【作者】 黄文武；

【导师】 谢洪波； 郑宏兴；

【作者基本信息】 天津大学 ， 光学工程， 2005， 硕士

【摘要】 时域有限差分(FDTD)法是求解电磁波、弹性波、声波等波动问题的一种数值计算方法,它把带时间变量的波动微分方程转化为差分方程来求解波场各分量,得到时间系列的场分量的空间分布。自FDTD法创建以来,它广泛应用于电磁波、弹性波和声波的传播过程,以及与目标相互作用过程的研究中。超声检测是一种有效的医疗诊断技术,其物理基础是超声波在生物组织中的传播规律,也即利用各种组织声学特性的差异来区分不同组织,特别是区分正常组织和病变组织。超声传播规律的研究对诊断是十分重要的,其方法是先对生物组织进行复杂的建模,然后建立这个模型的波动方程,根据已知声源,求解声波在模型中的传播规律,从而得到声波在该生物组织中传播规律的近似。时域有限差分法对复杂模型的适用性,预示着这是研究超声传播规律的有效技术。本文进行时域有限差分法研究的目的就是解决医学超声探测的动态计算机仿真问题。生物组织的不同建模要求涉及到弹性波和声波问题。本文研究了弹性波和声波领域的时域有限差分原理,包括二维和三维问题的FDTD计算; 对FDTD算法的稳定性条件和数值色散做了简单的分析; 讨论并选取了激励源的合适形式,以及激励源的设置方式。吸收边界条件是时域有限差分法的一个重要问题,FDTD模拟的是有限区域的波场计算,因而必须在截断边界处设置特殊边界来吸收外向行波。本文采用了分解场分量的完全匹配层(PML)吸收边界条件来吸收外向行波,并对其进行改进,应用在弹性波和声波领域。最后,本文对弹性波和声波领域的FDTD算法的稳定性和PML吸收边界条件的吸收效果进行了检验。结果表明,本文编写的FDTD程序运行稳定,且PML边界吸收效果良好。利用该程序对弹性波和声波与目标相互作用问题进行了二维和三维的FDTD计算,也对分层异类媒质中的波动传播进行了FDTD模拟。更多还原

【Abstract】 The finite-difference time-domain method (FDTD) is one of the most powerful numerical methods for the forward modeling of the electromagnetic wave, elastic wave and acoustic wave propagation and scattering. Through transforming the partial-differential equations to the finite-difference equations, the wave field weight is obtained in the whole space. The FDTD method is a full wave technique that has been widely used to model wave propagation process,and interaction with certain or random object in electromagnetics, acoustics, and elastodynamics. Ultrasonic exploration is an efficacious medical diagnosis technique. The ultrasonic propagation rule in the biology tissue is the physics foundation of the ultrasonic diagnosis. Based on the difference of acoustics characteristics in different biology tissues, it distinguishes the dissimilar tissues, especially the natural tissue from the pathological tissue. The investigation of the ultrasonic propagation rule is important for the medical treatment. First, the method is to develop a complex model of the biology tissue, then to establish the wave equations of this model, and to seek to the acoustic propagation rule in the model base on the known source. Finally the approximate acoustic propagation rule in the biology tissue is found. The FDTD method is an effective technique for the research about ultrasonic propagation rule, because the FDTD is especially appropriate for complex models. The purpose of research on FDTD is to obtain the dynamic computer model of the medical ultrasonic exploration. The various modeling request of the biology tissue come down to the elastic wave and acoustic wave questions. In this thesis, the FDTD theory of the elastic and acoustic wave is mainly discussed, including two dimensional (2D) and three dimensional (3D) FDTD simulations. Then the stability condition of the FDTD method and numerical dispersive are analyzed,and the form and the sort of the power source, and the setting of the source are discussed and adopted. Absorbing boundary condition is an important problem of the FDTD method. Because FDTD simulates the wave field in the finite area, we must mount an especial boundary to absorb the outward travelling wave in the truncation boundary. A perfectly matched layer (PML) absorbing boundary condition is used to absorb the outward travelling wave, which is improved and applied in the elastic and acoustic wave simulation. In the end, the thesis verifies the stability of the elastic and acoustic wave’s FDTD method and the absorbing effect of the PML absorbing boundary condition. The result proves that the FDTD programs by the writer run stably and the PML boundary can absorb the outward travelling wave well. Moreover, we simulate the interaction of the elastic wave, acoustic wave and the object through 2D/3D FDTD programs, as well as the propagation of the elastic wave in the heterogeneous layered media.更多还原