徐肖飞 , 徐光楠 , 刘志远 , 吴鹏 , 彭金霖 , 许保磊 ,
引言：铁电薄膜材料是一类具有优异性能的功能材料而被广泛应用于电子元器件中。理想状态下铁电薄膜材料为绝缘体或宽禁带半导体，但实际中铁电薄膜材料会因为制备或者在元器件中因为界面引入带电粒子或缺陷，引起较大的电流，影响电子元器件的性能。我们建立了考虑挠曲电效应及带电粒子漂移扩散的相场模型用以研究挠曲电效应对 Pt/PZT/Pt 多层结构的 I-V 特性的影响。 COMSOL Multiphysics® 的使用：我们使用 COMSOL 建立了一个二维平面模型(如图1)，使用的是 PDE 接口，未使用案例库模型。 结果：我们通过模拟得到了不同挠曲电耦合系数下铁电薄膜的应变梯度云图(如图2)、极化云图(如图3)和电势云图(如图4)，做出了不同挠曲电耦合系数下铁电薄膜的 I-V 曲线。 结论：极化与纵向应变梯度之间的耦合会导致铁电薄膜内电势的降低，增加载流子空穴在铁电薄膜内的浓度 ...
P. Sandin , A. Lockby , M. Ögren , M. Gulliksson 
School of Science and Technology, Örebro, Sweden
We demonstrate a new method of finding stationary solutions to nonlinear equations using a dynamical damped oscillatory model to minimize an energy functional. The method can be used for diverse physical problems and is here demonstrated both for finding stationary solutions to the heat equation and to the nonlinear Schrödinger equation. The method is very general and can handle equations with ...
Inverse Problem and a New Device to Estimate Thermal Conductivity of Composite Phase Change Material
M. Karkri , A. Nachaoui 
 Université Paris-Est, CERTES, Créteil Cedex, France
 Département de Mathématiques 2, Nantes Cedex, France
A new experimental device has been developed in order to characterize the phase change material (PCM) thermal properties (thermal conductivity k, sensible and latent heat thermal energy storage, cp and Lf) in the solid phase, during the solid-liquid transition and in the liquid phase. It allows to measure cylindrical samples of maximum 60 mm radius and 10 mm thick. A typical measurement consists ...
A. Weddemann, and V. Thümmler
Bielefeld University, Germany
ALE-methods are frequently used to solve systems of partial differential equations (PDEs) on moving domains. The main idea of these methods is to incorporate the time evolution of the domain into the equations. However, the motion of the domain with respect to time induces convective fluxes in the resulting equations. These can lead to stability problems of the numerical method if they become ...
M. Gobbert, and S. Yang
Department of Mathematics and Statistics, University of Maryland, Baltimore, MD, USA
The convergence order of finite elements is related to the polynomial order of the basis functions used on each element, with higher order polynomials yielding better convergence orders. However, two issues can prevent this convergence order from being achieved: the lack of regularity of the PDE solution and the poor approximation of curved boundaries by polygonal meshes. We show studies for ...
I. Neitzel, U. Prüfert, and T. Slawig
DFG priority program SPP 1253, Technische Universität Berlin, Berlin, Germany
DFG research center Matheon, Technische Universität Berlin, Germany
DFG Cluster of Excellence The Future Ocean, DFG priority progam SPP 1253, Christian-Albrechts-Universität zu Kiel, Kiel, Germany
We use COMSOL Multiphysics to solve time-dependent optimal control problems for partial differential equations whose optimality conditions can be formulated as a PDE. For a class of linear-quadratic model problems we summarize known analytic results on existence of solutions and first order optimality conditions that exhibit the typical feature of time-dependent control problems, namely the fact ...
Bridging the Complexity Gap in Modern Engineering Education with COMSOL Multiphysics® Software - new
L. Fromme, C. Schröder
Bielefeld University of Applied Sciences, Bielefeld, Germany
Multiphysics simulations play an important role in researchanddevelopment in almost all disciplines. Therefore it is necessary to teach them at the universities to provide the industry with well-trained graduate students. In our lectures about the finite element method we use a simple but rich enough example problem, which can be solved analytically. By comparing numerical and analytical ...
Relativistic Quantum Mechanics Applications Using the Time Independent Dirac Equation in COMSOL Multiphysics® Software
A. J. Kalinowski ,
 Consultant, East Lyme, CT, USA
The paper illustrates the use of the COMSOL Multiphysics® software (via the “Coefficient-Form PDE” option) for obtaining the relativistic quantum mechanics wave function ψm(x,y,ω), m=1,4 as a solution to the time independent Dirac equations. Once having ψm(x,y,ω), it can be used to compute the probability density ρ′=Σ|ψm|^2 of a particle being at a specific point within the spatial field under ...
Finite Element Convergence and Speed-Up Studies Using COMSOL Multiphysics and LiveLink™ for MATLAB® with Large Assembly Models
H. Pourzand, A.H. Aziz, A. Singh
Pennsylvania State University, State College, PA, USA
COMSOL Multiphysics along with its LiveLink™ for MATLAB® is used to investigate the needed number of elements and the required order of Lagrangean p element for a number of different simulation models. For this task, convergence study, speed up testing and interactive meshing is performed on a large assembly model which is also imported using the LiveLink™ for SolidWorks®. As a test bench, the ...
V. S. Nagaraja, Ramanuja H. S., Deepak K, S. L. Pinjare
Electronics and Communication Engineering, Nitte Meenakshi Institute of Technology, Bangalore, Karnataka, India
In this work, a MEMS based condenser microphone [1,2] using Polyimide as the diaphragm has been designed. The microphone structure has a backplate placed on top of the diaphragm. The backplate and the diaphragm are made up of polyimide. The two polyimide plates are separated by air gap which is achieved by using Aluminium as a sacrificial layer in between, which is etched away to create the air ...