Dual Formulations of Mixed Finite Element Methods with Applications

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.     

圆筒谐振式密度传感器的计算及有限元分析

谐振式传感器是一种新型高精度的传感器.选用薄壁圆筒作为谐振子,设计了短管谐振式密度传感器.用有限元法建立了圆筒谐振子的模型,通过MATLAB软件编程,计算出合理的谐振子参数,对其频率密度特性进行了分析,并给出了振子的振型分布.仿真结果表明,传感器系数为K0=-181.59 kg/m3,K1=1.17×10-8 kg/m3·s,K2=4.93×10 8 kg/m3·s2.     

功能梯度三相复合材料圆柱壳的非线性振动研究

论文研究了一种由环氧树脂、石墨烯纳米片、碳纤维制成的功能梯度三相复合材料圆柱壳的非线性振动响应.基于一阶剪切变形理论和von-Karman几何非线性关系,考虑到温湿效应、气动力和外激励的共同作用,利用Hamilton原理建立了两端固支圆柱壳的非线性偏微分运动方程.利用Galerkin法将非线性偏微分运动方程离散成一组相互耦合的二阶非线性常微分方程,利用伪弧长延拓法求解非线性常微分方程组,给出对应的幅频响应曲线.本论文中仅考虑湿度和外激励等参数的变化对新型三相复合材料圆柱壳结构非线性振动响应的影响,分析了湿度和外激励的变化对功能梯度三相复合材料圆柱壳共振响应的影响.     

机翼机身对接接头非线性有限元分析

接头是飞机结构中常见的结构连接形式,也往往是强度破坏或疲劳破坏的部位.有时为了更大的挖掘接头结构的承载能力,甚至还要考虑结构局部进入塑性区应力分布,属于材料非线性和力边界非线性的耦合问题.试图通过直接求解偏微分方程得到接头接触问题的解析解是很难的,甚至可以说是不可能的.基于非线性有限元分析方法,借助大型通用有限元软件MARC的弹塑性接触分析模块,通过不断细化网格的方法来对机翼机身对接接头进行非线性耦合分析.建立了对接接头的弹塑性接触有限元模型,给出了接头的应力分布以及屈服状况.数值模拟结果与实际情况相符,数值模拟结果为机身机翼对接接头的设计提供了重要的数据.     

An incremental elastic-plastic Finite Element solver in a workstation cluster environment Part I. Formulations and parallel processing

We discuss solution schemes for the incremental elastic-plastic structural problem, discretized by means of the Finite Element method. Attention is focused on their formulation and implementation in a parallel computing environment defined by a cluster of workstations connected by means of a network. The availability of parallel computers allows one to consider possible formulations and solution strategies so far not considered competitive with the classical Newton-like schemes implying the definition of an elastic-plastic tangent stiffness matrix. The solution strategies herein considered are based on the explicit integration of the actual elastic-plastic rate problem. This, in turn, is phrased in terms of two different formulations, whose relative advantages—particularly with respect to their integration in parallel—are discussed. A − gl (displacemen plastic multiplier) formulation of the structural rate theory of plasticity [1], integrated by means of an explicit, element-by-element scheme, seems to be the most promising one.     

八节点四边形等参元非线性有限元分析

应用几何非线性有限元方法 ,研究了大变形问题中的纸张力学特性 ,采用修正的拉格朗日格式 ,推导了八节点四边形等参元用于非线性问题分析时的增量平衡方程 ,并编写了有关有限元计算程序 .应用该程序 ,对纸张在悬臂状态及自重作用下的静变形、无阻尼动态响应以及有阻尼动态响应分别进行计算 ,并与日本理光公司提供的试验数据以及MARC的计算结果进行比较 ,证实了该方法对于纸张的非线性力学特性的分析是有效的 ,可以为办公设备的合理设计提供科学依据     

Unreinforced Masonry Walls: Nonlinear Finite Element Analysis with a Unified Constitutive Model

This paper presents a unified model for characterizing the behavior of masonry structures. The model is based on the Disturbed State Concept (DSC) with modified hierarchical single yield surface (HISS) plasticity, which is called DSC/HISS-CT and which is used to simulate the behavior of masonry structures. The model uses two HISS yield surfaces for compressive and tensile behavior. The proposed constitutive model is verified by comparing numerical predictions with results available from test data; the comparisons are found to be highly satisfactory. A new explicit formula is also presented to estimate the strength of unreinforced masonry structures.     

Context-Aware Navigation Element for Collaborative Nonlinear Video Authoring Tool

In recent years, online video streaming service has become more popular. High internet bandwidth, powerful mobile devices, and advance of video annotation techniques have raised the popularity of the rapidly growing interactive video genre. This research focuses on enabling collaboration among authors of interactive nonlinear videos that provide alternative story plots for viewers to choose as part of their interactive behaviors. We discuss the “irrelevant navigation elements” problem, which could occur when multiple nonlinear video authors want to reuse a shared interactive video. Then, we propose a system called MAVINS, a managed navigation element for interactive nonlinear videos, to solve the aforementioned problem. The system is implemented as a web-based authoring tool and interactive video player for user-creator and user-viewer, respectively. Experimentation in self-directed learning was conducted to demonstrate the problem that occurs in current approaches as well as to evaluate the effectiveness of the proposed system to solve that particular problem. As the result, the proposed system eliminated all the irrelevant navigation elements and, on average, reduced 54.55% of the total amount of displayed navigation elements on the shared videos.     

