快速多极边界元法用于扩散光学断层成像研究

在求解扩散光学断层成像中的正向问题时, 目前普遍采用有限元法, 但是随着实际模型规模的增大, 有限元法的计算量问题日益显著, 而边界元法则由于可以降低计算维度使计算量减少而备受关注. 本文以均匀的高散射介质为模型, 研究了将快速多极边界元法用于扩散光学断层成像的正向问题. 快速多极边界元法利用核函数的多极展开, 将常规边界元法中系数矩阵和迭代矢量的乘积项等价为相应四叉树结构的一次递归, 再结合广义最小残量法进行迭代求解. 将计算结果和蒙特卡罗法的模拟结果进行了比较, 表明利用快速多极边界元法的模拟结果和蒙特卡罗法的结果有很好的一致性. 研究结果验证了快速多极边界元法可以用于扩散光学断层成像, 为其大规模和实时成像带来可观的前景. 关键词： 扩散光学断层成像 边界元法 快速多极边界元法     

热传导问题的边界元法

前言 边界元法是基于经典积分方程和有限元概念的一种数值方法,它主要应用于弹性力学和势理论问题。近些年来,用边界元法求解热传导问题已经引起注意。 本文从格林公式入手,对稳态和非稳态的热传导问题推出其边界元法的基本方程。对二个算例的计算结果表明,边界元法求解热传导问题节省计算工作量,精度较高。     

分区均匀介质静电场的求解

1分区均匀介质静电场求解方法的回顾分区均匀介质静电场的求解是电磁学课程中比较有难度和有特色的内容.有两种情形的分区均匀介质静电场问题可以解析求解:一种是介质-介质界面与撤去电介质时的电场线平行;另一种是介质-介质界面与撤去电介质时的电场线垂直.它是唯一性定理应用的一个生动的实例,并且涉及到静     

具有线性温度梯度的管道及消声器声学特性的边界元法计算

采用摄动法将具有线性温度梯度介质中的声传播方程化为Ｈｅｌｍｈｏｌｔｚ方程，然后用边界元法进行计算，由边界元法计算出消声器的四极参数，从而预测传递损失等消声量。文中计算了直管段的四极参数及膨胀腔的传递损失，并与一维理论结果进行了比较。     

多网格谱元法及其在高性能计算中的应用*

针对传统谱元法在每个单元内只能存在单一均匀介质,应用在复杂非均匀介质的波传播模拟中可能造成极大计算规模的问题,发展了多网格谱元法。该方法在谱元法单元内引入独立的辅助网格,用于精细描述单元内的介质和外力分布变化,在较稀疏的主网格上进行波场的求解。基于声波和弹性波方程推导了多网格谱元法公式,并对几种典型模型进行了波场的数值模拟。与传统谱元法的对比结果表明,此算法在复杂非均匀介质的弹性波传播模拟中可以利用较少的网格点数达到不低于传统算法的精度。此外,实现了并行化的多网格谱元法,获得了较好的并行效率。     

面向杆系结构的离散元异步长计算方法

为了提升离散元法处理连续介质问题的计算效率, 提出一种基于重叠颗粒的离散元分区异步长计算方法来处理连续介质问题。该方法采用颗粒分割将连续介质划分为若干子分区, 各分区采用velocity-Verlet积分格式求解运动方程。相邻分区通过重叠颗粒构成局部耦合区域, 边界数据传递过程中不涉及插值和截断过程。数值算例表明, 该方法在保证高精度的同时有效地降低了计算时间。在实际应用中可以有针对性地将连续介质划分为不同尺度颗粒的分区, 根据问题规模及分区颗粒尺度特性采用不同时间步长, 节省存储空间且大幅提升计算效率。     

管道及消声器学特性的边界元法计算

从流体力学的基本方程出发，导出等截面管内具有平均流和线性温度梯度时的三维声传播方程，然后采用迭代法将其化成可用边界积分方程表示的形式，最后用边界元法求解，由边界元法计算消声器的四极参数，从而可预测传递损失等声学特性，文中计算了膨胀腔内传递损失，并与一维理论结果进行了比较。     

