasticity

ArXiv, 2021

We continue the investigation on the spectrum of operators arising from the discretization of par... more We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit.

Research paper thumbnail of Computation of Eigenvalues in Linear Elasticity with Least-Squares Finite Elements: Dealing with the Mixed System

14th WCCM-ECCOMAS Congress, 2021

In this paper we discuss some aspects related to the practical implementation of a method that ha... more In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted.

Research paper thumbnail of Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence

Fluids, 2021

The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotatio... more The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurat...

Research paper thumbnail of COMBINATORIAL EXTENSIONS OF CERTAIN t-DESIGNS

King Abdulaziz University, 2005

Research paper thumbnail of On the stabilization of a virtual element method for an acoustic vibration problem

arXiv (Cornell University), Jan 8, 2024

In this paper we introduce an abstract setting for the convergence analysis of the virtual elemen... more In this paper we introduce an abstract setting for the convergence analysis of the virtual element approximation of an acoustic vibration problem. We discuss the effect of the stabilization parameters and remark that in some cases it is possible to achieve optimal convergence without the need of any stabilization. This statement is rigorously proved for lowest order triangular element and supported by several numerical experiments.

Research paper thumbnail of Prospective study of depression among dialysis patients in Saudi Arabia

International Urology and Nephrology, 2015

Research paper thumbnail of Multi-Step Preconditioned Newton Methods for Solving Systems of Nonlinear Equations

The study of different forms of preconditioners for solving a system of nonlinear equations, by u... more The study of different forms of preconditioners for solving a system of nonlinear equations, by using Newton’s method, is presented. The preconditioners provide numerical stability and rapid convergence with reasonable computation cost, whenever chosen accurately. Different families of iterative methods can be constructed by using a different kind of preconditioners. The multi-step iterative method consists of a base method and multi-step part. The convergence order of base method is quadratic and each multi-step add an additive factor of one in the previously achieved convergence order. Hence the convergence of order of an m-step iterative method is m + 1. Numerical simulations confirm the claimed convergence order by calculating the computational order of convergence. Finally, the numerical results clearly show the benefit of preconditioning for solving system of nonlinear equations.

Research paper thumbnail of On the Spectrum of an Operator Associated with Least-Squares Finite Elements for Linear Elasticity

Computational Methods in Applied Mathematics

In this paper we provide some more details on the numerical analysis and we present some enlighte... more In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced recently. We show that, although the formulation is robust in the incompressible limit for the source problem, its spectrum is strongly dependent on the Lamé parameters and on the underlying mesh.

Research paper thumbnail of Assessment of local and non–local turbulent flow components on turbulence–flame interaction

Journal of Physics: Conference Series, 2021

In the framework of turbulence-flame interaction, the flame is characterized by the gradient of a... more In the framework of turbulence-flame interaction, the flame is characterized by the gradient of a reactive scalar such as the progress variable, whereas the turbulence is represented by the vorticity and the strain rate. Quantitative assessment of this interaction is performed trough the study of the coupled transport between these quantities that are subject to the effects of heat release and chemical reactions. The present analysis aims at improving the understanding of the small scale turbulence – flame interaction properties, through the introduction of an additive decomposition of the strain rate and vorticity fields into their local and non-local components. The respective role of the local and non-local effects is studied for a broad range of Karlovitz numbers, by virtue of direct numerical simulations (DNS) of turbulent, premixed, lean, and statistically planar flames of methane-air. In the conditions of the present study, the alignment between flame front normals and the st...

Research paper thumbnail of On the spectrum of the finite element approximation of a three field formulation for linear elasticity

ArXiv, 2021

We continue the investigation on the spectrum of operators arising from the discretization of par... more We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares approximation of linear elasticity. We discuss in particular the distribution of the discrete eigenvalues in the complex plane and how they approximate the positive real eigenvalues of the continuous problem. The dependence of the spectrum on the Lamé parameters is considered as well and its behavior when approaching the incompressible limit.

Research paper thumbnail of Computation of Eigenvalues in Linear Elasticity with Least-Squares Finite Elements: Dealing with the Mixed System

14th WCCM-ECCOMAS Congress, 2021

In this paper we discuss some aspects related to the practical implementation of a method that ha... more In this paper we discuss some aspects related to the practical implementation of a method that has been introduced recently for the approximation of the eigenvalues of the linear elasticity problem. The scheme, based on a least-squares finite element formulation, gives rise to a non-symmetric discrete formulation that may have complex eigenvalues. Moreover the algebraic eigenvalue problem to be solved is singular, so that the theoretical estimates about the convergence of the scheme should be carefully interpreted.

Research paper thumbnail of Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence

Fluids, 2021

The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotatio... more The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurat...

Research paper thumbnail of COMBINATORIAL EXTENSIONS OF CERTAIN t-DESIGNS

King Abdulaziz University, 2005