Error Analysis of Mixed Finite Element Methods for Nonlinear Parabolic Equations

In this paper, we prove a discrete embedding inequality for the Raviart–Thomas mixed finite element methods for second order elliptic equations, which is analogous to the Sobolev embedding inequality in the continuous setting. Then, by using the proved discrete embedding inequality, we provide an optimal error estimate for linearized mixed finite element methods for nonlinear parabolic equations. Several numerical examples are provided to confirm the theoretical analysis.     

三维互连阻抗的混合边界积分方程提取算法

基于混合边界元三维互连阻抗提取方法,针对其离散线性方程组的特点,提出有效的稀疏矩阵组织和矩阵行列调整技术,以及一种预条件迭代求解技术,这些技术结合起来形成了一种有效的三维互连阻抗提取算法.该算法在保证计算精度的同时,速度优于MIT最新的提取算法FastImp.最后通过2个典型互连结构的数值实验验证了该算法的有效性.     

Two-Grid Method for Nonlinear Reaction-Diffusion Equations by Mixed Finite Element Methods

In this paper, we investigate a scheme for nonlinear reaction-diffusion equations using the mixed finite element methods. To linearize the mixed method equations, we use the two-grid algorithm. First, we solve the original nonlinear equations on the coarse grid, then, we solve the linearized problem on the fine grid used Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O(h^frac12)H=mathcal{O}(h^{frac{1}{2}}). As a result, solving such a large class of nonlinear equations will not much more difficult than the solution of one linearized equation.     

基于接触有限元模型的虚拟手指力建模研究

触觉反馈是虚拟现实应用中使人获得沉浸感的重要方式。随 显示技术的日趋成熟,触觉和力反馈的研究的焦点之一,如何度量虚拟手在接触物体时反馈的力的大小 是力反馈中的首要一步,对此,该文在研究了力反馈类型的基础上,给和指与虚拟物体间的接触数学模型,提出了基于接触有限元的接触数学模型,并有杉ＡＮＳＹＳ对霏 均匀有理Ｂ样条的手指表面和虚拟按钮间的接触变形和力分布情况进行了计算,得出了力反馈所需要的接触力大小。     

A Posteriori Error Estimates of Two-Grid Finite Element Methods for Nonlinear Elliptic Problems

In this article, we study the residual-based a posteriori error estimates of the two-grid finite element methods for the second order nonlinear elliptic boundary value problems. Computable upper and lower bounds on the error in the \(H^1\)-norm are established. Numerical experiments are also provided to illustrate the performance of the proposed estimators.     

Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation

Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.     

Poisson-Boltzmann方程的并行有限元求解及网格自适应生成

说明如何利用并行自适应有限元软件平台PHG 求解生物分子溶液体系的非线性Poisson-Boltzmann方程,并介绍一种解决这类问题的方法,它将网格生成与自适应计算过程结合在一起,可自动产生合适的网格,避免复杂的曲面网格生成步骤.之前的网格生成工作有：（1） TMSmesh生成高斯曲面的三角网格; （2） TransforMesh删除自相交的三角网格; （3） ISO2Mesh提高表面网格质量3个步骤.而基于PHG的自适应加密模块可以在逐次调整网格的同时保持动态负载平衡,高效地得到计算网格用于近似求解非线性Poisson-Boltzmann方程.计算了小球模型和AChE系统,分别从误差指示子下降阶和溶剂化能收敛的角度验证了方法的有效性,并且还将网格生成算法成功地应用于gA离子通道.     

非直线排列剥叶元件的疲劳寿命分析

阐述了整杆式甘蔗收获机械非直线排列剥叶元件疲劳分析的总体思路．利用计算机仿真分析的方法分析了剥叶元件装夹参数及其注塑加工过程中产生的缺陷对元件寿命的影响，提出了不同工况剥叶元件疲劳分析的有限元计算模型．通过仿真分析，方便、快捷地得出剥叶元件疲劳寿命预估值，并用试验证明了其有效性．     

Parallel Formulations of Decision-Tree Classification Algorithms

Classification decision tree algorithms are used extensively for data mining in many domains such as retail target marketing, fraud detection, etc. Highly parallel algorithms for constructing classification decision trees are desirable for dealing with large data sets in reasonable amount of time. Algorithms for building classification decision trees have a natural concurrency, but are difficult to parallelize due to the inherent dynamic nature of the computation. In this paper, we present parallel formulations of classification decision tree learning algorithm based on induction. We describe two basic parallel formulations. One is based on Synchronous Tree Construction Approach and the other is based on Partitioned Tree Construction Approach. We discuss the advantages and disadvantages of using these methods and propose a hybrid method that employs the good features of these methods. We also provide the analysis of the cost of computation and communication of the proposed hybrid method. Moreover, experimental results on an IBM SP-2 demonstrate excellent speedups and scalability.     

Optimal Control Formulations of Vibration Reduction Problems

Design of controls to move a flexible body such as a robot arm while minimizing unwanted vibrations has been described in many papers and presented in many forms. For the vibration reduction issue alone, it is shown that almost all the proposed designs can be formulated as optimal controls of either the fixed final time or the minimum time type. Furthermore, it is shown that under reasonable assumptions the two types have the same solution and are thus equivalent. Continuous time, tapped-delay-line input shaping filters, and discrete controls are considered. It is shown that the discrete equivalent of the general vibration reduction problem is a convex problem for the fixed final time case and quasi-convex for the free final time problem. The two formulations are compared in terms of computation complexity as well as practical implementation issues.