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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010167307 | TK7872.M25 P73 2008 | Open Access Book | Book | Searching... |
Searching... | 30000010193670 | TK7872.M25 P73 2008 | Open Access Book | Book | Searching... |
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Summary
Summary
The Method of Lines (MOL) is a versatile approach to obtaining numerical solutions to partial differential equations (PDEs) as they appear in dynamic and static problems. This method, popular in science and engineering, essentially reduces PDEs to a set of ordinary differential equations that can be integrated using standard numerical integration methods. Its significant advantage is that the analysis algorithms follow the physical wave propagation and are therefore efficient. This is because the fields on the discretisation lines are described by generalised transmission line (GTL) equations. With this formulation we have a connection to the well known transmission line theory and resulting in an easy understanding.
The method of lines is a very accurate and powerful way to analyze electromagnetic waves, enabling a full-wave solution without the computational burden of pure finite element or finite difference methods.
With Analysis of Electromagnetic Fields and Waves, Reinhold Pregla describes an important and powerful method for analyzing electromagnetic waves. This book:
Describes the general analysis principles for electromagnetic fields. Includes applications in microwave, millimetre wave and optical frequency regions. Unifies the analysis by introducing generalised transmission line (GTL) equations for all orthogonal coordinate systems and with materials of arbitrary anisotropy as a common start point. Demonstrates a unique analysis principle with the numerical stable impedance/admittance transformation and a physical adapted field transformation concept that is also useful for other modelling algorithms. Includes chapters on Eigenmode calculations for various waveguides, concatenations and junctions of arbitrary number of different waveguide sections in complex devices, periodic structures (e.g. Bragg gratings, meander lines, clystron resonators, photonic crystals), antennas (e.g. circular and conformal). Enables the reader to solve partial differential equations in other physical areas by using the described principles. Features an accompanying website with program codes in Matlab© for special problems.Analysis of Electromagnetic Fields and Waves will appeal to electromagnetic field practitioners in primary and applied research as well as postgraduate students in the areas of photonics, micro- and millimetre waves, general electromagnetics, e.g. microwave integrated circuits, antennas, integrated and fibre optics, optoelectronics, nanophotonics, microstructures, artificial materials.
Author Notes
Reinhold Pregla is a consultant and professor at the FernUniversitat in Germany.
Table of Contents
| Contents |
| Preface |
| 1 The Method of Lines |
| 1.1 Introduction |
| 1.2 MOL: Fundamentals of Discretisation |
| 2 Basic Principles of the Method of Lines |
| 2.1 Introduction |
| 2.2 Basic Equations |
| 2.3 Eigenmodes in Planar Waveguide Structures with Anisotropic Layers |
| 2.4 Analysis of Planar Circuits |
| 2.5 Field and Impedance/Admittance Transformation |
| 3 Analysis of Rectangular Waveguide Circuits |
| 3.1 Introduction |
| 3.2 Concatenations of Waveguide Sections |
| 3.3 Waveguide Junctions |
| 3.4 Analysis of 3D Waveguide Junctions |
| 4 Analysis of Waveguide Structures in Cylindrical Coordinates |
| 4.1 Introduction |
| 4.2 Generalised Transmission Line (GTL) Equations |
| 4.3 Discretisation Of The Fields And Solutions |
| 4.4 Solution in Radial Direction |
| 4.5 Discontinuities in Circular Waveguides - One-Dimensional Discretisation in Radial Direction |
| 4.6 Analysis of General Axially Symmetric Antennas with Coaxial Feed Lines |
| 4.7 Devices in Cylindrical Coordinates - Two-Dimensional Discretisation |
| 5 Analysis of Periodic Structures |
| 5.1 Introduction |
| 5.2 Principle Behaviour of Periodic Structures |
| 5.3 General Theory of Periodic Structures |
| 5.4 Numerical Results for Periodic Structures in One Direction |
| 5.5 Analysis of Photonic Crystals |
| 6 Analysis of Complex Structures |
| 6.1 Layers of Variable Thickness |
| 6.2 Microstrip Sharp Bend |
| 6.3 Impedance Transformation at Discontinuities |
| 6.4 Analysis of Planar Waveguide Junctions |
| 6.5 Numerical Results |
| 7 Precise Resolution with an Enhanced and Generalised Line Algorithm |
| 7.1 Introduction |
| 7.2 Crossed Discretisation Lines and Cartesian Coordinates |
| 7.3 Special Structures in Cartesian Coordinates |
| 7.4 Crossed Discretisation Lines and Cylindrical Coordinates |
| 7.5 Numerical Results |
| 8 Waveguide Structures with Materials of General Anisotropy in Arbitrary Orthogonal Coordinate Systems |
| 8.1 Generalised Transmission Line Equations |
| 8.2 Discretisation |
| 8.3 Solution of the Differential Equations |
| 8.4 Analysis of Waveguide Junctions and Sharp Bends with General Anisotropic Material by Using Orthogonal Propagating Waves |
| 8.5 Numerical Results |
| 8.6 Analysis of Waveguide Structures in Spherical Coordinates |
| 8.7 Elliptical Coordinates |
| 9 Summary and Prospect for the Future |
| A Discretisation Schemes and Difference Operators |
| A.1 Determination of the Eigenvalues and Eigenvectors of P |
| A.1.1 Calculation of the matrices I' |
| A.1.2 Derivation of the eigenvalues of the Neumann problem from those of the Dirichlet problem |
| A.1.3 The component of I?r at an abrupt transition |
| A.1.4 Eigenvalues and eigenvectors for periodic boundary Conditions |
| A.1.5 Discretisation for non-ideal places of the boundaries |
| A.2 Absorbing Boundary Conditions (ABCs) |
| A.2.1 Introduction |
| A.2.2 Factorisation of the Helmholtz equation |
| A.2.3 PadA'e approximation |
| A.2.4 Polynomial approximations |
| A.2.5 Construction of the difference operator for ABCs |
| A.2.6 Special boundary conditions (SBCs) |
| A.2.7 Numerical results |
| A.2.8 ABCs for cylindrical coordinates |
| A.2.9 Periodic boundary conditions |
| A.3 Higher-Order Difference Operators [11] |
| A.3.1 Introduction |
| A.3.2 Theory |
| A.3.3 Numerical results |
| A.4 Non-Equidistant Discretisation |
| A.4.1 Introduction |
| A.4.2 Theory |
| A.4.3 Interpolation |
| A.4.4 Numerical results |
| A.5 Reflections in Discretisation Grids |
| A.5.1 Introduction |
| A.5.2 Dispersion relations |
| A.5.3 Reflections at discretisation transitions |
| A.6 Field Extrapolation for Neumann Boundary Conditions |
| A.7 |