特解边界元法数值解三维Pennes方程及其应用

应用特解边界元法对非稳态的三维Pennes方程求解,将解分为一满足泊松方程的通解与一特解之和,通解按照边界元法求解,特解用分离变量法给出,与位置有关的部分采用截断多项式,逐时间段计算边界元的温度及热流值,然后计算域内点的值,并将该方法用于热疗温度场的数值实例计算。     

叶栅绕流的边界元法

一、前言 边界元法是继差分法和有限元法之后发展起来的一种新的数值计算方法。由于它有输入数据少,计算时间短,解的精度高等特点,引起了世界各国的重视。近几年,我国也开始了边界元法的研究,但在叶轮机械方面,边界元法的应用甚少。本文的目的就是探讨将边界元方法用于求解叶栅中的气体流动问题。     

任意迴转面叶栅气动边界元计算

一、前言 本文是作者继文献[1]之后在叶轮机中推广应用边界元法解决气动问题的又一次尝试。文中应用边界元法求解了任意迴转面叶栅气动正问题。计算了一个压气机叶栅和一个透平叶栅。     

Control of extraordinary light transmission through perforated metal films using liquid crystals

We calculate the effective dielectric tensor of a metal film penetrated by cylindrical holes filled with a nematic liquid crystal (NLC). We assume that the director of the NLC is parallel to the film, and that its direction within the plane can be controlled by a static magnetic field, via the Freedericksz effect. To calculate the effective dielectric tensor, we consider both randomly distributed holes (using a Maxwell-Garnett approximation) and a square lattice of holes (using a Fourier technique). Both the holes and the lattice constant of the square lattice are assumed small compared to the wavelength. The films are found to exhibit extraordinary light transmission at special frequencies related to the surface plasmon resonances of the composite film. Furthermore, the frequencies of peak transmission are found to be substantially split when the dielectric in the holes is anisotropic. For typical NLC parameters, the splitting is of order 5–10% of the metal plasma frequency. Thus, the extraordinary transmission can be controlled by a static magnetic or electric field whose direction can be rotated to orient the director of the NLC. Finally, as a practical means of producing the NLC-filled holes, we consider the case where the entire perforated metal film is dipped into a pool of NLC, so that all the holes are filled with the NLC, and there are also homogeneous slabs of NLC on both sides of the film. The transmission in this geometry is shown to have similar characteristics to that in which the NLC-filled screen is placed in air.     

Transmission of light through a plane-parallel plate of a two-dimensional resonant photonic crystal

The transmission spectra of two-dimensional resonant photonic crystals of two types have been investigated. Crystals of one type consist of dielectric cylinders forming a square lattice filled by a resonant gas with mercury atoms, and crystals of the other type consist of cylindrical holes filled with a gas and forming a square lattice in a dielectric matrix. It has been established that characteristics of the spectrum of additional transmission arising in the band gap of the photonic crystal can be changed significantly by varying the gas pressure and the angle of incidence. It has been demonstrated that the calculated features in the transmission spectrum of the photonic crystal are stable with respect to a significant increase in the width of the atomic resonance.     

Measuring the Dielectric Parameters of Frozen Sand in Microwave Resonators

We measure the dielectric parameters of frozen sand by using a rectangular cavity resonator at frequencies 5.3–8.4 GHz. The transmission spectrum of the resonator completely filled with frozen sand shows supplementary resonances absent in the case where the resonator is filled with dry homogeneous sand. The difference of the resonance curves was observed for the cases of wetting the sand by ordinary (H₂O) and heavy (D₂O) water. It is supposed that the observed effects are related to percolation due to the existence and specific properties of the conducting liquid films of water on the surfaces of mineral particles. To verify this assumption, we performed measurements for the special medium consisting of a mixture of dry sand and small metal particles. This experiment showed that supplementary resonant peaks in the transmission spectrum of the resonator arise for a certain concentration of metal particles. The same effect is also observed in the case of incomplete filling of the resonator with dry sand. These anomalies can be explained by the appearance of negative dispersion of waves in the waveguide.     

