Study on generalized magneto-thermoelastic problems by FEM in time domain

This paper presents an investigation of temperature, displacement, stress, and induced magnetic field in a half space perfectly-conductive plate. Finite element equations regarding generalized magneto-thermoelasticity problems with two relaxation times （i.e., the G-L theory） are derived using the principle of virtual work. For avoiding numerical complication involved in inverse Laplace and Fourier transformation and low precision thereof, the equations are solved directly in time-domain. As a numerical example, the derived equation is used to investigate the generalized magneto-thermoelastic behavior of a semi-infinite plate under magnetic field and subjecting to a thermal shock loading. The results demonstrate that FEM can faithfully predict the deformation of the plate and the induced magnetic field, and most importantly can reveal the sophisticated second sound effect of heat conduction in two-dimensional generalized thermoelastic solids, which is usually difficult to model by routine transformation methods. A peak can be observed in the distribution of stress and induced front and the magnitude of magnetic field at the heat wave the peak decreases with time, which can not be obtained by transformation methods. The new method can also be used to study generalized piezo-thermoelastic problems.

Optimization of a precise integration method for seismic modeling based on graphic processing unit

General purpose graphic processing unit （GPU） calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method （PIM） for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.

High order symplectic conservative perturbation method for time-varying Hamiltonian system

This paper presents a high order symplectic con- servative perturbation method for linear time-varying Hamil- tonian system. Firstly, the dynamic equation of Hamilto- nian system is gradually changed into a high order pertur- bation equation, which is solved approximately by resolv- ing the Hamiltonian coefficient matrix into a ＂major compo- nent＂ and a ＂high order small quantity＂ and using perturba- tion transformation technique, then the solution to the orig- inal equation of Hamiltonian system is determined through a series of inverse transform. Because the transfer matrix determined by the method in this paper is the product of a series of exponential matrixes, the transfer matrix is a sym- plectic matrix; furthermore, the exponential matrices can be calculated accurately by the precise time integration method, so the method presented in this paper has fine accuracy, ef- ficiency and stability. The examples show that the proposed method can also give good results even though a large time step is selected, and with the increase of the perturbation or- der, the perturbation solutions tend to exact solutions rapidly.

A Model-free Approach to Fault Detection of Continuous-time Systems Based on Time Domain Data

In this paper, a model-free approach is presented to design an observer-based fault detection system of linear continuoustime systems based on input and output data in the time domain. The core of the approach is to directly identify parameters of the observer-based residual generator based on a numerically reliable data equation obtained by filtering and sampling the input and output signals.

Multiresolution method for bending of plates with complex shapes

A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.

精细积分方法的发展与扩展应用

钟万勰院士于1991年首先提出计算矩阵指数的精细积分方法,其要点是2N类算法和增量存储。精细积分方法可给出矩阵指数在计算机意义上的精确解,为常微分方程的数值计算提供了高精度、高稳定性的算法,现已成功应用于结构动力响应、随机振动、热传导以及最优控制等众多领域。本文首先介绍矩阵指数精细积分方法的提出、基本思想和发展;然后依次介绍在时不变/时变线性微分方程、非线性微分方程以及大规模问题求解中发展起来的各种精细积分方法,分析了其优缺点和适用范围;最后介绍了精细积分方法的基本思想在两点边值问题、椭圆函数和病态代数方程等问题的扩展应用,进一步展示了该思想的特色。

EFFICIENT TIME DOMAIN ANALYSIS of ARBITRARILY SHAPED CONDUCTING WIRE STRUCTURES

We developed an efficient analysis the current induced in the wire structure. The analysis based on the time-Domain Integral Equation, in which a thin wire approximation is used. The time-domain electric field integral equation is used with the moment method to develop a numerical procedure for treating problems of scattering by arbitrary shaped bodies. We present an efficient numerical method for calculating the electromagnetic scattering from arbitrary shaped conducting bodies in the time domain with a comprehensive treatment of a single, straight thin wire. A time domain electric field integral equation is formulated for the problem of an arbitrary shape. The solution method is based on the moment method to solve the straight thin-wire problem.

基于时域积分的温差流量传感器仿真与试验

目前对于温差流量传感器的研究处于摸索阶段,传感器温度场与流量关系不明确,开展传感器的模拟仿真和试验有助于进一步提高传感器的分辨率和稳定性。为此,通过COMSOL仿真软件对测速传感器温度场进行了仿真分析和试验研究,探究了流量和持水率对测速传感器温度场的影响规律,明确了流量和持水率与时域积分结果的关系。试验结果表明:流量和持水率与积分结果均呈单调递减关系,与仿真结果一致,且在流量0~30 m^(3)/d,持水率0~100%的条件下,测速传感器的分辨率达到了1 m^(3)/d。所得结论可为温差流量检测方法的应用提供理论参考。

