Higher-order techniques in computational electromagnetics / Roberto D. Graglia, Andrew F. Peterson.

Format:

Book

Author/Creator:

Graglia, Roberto D., author.

Peterson, Andrew F., author.

Series:

Mario Boella Series on Electromagnetism in Information and Communication

Language:

English

Subjects (All):

Electromagnetic fields--Measurement.

Electromagnetic fields.

Electromagnetic fields--Mathematics.

Physical Description:

1 online resource (409 p.)

Place of Publication:

[Place of publication not identified] : Scitech Publishing, 2016.

Language Note:

English

Summary:

Higher-order Techniques in Computational Electromagnetics takes a different approach to computational electromagnetics and looks at it from the viewpoint of vector fields and vector currents. It gives a more detailed treatment of vector basis function than that currently available in other books. It also describes the approximation of vector quantities by vector basis functions, explores the error in that representation, and considers various other aspects of the vector approximation problem. This unique guide is the perfect reference guide for those who need to understand and use numerical techniques for electromagnetic fields.

Contents:

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 Cells2.7 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 Bases3.7 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 Bases4.3 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 Equations6.1 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

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on online resource; title from PDF title page (ebrary, viewed January 25, 2016).

ISBN:

1-5231-0101-6

1-61353-037-4