环状烯烃聚合物基底材料的太赫兹复介电常数和损耗特性研究

太赫兹时域光谱(THz-TDS)已被用于研究包括液体,半导体,爆炸物和气体等多种材料。然而自由空间太赫兹光谱系统存在着一些检测局限性,如微量物质难以被检测、系统尺寸难以实现微型化、空气中水的强烈吸收引起的信号衰减较大等问题。为了解决这些问题,研究人员设计了基于金属波导传输线结构的太赫兹芯片集成器件,通过飞秒红外激光激励传输线上的光电导材料实现太赫兹波的产生和检测。然而,在这些芯片上传输的太赫兹信号的频谱宽度很难达到自由空间太赫兹时域光谱系统的频带宽度,一个重要原因是由于传输信号受到随频率增加的传输线损耗所导致的衰减。通常这些损耗主要由三个部分组成：导体损耗,介电损耗和辐射损耗。研究表明：使用低介电常数材料作为共面传输线的衬底,将减少这种介电常数的失配,从而避免冲击波辐射损失;使用具有低损耗角正切的基底材料可以减少太赫兹传输线的损耗。环烯烃聚合物(COP)是一种具有环状烯烃结构的非晶性透明共聚物的材料,在太赫兹波段具有很高的透射率,为了探究这种材料是否能用于共面传输线的衬底,需要通过太赫兹时域光谱技术和介电函数理论分析它在太赫兹频段的光谱和介电特性,以及对这种材料作为基底时用在太赫兹传输线的传输特性进行仿真计算分析。使用透射式太赫兹时域光谱系统,对三种COP、熔融石英和PMMA进行了光谱测试,提取了它们的透射时域信号,采用Dorney和Duvillaret等提出的物理模型计算复介电函数。实验表明：与其他两种材料相比,COP材料在1 THz处的透过率更高,可以达到94.5%,同时介电损耗和介电常数更低,其中介电损耗在1 THz处达到4.31×10-4,因此将COP作为传输线基底材料时能有效减少基底的介电损耗。同时COP材料的介电常数在0.2～2.8 THz范围内维持在约2.3的水平,也有效减弱了辐射损耗。对实验材料基底组成的共面波导传输线进行了HFSS模拟,获得了它们的正向传输衰减系数(S₂₁ parameter),并对由基底引起的介电损耗和辐射损耗进行了计算分析。模拟和计算结果也表明在同一传输线结构下,与其他材料相比COP作为基底时的损耗更小。通过太赫兹时域光谱法与介电响应分析,表明了在太赫兹波段具有较低介电常数的COP材料更适合作为太赫兹传输线结构的基底材料,它可以有效的降低因基底引起的介电损耗和辐射损耗。这为太赫兹传输线的设计过程中衬底材料的选择与应用提供了实验和理论依据。     

Accelerated boundary element method for diffuse optical imaging

The boundary element method (BEM) is a useful tool in diffuse optical imaging (DOI) when modelling large optical regions whose parameters are piecewise constant, but are computationally expensive. We present here an acceleration technique, the single-level fast multipole method, for a highly lossy medium. The enhanced practicability of the BEM in DOI is demonstrated through test examples on single-layer problems, where order of magnitude reduction factors on solution time are achieved and on a realistic three-layer model of the neonatal head. Our experimental results agree very closely with theoretical predictions of computational complexity.     

Electrostatics and heat conduction in high contrast composite materials

We present a robust integral equation method for the calculation of the electrostatic and thermal properties of systems made of piecewise homogeneous, high contrast materials. By high contrast, we mean that the electrical or thermal conductivity ratios are high.Our approach involves a modification of the standard integral representation using, in electrostatic terms, the polarization charge as an unknown. It is related to the perturbation approach proposed by Tausch and White [J. Tausch, J. White, Capacitance extraction of 3-D conductor systems in dielectric media with high-permittivity ratios, IEEE Trans. Microwave Theory Tech., 47 (1999) 18–26], but based on a simple form of projection rather than on the solution of auxiliary integral equations. Numerical implementation is straightforward in the multiple dielectric case.     

