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

This paper is concerned with the numerical approximation of the solution of the coupled wave equation of Kirchhoff type with nonlinear boundary damping and memory term using a mixed finite element method. The Raviart-Thomas mixed finite element method is one of the most prominent techniques to discretize the second-order wave equations; therefore, we apply this scheme for space discretization. Furthermore, an L2-in-space error estimate is presented for this mixed finite element approximation. Finally, the efficiency of the method is verified by a numerical example. © 2021 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd

Analysis of a fully discretized FDM-FEM scheme for solving thermo-elastic-damage coupled nonlinear PDE systems

In this paper, we consider a nonlinear PDE system governed by a parabolic heat equation coupled in a nonlinear way with a hyperbolic momentum equation describing the behavior of a displacement field coupled with a nonlinear elliptic equation based on an internal damage variable. We present a numerical scheme based on a low-order Galerkin finite element method (FEM) for the space discretization of the time-dependent nonlinear PDE system and an implicit finite difference method (FDM) to discretize in the direction of the time variable. Moreover, we present a priori estimates for the exact and discrete solutions for the pointwise-in-time $L^2$-norm. Based on the a priori estimates, we rigorously prove the convergence of the solutions of the fully discretized system to the exact solutions. Denoting the properties of the internal parameters, we find the order of convergence concerning the discretization parameters

Hierarchical LU preconditioning for the time-harmonic Maxwell equations

The time-harmonic Maxwell equations are used to study the effect of electric and magnetic fields on each other. Although the linear systems resulting from solving this system using FEMs are sparse, direct solvers cannot reach the linear complexity. In fact, due to the indefinite system matrix, iterative solvers suffer from slow convergence. In this work, we study the effect of using the inverse of $\mathcal{H}$-matrix approximations of the Galerkin matrices arising from N\'ed\'elec's edge FEM discretization to solve the linear system directly. We also investigate the impact of applying an $\mathcal{H}-LU$ factorization as a preconditioner and we study the number of iterations to solve the linear system using iterative solvers

نقد و بررسی نقش رسانه‌های اجتماعی در دوران پاندمی کرونا با تکیه بر نظریۀ تکنوپولی

با شیوع ویروس کرونا، جهان شاهد اتفاقات جدیدی شد که تاکنون مشابه آن را ندیده بود. آثار پاندمی کرونا بی‌شک تا سال‌ها با بشر باقی خواهد ماند. رسانه‌های اجتماعی در جریان این همه‌گیری به‌شدت مورد استقبال کاربران قرار گرفتند. این توجه تنها از سوی افراد نبود و دولت‌ها و سازمان‌های مختلف هم توجه ویژه‌ای به این رسانه‌ها داشتند. این افزایش اهمیت رسانه‌ها، لزوم بررسی نقش رسانه‌های اجتماعی در جریان همه‌گیری را بسیار پراهمیت می‌کند. در نقد و بررسی تأثیرات رسانه‌، تکنوپولی از کلان‌ترین نظریات موجود است. این نظریه، کنترل فرهنگ و تفکر توسط تکنولوژی جهان امروز را پیش‌بینی می‌کند و ابزار مناسب برای بررسی نقش رسانه‌ها را در اختیار ما می‌گذارد. در این مقاله، کوشیده‌ایم تا با استفاده از روش تحلیلی-انتقادی و استفاده از نظریة تکنوپولی نقش رسانه‌های اجتماعی را در دوران پاندمی کرونا مورد نقد و بررسی قرار دهیم. در ابتدا، نظریۀ تکنوپولی تبیین شده، سپس نقش و تأثیرات رسانه‌های ‌اجتماعی در دوران پاندمی کرونا با استفاده از این نظریه مورد نقد و بررسی قرار می‌گیرد. یافته‌های پژوهش، حاکی از آن است که نیل پستمن در نظریۀ تکنوپولی بسیاری از آثار منفی رسانه‌ها که اکنون با آن رو‌به‌رو هستیم را پیش‌بینی کرده بود و می‌توانیم این آثار را با توجه به‌نقد پستمن کاهش دهیم؛ همان‌طورکه پستمن احتمال می‌داد، امکان داد و ستد با تکنولوژی و رسانه وجود دارد. در موارد گوناگون، بشر موفق شده است تا تکنولوژی را به‌خدمت درآورد و از آن در جهت کمک برای رفع مشکلات پاندمی کرونا استفاده کند

A Bayesian estimation method for variational phase-field fracture problems

In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values. © 2020, The Author(s)

Using layer-wise training for Road Semantic Segmentation in Autonomous Cars

A recently developed application of computer vision is pathfinding in self-driving cars. Semantic scene understanding and semantic segmentation, as subfields of computer vision, are widely used in autonomous driving. Semantic segmentation for pathfinding uses deep learning methods and various large sample datasets to train a proper model. Due to the importance of this task, accurate and robust models should be trained to perform properly in different lighting and weather conditions and in the presence of noisy input data. In this paper, we propose a novel learning method for semantic segmentation called layer-wise training and evaluate it on a light efficient structure called an efficient neural network (ENet). The results of the proposed learning method are compared with the classic learning approaches, including mIoU performance, network robustness to noise, and the possibility of reducing the size of the structure on two RGB image datasets on the road (CamVid) and off-road (Freiburg Forest) paths. Using this method partially eliminates the need for Transfer Learning. It also improves network performance when input is noisy

COVID-19: Preliminary Clinical Guidelines for Ophthalmology Practices

The zoonotic Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) and its resultant human coronavirus disease (COVID-19) recently appeared as a global health threat that can cause severe respiratory infection and terminal respiratory distress. By the first week of April, more than 1.3 million people had been globally infected and more than 70,000 had lost their lives to this contagious virus. Clinical manifestations occur shortly after exposure, or a few days later. There is controversy regarding the transmission of the virus through the tear and conjunctiva; however, there are reports that the ocular surface might be a potential target for COVID-19. The ease of transmission of this virus at close proximity presents a risk to eyecare workers. Several recommendations have been issued by local and national organizations to address the issue of safe ophthalmic practice during the ongoing COVID-19 pandemic. These guidelines have numerous similarities; however, subtle differences exist. The purpose of this paper was to discuss measures, with a specific focus on standard precautions, to prevent further dissemination of COVID-19 at Eye Clinics. We have proposed procedures to triage suspected cases of COVID-19, considering emergency conditions.Photo Courtesy of Majid Moshirfar, MD FACS