En
  • دکتری (1387)

    ریاضی کاربردی

    دانشگاه صنعتی امیرکبیر، تهران، ایران

  • کارشناسی‌ارشد (1382)

    ریاضی کاربردی

    دانشگاه صنعتی شریف، تهران، ایران

  • کارشناسی (1378)

    ریاضی کاربرد در کامپیوتر

    دانشگاه صنعتی امیرکبیر، تهران، ایران

  • بهینه سازی، حساب تغییرات و مسایل کنترل بهینه.
  • آنالیز عددی، محاسبات ماتریسی (روشهای عددی در جبر خطی).
  • پردازش تصویر.
  • حسابان کسری.
  • نظریه تقریب.
  • روشهای عددی در علوم و مهندسی.
  • حل عددی مدلهای زیستی.
  • مدل سازی ریاضی.
  • ٍطراحی هندسی.

    محمدرضا اصلاحچی، استاد دانشگاه تربیت مدرس. او دارای مدرک M.S. از دانشگاه صنعتی شریف (1382) و دکتری بهینه سازی از دانشگاه صنعتی امیرکبیر (پلی تکنیک تهران) (1387). او عضو بنیاد ملی نخبگان ایران است. علایق تحقیقاتی او شامل بهینه سازی غیرخطی، محاسبات ماتریسی و کاربردهای آن در علوم داده و یادگیری ماشین است. او بیش از 70 مقاله در زمینه آنالیز عددی، بهینه سازی و کاربردها منتشر کرده است.

    ارتباط

    رزومه

    Image Denoising by a Novel Variable-order Total Fractional Variation Model

    Fariba Kazemi Golbaghi, M. R Eslahchi, Mansour Rezghi
    Journal PapersMathematical Methods in the Applied Sciences , 2021 January , {Pages }

    Abstract

    The total variation model performs very well for removing noise while preserving edges. However, it gives a piecewise constant solution which often leads to the staircase effect, consequently small details such as textures are filtered out in the denoising process. Fractional‐order total variation method is one of the major approaches to overcome such drawbacks. Unlike their good quality of fractional order, all these methods use a fixed fractional order for the whole of the image. In this paper, a novel variable‐order total fractional variation model is proposed for image denoising, in which the order of fractional derivative will be allocated automatically for each pixel based on the context of the image. This kind of selection is abl

    Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery

    Farzaneh Nasresfahani, M. R Eslahchi
    Journal PapersApplied Mathematics and computation , 2021 January , {Pages }

    Abstract

    The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolics, one elliptic and one ordinary differential equations that are coupled together and describe the growth of a plaque in the artery. We start our discussion by using the front fixing method to fix the free domain and simplify the model by changing the mix boundary condition to a Neumann one by applying suitable changes of variables. Then, after employing a nonclassical finite difference and the collocation method on this model, we prove the stability and convergence of methods. Finally, some numerical results are considered to show the efficiency of the method.

    Application of finite difference method in solving a second‎- ‎and fourth-order PDE blending denoising model

    MR ‎Eslahchi, S Esmaili, N Namaki, R Salehi
    Journal Papers , , {Pages }

    Abstract

    A New PDE Learning Model for Image Denoising

    F Ashoori, MR Eslahchi
    Journal Papers , , {Pages }

    Abstract

    M\" untz Sturm-Liouville Problems: Theory and Numerical Experiments

    H khosravian Arab, MR Eslahchi
    Journal Papers , , {Pages }

    Abstract

    Optimal Control for a Nonlinear Stochastic Parabolic Model of Language Competition

    Sakine Esmaili, MR Eslahchi
    Journal PapersarXiv preprint arXiv:2001.00206 , 2020 January 1, {Pages }

    Abstract

    In this investigation, an optimal control problem for a stochastic mathematical model of language competition is studied. We have considered the stochastic model of language competition by adding the stochastic terms to the deterministic model to take into account the random perturbations and uncertainties caused by the environment to have more reliable model. The model has formulated the population densities of the speakers of two languages, which are competing against each other to be saved from destruction, attract more speakers and so on, using two nonlinear stochastic parabolic equations. Four factors including the status of the languages and the growth rates of the populations are considered as the control variables (which can be cont

