电磁与弹性波的积分方程方法

Green’s
Function
Integral
equation
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"Integral equation methods是解决电磁波和弹性波问题的一种强大工具，由Weng Cho Chew、Mei Song Tong和Bin Hu共同探讨。本书详细介绍了如何利用积分方程方法来处理这两种物理现象中的波动问题。它涵盖了Green's函数、积分方程等相关概念，并在电磁学和固体力学的背景下进行了深入讨论。该书适用于科研人员和学生，旨在提供计算电磁学和计算力学领域的理论基础和应用实例。" 积分方程方法是分析和求解复杂边界条件下的电磁和弹性波问题的有效途径。这些方法基于场量之间的关系，通常将偏微分方程转化为边界上的积分方程，从而简化问题的求解。在电磁学中，这种方法常用于研究天线、雷达散射、微波器件以及光子晶体等领域的现象。在弹性波传播中，它们则被用来解决地震波、声波在复杂介质中的传播问题，或者在结构工程中分析材料的振动和应力分布。 Green's函数是积分方程方法的核心组成部分，它是描述在特定边界条件下任意点处的场响应与源位置之间关系的函数。在电磁学中，Green's函数可以表示为一个点电荷或磁偶极子在空间中产生的场；在弹性波问题中，它对应于一个点源在介质中引起的位移场。通过解析或数值计算得到Green's函数，然后可以求解整个区域内的场分布。 积分方程通常以边界值问题的形式出现，例如Lippmann-Schwinger方程或Sommerfeld积分方程。这些方程可以直接对边界上的场或其导数进行操作，而无需考虑边界内部的细节。这使得积分方程方法特别适合处理具有复杂几何形状或不规则边界的场景，因为它们只需要在边界上定义问题，而不需要在整个域内进行离散化。 该书详细阐述了积分方程方法的理论基础，包括Fredholm第一型和第二型积分方程的求解策略，以及相关的数值方法，如矩量法（Method of Moments, MoM）和边界元方法（Boundary Element Method, BEM）。这些数值技术允许将积分方程转化为线性代数系统，进而用计算机求解。 此外，书中可能还涵盖了迭代解法，如迭代MoM，以及加速收敛的技术，如预条件器和多极展开。作者可能会讨论各种物理现象的实际应用，比如射线光学、波导模式分析、声学散射、结构动力学等，以展示积分方程方法的实用性。 《Integral Equation Methods for Electromagnetic and Elastic Waves》是一本深入介绍积分方程在电磁学和弹性波领域应用的著作，对于希望理解和应用这些方法的科研人员和学生来说，是一份宝贵的资源。

For macroscopically anisotropic media in which the variations in the phase stiffness tensor are small, formal solutions to the boundary-value problem have been developed in the form of perturbation series (Dederichs and Zeller, 1973; Gubernatis and Krumhansl, 1975 ; Willis, 1981). Due to the nature of the integral operator, one must contend with conditionally convergent integrals. One approach to this problem is to carry out a “renormalization” procedure which amounts to identifying physically what the conditionally convergent terms ought to contribute and replacing them by convergent terms that make this contribution (McCoy, 1979). For the special case of macroscopically isotropic media, the first few terms of this perturbation expansion have been explicitly given in terms of certain statistical correlation functions for both three-dimensional media (Beran and Molyneux, 1966 ; Milton and Phan-Thien, 1982) and two-dimensional media (Silnutzer, 1972 ; Milton, 1982). A drawback of all of these classical perturbation expansions is that they are only valid for media in which the moduli of the phases are nearly the same, albeit applicable for arbitrary volume fractions. In this paper we develop new, exact perturbation expansions for the effective stiffness tensor of macroscopically anisotropic composite media consisting of two isotropic phases by introducing an integral equation for the so-called “cavity” strain field. The expansions are not formal but rather the nth-order tensor coefficients are given explicitly in terms of integrals over products of certain tensor fields and a determinant involving n-point statistical correlation functions that render the integrals absolutely convergent in the infinite-volume limit. Thus, no renormalization analysis is required because the procedure used to solve the integral equation systematically leads to absolutely convergent integrals. Another useful feature of the expansions is that they converge rapidly for a class of dispersions for all volume fractions, even when the phase moduli differ significantly.

2023-06-02 上传
针对宏观各向异性介质，其中相位刚度张量的变化很小，边值问题的形式解已经通过摄动级数的形式得到了发展（Dederichs和Zeller，1973年；Gubernatis和Krumhansl，1975年；Willis，1981年）。由于积分算子的性质，必须...

根据论文“Analysis of the first variation and a numerical gradient flow for integral Menger curvature”中的计算 integral Menger curvature的公式编写计算空间曲线integral Menger curvature的matlab代码

2023-05-25 上传
根据论文中的公式，计算空间曲线integral Menger ... Analysis of the first variation and a numerical gradient flow for integral Menger curvature. Computer Aided Geometric Design, 29(7):488-501, 2012.

Please use C language and pointers to define a function to compute the integral of any unary function.

2023-03-29 上传
Here is an example implementation of a function to compute the integral of any unary function using C language and pointers: ```c #include double integral(double (*f)(double), double a, double b, ...

Define a procedure integrate-series-tail that, given a series returns the integral of the series (except for the constant term) Turn in a listing of your procedure and demonstrate that it works by computing integrate-series-tail of the series S2 from problem 1.

2023-06-07 上传
The `integrate-series-tail` procedure takes a series `s` as input and returns a list of coefficients that represent the integral of the series (except for the constant term). The integration is ...

integral_approximation = 0 for i in range(n): x_i = a + i * h integral_approximation += func(x_i) * h integral_approximation是什么

2024-09-08 上传
`integral_approximation` 是数值积分的一个近似计算过程[^1]。在这个过程中，它采用了梯形法则（也称为矩形法）来估算给定函数 `func(x)` 在区间 `[a, a+n*h]` 的定积分。具体来说，`n` 表示等分区间次数，`h` 是每...

Integral library based on C++

2023-04-05 上传
1. GNU Scientific Library (GSL) - A library for numerical analysis and scientific computing. 2. The C Math Library - A library that provides a set of mathematical functions for C programming language....

integral3 Vectorized input

2023-06-10 上传
For example, in Python with NumPy, you can define a function that takes a NumPy array as input and returns a NumPy array of the same shape. You can then use the NumPy function `numpy.vectorize()` to ...

matlab integral3 Vectorized input

2023-06-10 上传
In MATLAB, you can use the `integral3` function to compute the triple integral of a function over a 3D region. To handle vectorized input, you can use the `arrayfun` function to apply the `integral3` ...

matlab ingegrator

2023-07-09 上传
Keep in mind that numerical integration methods have limitations and may not always provide accurate results for all types of functions. It's important to understand the characteristics of your ...

integral(@(s)Fm(s),-inf,t)

2023-04-05 上传
Then, evaluate the integral of Fm(s) between x and t, and take the limit as x approaches negative infinity. In practice, this can be difficult to calculate analytically, especially if Fm(s) is a ...
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