Selected Asymptotic Methods with Applications to Electromagnetics and Antennas (Synthesis Lectures on Computational Electromagnetics)

George Fikioris, Ioannis Tastsoglou, Odysseas N. Bakas

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商品描述

This book describes and illustrates the application of several asymptotic methods that have proved useful in the authors' research in electromagnetics and antennas. We first define asymptotic approximations and expansions and explain these concepts in detail. We then develop certain prerequisites from complex analysis such as power series, multivalued functions (including the concepts of branch points and branch cuts), and the all-important gamma function. Of particular importance is the idea of analytic continuation (of functions of a single complex variable); our discussions here include some recent, direct applications to antennas and computational electromagnetics. Then, specific methods are discussed. These include integration by parts and the Riemann-Lebesgue lemma, the use of contour integration in conjunction with other methods, techniques related to Laplace's method and Watson's lemma, the asymptotic behavior of certain Fourier sine and cosine transforms, and the Poisson summation formula (including its version for finite sums). Often underutilized in the literature are asymptotic techniques based on the Mellin transform; our treatment of this subject complements the techniques presented in our recent Synthesis Lecture on the exact (not asymptotic) evaluation of integrals.

Throughout, we provide illustrative examples. Some of them are applications to special functions of mathematical physics. Others, taken from our published research, include the application of elementary methods to develop certain simple formulas for transmission lines, examples illustrating the difficulties in solving fundamental integral equations of antenna theory, an examination of the fundamentals of the Method of Auxiliary Sources (MAS), and a study of the near fields of certain unusual types of radiators.

Table of Contents: Preface / Introduction: Simple Asymptotic Approximations / Asymptotic Approximations Defined / Concepts from Complex Variables / Laplace's Method and Watson's Lemma / Integration by Parts and Asymptotics of Some Fourier Transforms / Poisson Summation Formula and Applications / Mellin-Transform Method for Asymptotic Evaluation of Integrals / More Applications to Wire Antennas / Authors' Biographies / Index

商品描述(中文翻譯)

本書描述並說明了幾種在作者在電磁學和天線研究中證明有用的漸近方法的應用。我們首先定義了漸近逼近和展開,並詳細解釋了這些概念。然後,我們從複雜分析中發展了一些必要的先備知識,例如冪級數、多值函數(包括分支點和分支切割的概念)以及非常重要的伽馬函數。其中一個特別重要的概念是解析延拓(對於單一複雜變數的函數);我們在這裡的討論包括一些最近的直接應用於天線和計算電磁學的例子。然後,我們討論了具體的方法。這些方法包括分部積分和黎曼-勒貝格引理,與其他方法結合使用的等高線積分,與拉普拉斯方法和華生引理相關的技術,某些傅立葉正弦和餘弦變換的漸近行為,以及泊松求和公式(包括其有限求和版本)。在文獻中往往被低估的是基於梅林變換的漸近技術;我們對這個主題的處理補充了我們最近在精確(非漸近)積分評估上的合成講義中所介紹的技術。

在整本書中,我們提供了一些例子作為說明。其中一些是應用於數學物理特殊函數的應用。其他例子則來自我們發表的研究,包括應用基本方法來發展某些傳輸線的簡單公式的例子,展示解決天線理論中基本積分方程的困難的例子,對輔助源方法(MAS)的基本原理進行研究的例子,以及對某些不尋常類型輻射器的近場進行研究的例子。

目錄:前言 / 引言:簡單的漸近逼近 / 定義漸近逼近 / 複變數的概念 / 拉普拉斯方法和華生引理 / 分部積分和某些傅立葉變換的漸近行為 / 泊松求和公式及其應用 / 梅林變換方法用於漸近積分評估 / 更多應用於導線天線 / 作者簡介 / 索引