基于双积分滑模控制的DAB电压控制研究

提出一种基于双积分滑模控制的双向有源全桥(DAB)DC-DC变换器电压控制策略,该策略在模型精度要求低、控制器设计流程简单的情况下,可以获得良好的控制效果。首先,基于单移相调制方式建立变换器的降阶模型。然后,采用双积分滑模控制理论设计变换器的输出电压控制器。设计过程通过引入时域分析法进行滑模面系数的选取分析。最后,仿真和实验结果表明了所提控制策略的有效性。

基于时域二端口模型的综合能源系统气网动态仿真算法

为实现能源多梯度利用并减少环境污染,气-电耦合的综合能源系统(integrated energy system,IES)逐渐占据全球能源结构的重要部分。为明晰系统运行特性并充分挖掘能源子网调度潜力,综合能源系统动态仿真研究逐渐深入。天然气网中,管道传输过程深刻影响着其动态过程。然而现有管道传输过程时域仿真算法存在着精度与效率的两难。为解决上述问题,提出一种基于时域二端口模型的综合能源系统气网动态仿真算法。首先基于特征线法,构建气网源荷节点关系矩阵,进一步给出时域二端口模型;随后参考特征线法数值格式,构建状态量空间分布矩阵,用于获取气网状态量分布,并提出基于时域二端口模型和分布矩阵的气网动态仿真算法。算例结果表明,所提出的方法具有高效率和高精度两大优势,适合于气-电耦合的综合能源系统的较长时间仿真。

集成电路封装设计领域中一种高精度泪滴生成方法研究

本文旨在应对集成电路封装设计领域中泪滴形成的高精度挑战,在探讨集成电路芯片封装过程中对于印刷电路板生产领域内泪滴技术存在的局限性进行深入分析的基础上,本文提出了一项提高泪滴形成精确度的新型方法。该技术在泪滴特性配置、初步处理、核心程序决策、准则操控等领域实现了重要进展,达到了泪滴构造的微观尺度精确度。本研究在技术层面展现了独创性并且在实践操作中显示了高效能、稳定性佳等优点,拥有宽广的商业成长空间。

基于预估-校正的Generalized-α法及其在非线性结构动力学中的应用

直接积分法是求解动力学方程的一种有效方法。应用一种预估-校正的Generalized-α法对结构大变形动力学问题进行分析求解,并与Newmark法和Bathe法进行对比研究。首先预估当前计算步的解,然后以预估值作为起始值进行非线性迭代计算,并对解不断校正,直到满足收敛条件,进入下一时间步的计算。在保证Generalized-α法性能的基础上,简化了非线性迭代公式,便于编程实现。通过壳和实体的大变形动力学算例,证明了本文方法具有较高的稳定性和精度。

Applying a Step Approach Method in Solving the Multi-Frequency Radiation From a Complex Obstacle

In this paper,a step approach method in the time domain is developed to calculate the radiated waves from an arbitrary obstacle pulsating with multiple frequencies.The computing scheme is based on the Boundary Integral Equation and derived in the time domain;thus,the time-harmonic Neumann boundary condition can be imposed.By the present method,the values of the initial conditions are set to zero,and the approach process is carried forward in a loop from the first time step to the last.At each time step,the radiated pressure on each element is updated.After several loops,the correct radiated pressures can be obtained.A sphere pulsating with a monopole frequency in an infinite acoustic domain is calculated first.This result is compared with the analytical solution,and both of them are in good agreement.Then,a complex-shaped radiator is taken as the studied case.The pulsating frequency of this case is multiple,and the waves propagate in half space.It is shown that the present method can treat multiple-frequency pulsation well,even when the radiator is a complex shape,and a robust convergence can be attained quickly.

MEASURING PRECISION OF INDUCED POLARIZATION METHOD

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传输线方程高精度直接积分的数值求解方法

提出一种基于精细积分法与时域微分求积法相结合的传输线方程的数值求解方法。首先将传输线方程采用基于紧致有限差分法的四阶差分格式进行空间离散,得到关于时间的一阶线性常微分方程组,四阶差分格式对于空间微分有很好的近似精度。然后利用精细积分法与微分求积法对一阶线性常微分方程组进行数值求解。通过理论分析可知,与传统的传输线方程数值求解方法——时域有限差分法(Finite difference time domain,FDTD)相比,所提方法不涉及到状态矩阵求逆运算,保证了数值求解精度,并且其数值稳定性与计算时间、空间步长无关,可采用大步长进行数值计算,能够有效提高计算效率。最后利用仿真实例进行算法验证,结果显示,相比于时域有限差分法,所提方法能够抑制数值振荡,提高了计算精度。