    Extension of Tikhonov regularization method using Linear Fractional Programming

    S Mohammady, M. R. Eslahchi
    Journal PapersJournal of Computational and Applied Mathematics , 2020 January , {Pages }

    Abstract

    This paper presents an extended form of the Tikhonov regularization method. This method is obtained by adding some parameters to the Tikhonov regularization method. The added parameters are obtained by solving a linear fractional programming problem. Finally, some numerical examples are given to show the efficiency and validity of the new method.

    The convergence and stability analysis of a numerical method for solving a mathematical model of language competition

    Sakine Esmaili, M. R Eslahchi
    Journal PapersApplied Numerical Mathematics , Volume 151 , 2020 January , {Pages 119-140 }

    Abstract

    In this study, a combination of spectral and fixed point methods is applied to solve a mathematical model of language competition. The considered model has formulated the competition between two languages in which the population density of speakers of each language is modeled by a nonlinear parabolic equation. Due to the fact that the problem is nonlinear, the fixed point method is employed to change the problem to a linear one in each step of iterations. After that, the coupled parabolic equations are solved using the spectral method in each step. It is proven that the constructed sequence converges to the exact solution of the problem, which results in the convergence of the method. Then, by applying the method for solving the perturbed p

    Optimal Control for a Nonlinear Stochastic Parabolic Model of Population Competition

    Sakine Esmaili, M. R Eslahchi
    Journal PapersOptimization , 2020 January , {Pages }

    Abstract

    Analysis of Ciarlet–Raviart mixed finite element methods for solving damped Boussinesq equation

    Maryam Parvizi, Amirreza Khodadadian, M. R. Eslahchi
    Journal PapersJournal of Computational and Applied Mathematics , 2020 January , {Pages }

    Abstract

    In this paper, we consider the numerical solution of damped Boussinesq equation using Ciarlet–Raviart mixed finite element method. An implicit finite difference scheme is used for the time discretization. A priori error estimates are analyzed and stability analysis of the method is shown. We obtain an optimal error estimate in L 2 norm with quadratic or higher-order element, for both semi-and fully discrete finite element approximations. Finally, numerical examples are given to verify the theoretical results.

    Muntz Pseudo Spectral Method: Theory and Numerical Experiments

    Hassan Khosravian-Arab, Mohammad Reza Eslahchi
    Journal Paperscommunications in nonlinear science and numerical simulation , 2020 January , {Pages }

    Abstract

    This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-M?ntz functions presented by the authors recently. These basis functions are, in fact, generalized forms of the newly generated Jacobi based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail. The pseudo-spectral differentiation (and integration) matrices have been extracted in two different manners. Some numerical experiments are provided to show the efficiency and capability of these newly generated non-classical Lagrange basis functions.

    A Hybrid Image Denoising Method Based on Integer and Fractional-order Total Variation

    Fariba Kazemi Golbaghi, Mansoor Rezghi, M. R Eslahchi
    Journal PapersIranian Journal of Science and Technology, Transactions A: Science , 2020 January , {Pages }

    Abstract

    This paper introduces a new hybrid fractional model for image denoising. This proposed model is a combination of two models Rudin–Osher–Fatemi and fractional-order total variation. We try to use the advantages of two mentioned models. In this regard, after introducing an appropriate norm space, we prove the existence and uniqueness of the presented model. Furthermore, finite difference method is employed for numerically solving the obtained equation. Finally, the results illustrate the efficiency of the proposed model that yields good visual effects and a better signal-to-noise ratio.

