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Papers by Mehrzad Ghorbani

We need differential equations for modeling and analyzing a huge amount of issues. Fractional cal... more We need differential equations for modeling and analyzing a huge amount of issues. Fractional calculus is a branch of mathematical analysis that is used in many fields of mathematical and engineering sciences such as electrical networks, fluid mechanics, control theory, electromagnetism, biology, chemistry, propagation and viscoelasticity. The most important topics in mathematics are differential equations and integral equations which are very practical and have a special place in various sciences, especially engineering sciences. We used approximate methods to obtain the results because we cannot use analytical clustering for this kind of equations. The aim of this paper is to investigate the operational matrix in order to solve the partial differential equation.

In this work, we approximate a typical model form of bivariate static Schrodinger Equation by an ... more In this work, we approximate a typical model form of bivariate static Schrodinger Equation by an appropriate approach based on bilinear finite element method (FEM), then we obtain the results of the PDE on a new type 3 feather rose coefficient function in a rectangular domain i. e., eigenfunctions or solutions. In fact, we search for influence of 3-feather rose and pass by a weak singularity barrier in the origin. We also obtain approximate eigenvalues and final stiffness matrix elements. This paper is accompanied by examples of the novel Schrodinger’s model.

Optical and Quantum Electronics, 2021

In this paper, we investigated the electronic properties of two dimensional multiabloom nanoflowe... more In this paper, we investigated the electronic properties of two dimensional multiabloom nanoflower. Also, we approximated a typical form of the Schrödinger equation through an appropriate 2-D finite element approach, and then, we have investigated the effects of different parameters such as number of ablooms, number of rose, variety geometric domain shape and systems size on the energy levels, eigenfunctions, and dipole matrix elements.

Physics Letters A, 2020

Abstract The filamentation instability and the nonlinear dynamics of the magnetic field produced ... more Abstract The filamentation instability and the nonlinear dynamics of the magnetic field produced in a current-carrying plasma are investigated in the diffusion regime. Starting the coupled fluid equations for electrons and ions and using the Ampere-Maxwell equation, a nonlinear partial differential equation for the magnetic field diffusion is obtained. This paper presents an efficient meshless method of lines using radial basis functions to approximate this equation and consequently to analyze the magnetic field diffusion and the electron density distribution in the plasma. For this purpose, we applied the multi-quadric radial basis functions on some points and found appropriate approximations. Our method provides an expansion which is smooth enough for applying on high order differential equations. This method does not depend on any meshing procedure and has good accuracy, but is seriously parameter dependent. Finally, we have compared our results with two previously well-established finite difference and Adomian decomposition methods.

In many applications, one encounters the problem of approximating 1-D curve and 2-D surfaces from... more In many applications, one encounters the problem of approximating 1-D curve and 2-D surfaces from data given on a set of scattered points. Meshless methods strategy is based on some facts: (1) deleting mesh generation and re-meshing, (2) raising smooth degree of solution, (3) localization by using compact support weights. This research presented three generalizations for ancient pseudo interpolation, localization, appending a complete polynomial to the Shepard average weighted approximation and Hermite form of Shepard and MLS method. The new bases for relevant space of approximants are developed and, when evaluated directly, improves the accuracy of evaluation of the fitted method, especially the Hermite type. In this work, we develop some efficient schemes for computing global or local approximation curves and surfaces interpolating a given smooth data. Then we raise the smooth degree of approximation and use of derivatives data. The Hermite Shepard (HSH) is straightforward and efficient.

International Journal of Modern Physics B

In this paper, we have studied the effect of conduction band nonparabolicity on wave packet broad... more In this paper, we have studied the effect of conduction band nonparabolicity on wave packet broadening in different semiconducting mediums. Here, through a fourth derivative of the wavefunction, we have included the nonparabolicity effect into the one-dimensional Schrödinger equation. We have solved this equation by means of a meshless radial base function approach. We have compared five different semiconducting mediums GaAs, GaN, AlN, InSb and GaSb and showed that the wave packet broadens slower in systems with larger effective masses and smaller nonparabolicity parameters. Thus, we can manage and control the dispersion of a Gaussian wave packet utilizing the nonparabolicity and effective mass parameters.

Optical and Quantum Electronics

Engineering Analysis with Boundary Elements

Applied Mathematics and Computation, Oct 1, 2006

Corrected fundamental solution (CFS) is a meshless method for homogeneous elliptic problems that ... more Corrected fundamental solution (CFS) is a meshless method for homogeneous elliptic problems that corrects the density function in a simple layer potential integral. In the CFS method, we apply a new expansion of density function with variable coefficients which are approximated in a finite subspace of a complete space. These coefficients are determined by the moving least square method (MLS), using a suitable weight function that its support is in the real and artificial domain.

Journal of Applied Sciences, Mar 15, 2014

Applied Mathematical Sciences, 2010

Moving Meshless methods are new generation of numerical methods for unsteady partial differential... more Moving Meshless methods are new generation of numerical methods for unsteady partial differential equations that have shock, high gradient region, high oscillatory region, boundary layer. .. . These methods link the Moving Finite Element method (MFE) by Keith Miller to Meshless methods such as, DEM, EFGM, EFPGM, SPH, RKPH, PUM, h-p Clouds,.. .. Here grid coordinates are variable, time dependent, unknown and are found together with approximate solution of time dependent PDE. This implies, exertion of indirect or implicit equi-distribution of nodes without use of equi-distribution principles with various monitor functions. Weak form system is an ODE and will be found by Galerkin and Petrov-Galerkin method and its solution by finite difference and method of lines give us approximation and nodal coordinates. Proceeding time steps, nodes move smoothly into the high gradient region and concentrates there, for handling the shock and better approximation. A penalty appended to energy functional for preventing high velocity, colliding and collapsing of nodes, prevention of concentration all the nodes in the shock region, controls their motion and also tend to well conditioning of mass matrix. Numerical solution of heat and burger equation, demonstrate the accuracy of the approximation. Among Meshless methods we only use of EFPG method by T.Belytschko and introduce the Moving Element Free Petrov-Galerkin Viscous Method (MEFPGVM) by C 2 cubic hermite base functions as test functions.

… -CHINESE INSTITUTE OF …, 2004

Moving meshless methods are new generation of numerical methods for time dependent partial differ... more Moving meshless methods are new generation of numerical methods for time dependent partial differential equations that have shock or high gradient region. These methods couple the moving finite element methods (MFE) with meshless methods. Here, grid coordinates are time ...