Higher-order techniques in computational electromagnetics /

The book reviews developments in the following fields: interpolation, approximation, and error in one dimension; scalar interpolation in two and three dimensions; representation of vector fields in two and three dimensions using low-degree polynomials; interpolatory vector bases of arbitrary order;...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Graglia, Roberto D. (Autor), Peterson, Andrew F., 1960- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Edison, NJ : SciTech Publishing, 2015.
Colección:Mario Boella series on electromagnetism in information & communication.
Temas:
Electromagnetic fields > Measurement.
Electromagnetic fields > Mathematics.
Champs électromagnétiques > Mathématiques.
difference equations.
integral equations.
interpolation.
polynomials.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine generated contents note: 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
  • 1.2.1. Lagrange Interpolation
  • 1.2.2. Hermite Interpolation
  • 1.3. Error in the Representation of Functions
  • 1.3.1. Interpolation Error
  • 1.3.2. Spectral Integrity and Other Frequency Domain Considerations
  • 1.4. Approximation of Functions with Border Singularities
  • 1.4.1. Singular Expansion Functions
  • 1.4.2. Singular Functions that Comply with Exact Approximations in Terms of Singular Plus Polynomial Basis Functions
  • 1.4.3. Singular Functions that Do Not Permit Exact Approximations in Terms of Singular Plus Polynomial Basis Functions
  • 1.5. Summary
  • References
  • 2. Scalar Interpolation in Two and Three Dimensions
  • 2.1. Two- and Three-Dimensional Meshes and Canonical Cells
  • 2.1.1. Conforming Meshes and Fundamentals of Geometrical Database Structure
  • Note continued: 2.2. Interpolatory Polynomials of Silvester
  • 2.3. Normalized Coordinates for the Canonical Cells
  • 2.4. Triangular Cells
  • 2.4.1. Cell Geometry Representation and Local Vector Bases
  • 2.4.2. Lagrangian Basis Functions, Interpolation, and Gradient Approximation
  • 2.4.3. Interpolation Error
  • 2.4.4. Spectral Integrity and Other Frequency Domain Considerations
  • 2.4.5. Curved Cells
  • 2.5. Quadrilateral Cells
  • 2.5.1. Cell Geometry Representation and Local Vector Bases
  • 2.5.2. Lagrangian Basis Functions, Interpolation, and Gradient Approximation
  • 2.6. Tetrahedral Cells
  • 2.6.1. Cell Geometry Representation and Local Vector Bases
  • 2.6.2. Lagrangian Basis Functions
  • 2.7. Brick Cells
  • 2.7.1. Cell Geometry Representation and Local Vector Bases
  • 2.7.2. Lagrangian Basis Functions
  • 2.8. Triangular Prism Cells
  • 2.8.1. Cell Geometry Representation and Local Vector Bases
  • 2.8.2. Lagrangian Basis Functions
  • 2.9. Generation of Shape Functions
  • References
  • Note continued: 3. Representation of Vector Fields in Two and Three Dimensions Using Low-Degree Polynomials
  • 3.1. Two-Dimensional Vector Functions on Triangles
  • 3.1.1. Linear Curl-Conforming Vector Basis Functions
  • 3.1.2.A Simpler Curl-Conforming Representation on Triangles
  • 3.1.3. Alternate Approach: A Divergence-Conforming Representation on Triangles
  • 3.2. Tangential-Vector versus Normal-Vector Continuity: Curl-Conforming and Divergence-Conforming Bases
  • 3.2.1. Additional Terminology
  • 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
  • Note continued: 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 with Curved Cells
  • 3.11.1. Base and Reciprocal Base Vectors
  • 3.11.2. Covariant and Contravariant Projections
  • 3.11.3. Derivatives in the Parent Space
  • 3.11.4. Restriction to Surfaces
  • 3.11.5. Example: Quadrilateral Cells
  • 3.12. The Mixed-Order Nedelec 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
  • 4.5.1.Completeness of the High-Order Vector Bases for 2D Cells
  • 4.5.2.Completeness of the High-Order Vector Bases for 3D Cells
  • Note continued: 5.3.2. Quadrilateral and Brick Bases
  • 5.3.3. Prism Bases
  • 5.3.4. Condition Number Comparison
  • 5.4. Hierarchical Divergence-Conforming Vector Bases
  • 5.4.1. Reference Variables on the Face in Common to Adjacent Cells
  • 5.4.2. Tetrahedral Bases
  • 5.4.3. Prism Bases
  • 5.4.4. Brick Bases
  • 5.4.5. Numerical Results and Comparisons with Other 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
  • Note continued: 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
  • 7.3.1. Lowest Order Bases of the Substitutive Type
  • 7.3.2. Higher Order Bases of the Substitutive Type
  • 7.3.3. Additive Singular Basis Functions
  • 7.3.4. The Irrational Algebraic Scalar Basis Functions
  • 7.3.5. Example: Quadratic Basis with One Singular Degree
  • 7.3.6. Example: Cubic Basis with Two Singular Degrees
  • 7.3.7. Evaluation of Integrals of Singular Bases
  • 7.4. Numerical Results for Scalar Bases
  • 7.4.1. Eigenvalues of Waveguiding Structures with Edges
  • 7.4.2. Effect of Varying the Number of Radial and Azimuthal Terms
  • 7.5. Singular Vector Basis Functions for Triangles
  • 7.5.1. Substitutive Curl-Conforming Vector Bases
  • Note continued: 7.5.2. Additive Curl-Conforming Vector Bases
  • 7.6. Singular Hierarchical Meixner Basis Sets
  • 7.6.1. The Singularity Coefficients
  • 7.6.2. Auxiliary Functions
  • 7.6.3. Representation of Singular Fields
  • 7.6.4. Singular Scalar Bases
  • 7.6.5. Singular Static Vector Bases
  • 7.6.6. Singular Non-Static Vector Bases
  • 7.6.7. Numerical Evaluation of the Radial Functions Rn and Sn
  • 7.6.8. Example: p = 1.5 Basis with One Singular Exponent
  • 7.6.9. Example: p = 2.5 Basis with Two Singular Exponents
  • 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.

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