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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;...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Edison, NJ :
SciTech Publishing,
2015.
|
| Colección: | Mario Boella series on electromagnetism in information & communication.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 049 | |a UAMI | ||
| 100 | 1 | |a Graglia, Roberto D., |e author. | |
| 245 | 1 | 0 | |a Higher-order techniques in computational electromagnetics / |c Roberto D. Graglia, Andrew F. Peterson. |
| 264 | 1 | |a Edison, NJ : |b SciTech Publishing, |c 2015. | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (xv, 392 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Mario Boella series on electromagnetism in information & communication | |
| 504 | |a Includes bibliographical references (pages 378-379) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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; hierarchical bases; the numerical solution of integral and differential equations and an introduction to high-order bases for singular fields. | ||
| 505 | 0 | |a 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 | |
| 505 | 0 | |a 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 | |
| 505 | 0 | |a 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 | |
| 505 | 0 | |a 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 | |
| 505 | 0 | |a 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 | |
| 505 | 0 | |a 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 | |
| 505 | 0 | |a 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. | |
| 590 | |a Knovel |b ACADEMIC - Electronics & Semiconductors | ||
| 650 | 0 | |a Electromagnetic fields |x Measurement. | |
| 650 | 0 | |a Electromagnetic fields |x Mathematics. | |
| 650 | 6 | |a Champs électromagnétiques |x Mathématiques. | |
| 650 | 7 | |a Electromagnetic fields |x Mathematics. |2 fast |0 (OCoLC)fst00906535 | |
| 650 | 7 | |a Electromagnetic fields |x Measurement. |2 fast |0 (OCoLC)fst00906536 | |
| 650 | 7 | |a difference equations. |2 inspect | |
| 650 | 7 | |a integral equations. |2 inspect | |
| 650 | 7 | |a interpolation. |2 inspect | |
| 650 | 7 | |a polynomials. |2 inspect | |
| 700 | 1 | |a Peterson, Andrew F., |d 1960- |e author. | |
| 776 | 0 | 8 | |i Print version: |a Graglia, Roberto D. |t Higher-order techniques in computational electromagnetics |z 9781613530160 |w (OCoLC)939744634 |
| 830 | 0 | |a Mario Boella series on electromagnetism in information & communication. | |
| 856 | 4 | 0 | |u https://appknovel.uam.elogim.com/kn/resources/kpHOTCE001/toc |z Texto completo |
| 938 | |a YBP Library Services |b YANK |n 12802150 | ||
| 994 | |a 92 |b IZTAP | ||