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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Bibliographic Details
Main Authors: Graglia, Roberto D., (Author), Peterson, Andrew F., 1960- (Author)
Format: eBook
Language: English
Published: Edison, NJ : SciTech Publishing, 2015.
Series: Mario Boella series on electromagnetism in information & communication.
Subjects:
Electromagnetic fields > Measurement.
Electromagnetic fields > Mathematics.
elektronické knihy
electronic books
ISBN: 9781523101016
1523101016
9781613530375
1613530374
9781613530160
1613530161
Physical Description: 1 online resource (xv, 392 pages) : illustrations

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020 |a 1613530374  |q (PDF) 
020 |z 9781613530160 
020 |z 1613530161 
035 |a (OCoLC)944442787  |z (OCoLC)959910070  |z (OCoLC)961849249  |z (OCoLC)988653843  |z (OCoLC)999410350  |z (OCoLC)1026450870  |z (OCoLC)1066570636 
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. 
506 |a Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty 
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 Knovel (All titles) 
650 0 |a Electromagnetic fields  |x Measurement. 
650 0 |a Electromagnetic fields  |x Mathematics. 
655 7 |a elektronické knihy  |7 fd186907  |2 czenas 
655 9 |a electronic books  |2 eczenas 
700 1 |a Peterson, Andrew F.,  |d 1960-  |e author.  |1 https://id.oclc.org/worldcat/entity/E39PBJxWXHvVPV7fbmvkvMWbh3 
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://proxy.k.utb.cz/login?url=https://app.knovel.com/hotlink/toc/id:kpHOTCE001/higher-order-techniques?kpromoter=marc  |y Full text 

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