Higher-Order Techniques in Computational Electromagnetics.

Intro
Contents
Preface
Foreword
1. Interpolation, Approximation, and Error in One Dimension
1.1 Linear Interpolation and Triangular Basis Functions
1.2 Interpolation and Basis Functions of Higher Polynomial Order
1.3 Error in the Representation of Functions
1.4 Approximation of Functions with Border Singularities
1.5 Summary
References
2. Scalar Interpolation in Two and Three Dimensions
2.1 Two- and Three-Dimensional Meshes and Canonical Cells
2.2 Interpolatory Polynomials of Silvester
2.3 Normalized Coordinates for the Canonical Cells
2.4 Triangular Cells
2.5 Quadrilateral Cells
2.6 Tetrahedral Cells
2.7 Brick Cells
2.8 Triangular Prism Cells
2.9 Generation of Shape Functions
References
3. Representation of Vector Fields in Two and Three Dimensions Using Low-Degree Polynomials
3.1 Two-Dimensional Vector Functions on Triangles
3.2 Tangential-Vector versus Normal-Vector Continuity: Curl-Conforming and Divergence-Conforming Bases
3.3 Two-Dimensional Representations on Rectangular Cells
3.4 Quasi-Helmholtz Decomposition in 2D: Loop and Star Functions
3.5 Projecting between Curl-Conforming and Divergence-Conforming Bases
3.6 Three-Dimensional Representation on Tetrahedral Cells: Curl-Conforming Bases
3.7 Three-Dimensional Representation on Tetrahedral Cells: Divergence-Conforming Bases
3.8 Three-Dimensional Expansion on Brick Cells: Curl-Conforming Case
3.9 Divergence-Conforming Bases on Brick Cells
3.10 Quasi-Helmholtz Decomposition on Tetrahedral Meshes
3.11 Vector Basis Functions on Skewed Meshes or Meshes withCurved Cells
3.12 The Mixed-Order Nédélec Spaces
3.13 The De Rham Complex
3.14 Conclusion
References
4. Interpolatory Vector Bases of Arbitrary Order
4.1 Development of Vector Bases
4.2 The Construction of Vector Bases.

4.3 Zeroth-Order Vector Bases for the Canonical 2D Cells
4.4 Zeroth-Order Vector Bases for the Canonical 3D Cells
4.5 The High-Order Vector Basis Construction Method
4.6 Vector Bases for the Canonical 2D Cells
4.7 Vector Bases for the Canonical 3D Cells
4.8 Synoptic Tables
References
5. Hierarchical Bases
5.1 The Ill-Conditioning Issue
5.2 Hierarchical Scalar Bases
5.3 Hierarchical Curl-Conforming Vector Bases
5.4 Hierarchical Divergence-Conforming Vector Bases
5.5 Conclusion
References
6. The Numerical Solution of Integral and Differential Equations
6.1 The Electric Field Integral Equation
6.2 Incorporation of Curved Cells
6.3 Treatment of the Singularity of the Green's Function by Singularity Subtraction and Cancellation Techniques
6.4 Examples: Scattering Cross Section Calculations
6.5 The Vector Helmholtz Equation
6.6 Numerical Solution of the Vector Helmholtz Equation for Cavities
6.7 Avoiding Spurious Modes with Adaptive p-Refinement and Hierarchical Bases
6.8 Use of Curved Cells with Curl-Conforming Bases
6.9 Application: Scattering from Deep Cavities
6.10 Summary
References
7. An Introduction to High-Order Bases for Singular Fields
7.1 Field Singularities at Edges
7.2 Triangular-Polar Coordinate Transformation
7.3 Singular Scalar Basis Functions for Triangles
7.4 Numerical Results for Scalar Bases
7.5 Singular Vector Basis Functions for Triangles
7.6 Singular Hierarchical Meixner Basis Sets
7.7 Numerical Results
7.8 Numerical Results for Inhomogeneous Waveguiding Structures Containing Corners
7.9 Numerical Results for Thin Metallic Plates with Knife-Edge Singularities
7.10 Conclusion
References
About the Authors
Index.