基于时域模型的电-气综合能源系统分布式鲁棒状态估计

高效准确的状态估计(SE)技术是电-气综合能源系统(IEGS)安全稳定运行的关键。现有的IEGS-SE方法常采用有限元差分模型描述气网动态特性。该模型需引入冗余的时空微元,难以兼顾SE精度和计算复杂度。为此,提出一种基于时域模型的IEGS分布式鲁棒SE方法,在保证精度的前提下提升计算效率。首先,基于时域模型推导出以真实节点压强为状态量的气网状态空间模型,实现气网模型的简化和降维。在此基础上,以卡尔曼滤波算法为框架,提出有限边界信息交互的分布式IEGS-SE策略,以解决不同子系统多管理主体之间的信息壁垒问题。最后,利用噪声自适应算法准确跟踪时变噪声参数,提升所提方法的鲁棒性。仿真算例证明,所提方法在保护各子系统隐私的条件下,有效提高了SE精度,抑制了坏数据影响,且计算效率远高于传统有限元差分法。

基于多层面改进多域法的航行船舶时域水动力分析

针对航行船舶三维时域水动力分析问题,本文采用多域高阶边界元法(MDHOBEM, Multi-Domain Higher Order Boundary Element Method)开展研究,通过假设控制面,将计算域分为内域和外域两部分,内域采用Rankine面元法,外域使用自由面格林函数法,内外域联立求解。从内域、外域、波浪激励三个层面改进多域法的精度、计算效率,以适应不同工况需求。内域重新推导非线性边界条件,考虑入射波对绕辐射问题计算的影响,提高大幅波浪中运动计算精度;外域采用垂向积分形式自由面格林函数,提高格林函数积分计算的收敛性、稳定性及计算效率;波浪激励采用高阶谱(HOS, High Order Spectral)方法生成演化的波场,考虑波浪自身的非线性,提高对非线性现象的捕捉和模拟能力。以C11船为对象,研究内域非线性改进对船舶大幅运动计算精度的提高;以S175集装箱船为对象,验证外域垂向积分对运动及波阻增加计算效率和稳定性的提高;对比S175在线性波场和非线性波场中的运动,论证考虑非线性波场对运动计算的影响;以某内倾船为对象,研究不同层次改进对参数横摇现象捕捉的影响,验证非线性波浪激励对多域法非线性现象捕捉能力的提升;整体上形成不同层面改进多域法,为不同工况下时域水动力分析提供理论和程序支撑。

适用于有耗型德拜色散媒质电磁特性仿真的RI-CDI-FDTD方法及程序实现

提出了一种新的处理有耗型德拜色散媒质的单步蛙跳遵从发散隐式-时域有限差分(complying divergence implicit FDTD,CDI-FDTD)方法.从频域下的Maxwell方程出发,利用傅里叶变换将电磁场分量从频域转换到时域,并采用递归积分(recursive integration,RI)方法对频域-时域转换过程中存在的积分项进行近似处理.然后应用单步蛙跳隐式格式对时域Maxwell方程和辅助变量进行差分离散,推导出有耗型德拜色散媒质的RI-CDI-FDTD算法的迭代公式.接着利用von Neumann方法验证了基于RI方法的CDI-FDTD算法的无条件稳定特性,最后通过数值算例验证了本文所提方法的正确性和有效性.

基于锥形渐变耦合结构的可扩展多模弯曲波导

提出了一种基于锥形渐变耦合结构的可扩展多模弯曲波导。该器件利用模式等效折射率匹配原理,通过对称的锥形渐变耦合结构,实现高阶模式与基模的相互转化,完成多模弯曲传输功能。同时,结合时域有限差分方法和粒子群优化算法,优化锥形渐变耦合结构区域,提升器件性能。实验测试结果表明,在1520~1600 nm的波长范围内,当输入模式分别为TE_0、TE_1、TE_2、TE_(3)和TE_(4)时,该器件的插入损耗分别小于1.71 dB、3.04 dB、2.90 dB、3.16 dB和4.00 dB,对应的串扰分别小于-10.60 dB、-11.35 dB、-10.92 dB、-10.35 dB和-11.45 dB。

一种处理弹性动力边界元法中奇异积分的方法

利用边界元法求解瞬态弹性动力学问题时,时域基本解函数的分段连续性和奇异性为该问题的求解带来很大的困难。为了解决时域基本解中的奇异性问题,本文依据柯西主值的定义,对经过时间解析积分之后的时域基本解进行奇异值分解,将其分成奇异和正则积分两部分;其中正则部分可通过采用常规高斯积分方法来计算,而奇异部分具有简单的形式,可以利用解析积分计算。经过上述操作之后,就可以达到直接消除时域基本解中奇异积分的目的。和传统方法相比,本文方法并不依赖静力学基本解来消除奇异性,是一种直接求解方法。最后给定两个数值算例来验证本文提出方法的正确性和可行性,结果表明使用本文算法可以解决弹性动力学边界积分方程中的奇异性问题。