    A mixed finite element method for solving coupled wave equation of Kirchhofftype with nonlinear boundary damping and memory term

    Maryam Parvizi, Amirreza Khodadadian, Mohammad Reza Eslahchi
    Journal PapersAuthorea Preprints , 2020 April 13, {Pages }

    Abstract

    In this paper, we deal with the numerical approximation of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term. Since the equation is a nonlinear equation, the Raviart-Thomas mixed finite element method is one of the most suitable techniques to obtain the approximated solution. In this paper, we will show that using the Raviart-Thomas method the optimal convergence order of the scheme can be achieved. To that end, we prove the necessary lemmas and the main theorem. Finally, the efficiency of the method is certified by numerical examples.

    Application of reproducing kernel method for solving a class of two-dimensional linear integral equations with weakly singular kernel

    Mohammad Reza Eslahchi, Maryam Rezaeimirarkolaei
    Journal PapersJournal of New Researches in Mathematics , Volume 6 , Issue 25, 2020 August 22, {Pages 159-166 }

    Abstract

    In this paper, we will present a new method for solving a class of two-dimensional linear Volterra integral equation of the second kind with weakly singular kernel from Abel type in the reproducing kernel space. The reproducing kernel function is discussed in detail. Weak singularity of problem is removed by applying integration by parts. Further, improper integral belongs to L_2 (Ω). In our method the exact solution ϕ(x,t) is represented in the form of series in the reproducing kernel space W(ω), and the approximate solution ϕ_n (x,t) is constructed via truncating the series to n terms. Convergence analysis of the method is proved in detail. Some numerical examples are also studied to demonstrate the efficiency and accuracy of the pres

    Global convergence of a new sufficient descent spectral three-term conjugate gradient class for large-scale optimization

    M. R Eslahchi, Sanaz. Bojari
    Journal PapersOptimization Methods and Software , 2020 January , {Pages }

    Abstract

    To solve a large-scale unconstrained optimization problem, in this paper we propose a class of spectral three-term conjugate gradient methods. We indicate that the proposed class, in fact, generates sufficient descent directions and also fulfill Dai–Liao conjugacy condition. We prove the global convergence of the presented class for either uniformly convex or general smooth functions under some suitable conditions, in detail. Finally, in a set of numerical experiments which contains eight conjugate gradient methods and 260 standard problems, we illustrate the efficiency and effectiveness of our class.

    Error analysis of finite difference/collocation method for the nonlinear coupled parabolic free boundary problem modeling plaque growth in the artery

    Farzaneh Nasresfahani, Mohammad Reza Eslahchi
    Journal PapersarXiv preprint arXiv:1907.04097 , 2019 July 9, {Pages }

    Abstract

    The main target of this paper is to present a new and efficient method to solve a nonlinear free boundary mathematical model of atherosclerosis. This model consists of three parabolics, one elliptic and one ordinary differential equations that are coupled together and describe the growth of a plaque in the artery. We start our discussion by using the front fixing method to fix the free domain and simplify the model by changing the mix boundary condition to a Neumann one by applying suitable changes of variables. Then, after employing a nonclassical finite difference and the collocation method on this model, we prove the stability and convergence of methods. Finally, some numerical results are considered to show the efficiency of the method.

    Global convergence of a family of modified BFGS methods under amodified weak-Wolfe-Powell line search for nonconvex functions

    Sanaz Bojari, M. R Eslahchi
    Journal Papers4OR , 2019 January , {Pages }

    Abstract

    In this paper, we consider an unconstrained optimization problem and propose a new family of modified BFGS methods to solve it. As it is known, classic BFGS method is not always globally convergence for nonconvex functions. To overcome this difficulty, we introduce a new modified weak-Wolfe–Powell line search technique. Under this new technique, we prove global convergence of the new family of modified BFGS methods and the classic BFGS method, for nonconvex functions. Furthermore, all members of this family have at least error order. Our obtained results from numerical experiments on 77 standard unconstrained problems, indicate that the algorithms developed in this paper are promising and more effective than some similar alg

    Two families of scaled three-term conjugate gradient methods with sufficient descent property for nonconvex optimization

    Sanaz Bojari, M. R Eslahchi
    Journal PapersNumerical Algorithms , 2019 January , {Pages }