横磁模式下二维非磁化等离子体光子晶体的线缺陷特性研究

采用等离子体的分段线性电流密度卷积时域有限差分算法研究了横磁波入射时具有单一线缺陷的二维非磁化等离子体光子晶体的缺陷模特性. 从频域角度分析得到微分高斯脉冲的透射系数,并讨论该光子晶体的晶格常数、介质圆柱半径、周期常数、缺陷层参数和等离子体参数对缺陷模特性的影响. 结果表明,改变周期常数、缺陷层位置和等离子体碰撞频率不会改变缺陷模的频率,改变缺陷层介质圆柱的相对介电常数、半径和缺陷层到介质层的中心距离可以在不改变禁带宽度的前提下实现对缺陷模的调节,改变晶格常数、介质圆柱半径和等离子体频率能同时实现对禁带宽度和缺陷模的调节. 关键词： 等离子体 光子晶体 缺陷模 时域有限差分算法     

A millimeter wave dielectric waveguide antenna

This paper describes the theoretical and experimental results of a novel leaky-wave antenna incorporating a homogeneous dielectric transmission line and radiating aperture into a single structure. The primary objective of this investigation is to demonstrate the ability to control aperture radiation by simply cutting slots into a metal-free dielectric transmission line. Experimental line source antennas with identical periodic slots were designed to operate in the 35 GHz frequency region. The successful performance of these antennas resulted in the design of a dielectric line source antenna with a symmetrical amplitude taper which provided a lower sidelobe level. The design represents a significant breakthrough in achieving affordable, low-loss, lightweight antennas in the millimeter wave region. The most significant applications for this type of antenna include radar surveillance and tactical missile-seeker terminal guidance.     

Acoustic attenuation of hybrid silencers

The acoustic attenuation of a single-pass, perforated concentric silencer filled with continuous strand fibers is investigated first theoretically and experimentally. The study is then extended to a specific type of hybrid silencer that consists of two single-pass perforated filling chambers combined with a Helmholtz resonator. One-dimensional analytical and three-dimensional boundary element methods (BEM) are employed for the predictions of the acoustic attenuation in the absence of mean flow. To account for the wave propagation in absorbing fiber, the complex-valued characteristic impedance and wave number are measured. The perforation impedance facing the fiber is also presented in terms of complex-valued characteristic impedance and wave number. The effects of outer chamber diameter and the fiber density are examined. Comparisons of predictions with the experiments illustrate the need for multi-dimensional analysis at higher frequencies, while the one-dimensional treatment provides a reasonable accuracy at lower frequencies, as expected. The study also shows a significant improvement in the acoustic attenuation of the silencer due to fiber absorption. Multi-dimensional BEM predictions of a hybrid silencer demonstrate that a reactive component such as a Helmholtz resonator can improve transmission loss at low frequencies and a higher duct porosity may be effective at higher frequencies.     

有耗介质层上多导体传输线的电磁耦合时域分析方法

目前,针对空间电磁场作用有耗介质层上传输线的电磁耦合,仍缺乏有效的数值分析方法.因此,本文提出一种高效的时域混合算法,很好地解决了有耗介质层上传输线电磁耦合建模难的问题.首先,对经典传输线方程进行改进,推导了适用于有耗介质层上多导体传输线电磁耦合分析的修正传输线方程.然后,结合时域有限差分方法和相应插值技术,求解修正传输线方程,获得多导线及其端接负载上的电压和电流响应,并实现空间电磁场辐射与多导线瞬态响应的同步计算.最后,通过相应计算实例的数值模拟,与CST软件的仿真结果进行对比,验证了时域混合算法的正确性和高效性.