    Abstract

    In this paper, we present two families of modified three-term conjugate gradient methods for solving unconstrained large-scale smooth optimization problems. We show that our new families satisfy the Dai-Liao conjugacy condition and the sufficient descent condition under any line search technique which guarantees the positiveness of. For uniformly convex functions, we indicate that our families are globally convergent under weak-Wolfe-Powell line search technique and standard conditions on the objective function. We also establish a weaker global convergence theorem for general smooth functions under similar assumptions. Our numerical experiments for 260 standard problems and seven other recently developed conjugate gradient methods illustra

    Solving a fractional parabolic-hyperbolic free boundary problem which models the growth of tumor with drug application using finite difference-spectral method

    Sakine Esmaili, F Nasresfahani, MR Eslahchi
    Journal PapersarXiv preprint arXiv:1908.07386 , 2019 August 19, {Pages }

    Abstract

    In this paper, a free boundary problem modelling the growth of tumor is considered. The model includes two reaction-diffusion equations modelling the diffusion of nutrient and drug in the tumor and three hyperbolic equations describing the evolution of three types of cells (ie proliferative cells, quiescent cells and dead cells) considered in the tumor. Due to the fact that in the real situation, the subdiffusion of nutrient and drug in the tumor can be found, we have changed the reaction-diffusion equations to the fractional ones to consider other conditions and study a more general and reliable model of tumor growth. Since it is important to solve a problem to have a clear vision of the dynamic of tumor growth under the effect of the nutr

    M\" untz Pseudo Spectral Method: Theory and Numerical Experiments

    Hassan Khosravian-Arab, Mohammad Reza Eslahchi
    Journal PapersarXiv preprint arXiv:1908.02306 , 2019 August 6, {Pages }

    Abstract

    This paper presents two new non-classical Lagrange basis functions which are based on the new Jacobi-M?ntz functions presented by the authors recently. These basis functions are, in fact, generalizations form of the newly generated Jacobi based functions. With respect to these non-classical Lagrange basis functions, two non-classical interpolants are introduced and their error bounds are proved in detail. The pseudo-spectral differentiation (and integration) matrices have been extracted in two different manners. Some numerical experiments are provided to show the efficiency and capability of these newly generated non-classical Lagrange basis functions.

    دروس نیمسال جاری

    • دكتري
      مدل سازي و طراحي هندسي ( واحد)
      دانشکده علوم ریاضی، گروه رياضي كاربردي
    • دكتري
      مدل سازي و طراحي هندسي ( واحد)

    دروس نیمسال قبل

    • كارشناسي ارشد
      روش هاي عددي در جبر خطي ( واحد)
      دانشکده علوم ریاضی، گروه رياضي كاربردي
    • دكتري
      مباحث ويژه در نظريه تقريب ( واحد)
    • حسن , خسرویان عرب
    • 1396
      سلحشوري, زهرا
      كنترل همزماني در شبكه‌هاي پيچيده‌ي وزن‌دار
    • 1396
      سعادت سعادت ابادي, عاطفه
    • 1397
      محمودي, شهلا
    • 1392
      محمدي, سميه
      روش هاي منظم سازي جديد براي حل مسائل بد وضع گسسته خطي
    • 1394
      عاشوري قاضي محله, فاطمه
    • 1395
      نصراصفهاني, فرزانه
      داده ای یافت نشد
    • رییس دانشکده علوم ریاضی 1388
    • معاونت دانشجویی و فرهنگی دانشگاه تربیت مدرس 1388-1392
    • دانشجوی نمونه کشوری در مقطع دکتری در سال 1386.
    • رتبه اول مقطع دکتری ریاضی کاربردی دانشگاه صنعتی امیرکبیر.
    • رتبه اول مقطع کارشناسی ارشد ریاضی کاربردی دانشگاه صنعتی شریف.
    • رتبه اول مقطع کارشناسی ریاضی کاربرد در کامپیوتر دانشگاه صنعتی امیرکبیر.

    مهم

    جدید

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