The rapid development of computer techniques and information technologies in recent decades has fueled the need for efficient tools for electromagnetic modeling of millimeter–wave integrated circuits, high–speed and high–density VLSI circuits, microwave and antenna design, and scattering analysis for large and complex targets. The multiresolution time domain (MRTD) scheme has excellent potential for satisfying this need. Multiresolution Time Domain Scheme for Electromagnetic Engineering examines the MRTD scheme and shows how it can be used to satisfy a variety of these technical needs.
This comprehensive resource presents a combination of theoretically advanced mathematical topics and their application in time domain and Maxwell solution techniques, in particular:
- Concepts of signal space, the multiresolution analysis (MRA), and scaling and wavelet functions
- Construction of MRA families
- Interconnection among the MRTD, finite difference time domain (FDTD), and MoM
- MRTD boundary truncations
- MRTD plane wave incidence, near–to–far–field transform, and scattering analysis
- MRTD applications on microwave and millimeter wave integrated circuits
- Generalized differential matrix operators (GDMOs)
A comprehensive collection of integral relations, with detailed derivations of the MRTD update equations, is included for the reader′s convenience.
Multiresolution Time Domain Scheme for Electromagnetic Engineering is a self–contained reference that engineers and scientists can use to learn advanced mathematical topics of multiresolution analysis and its application through MRTD. It is also eminently suitable for a stand–alone course for senior undergraduates and graduate students in a range of fields including electrical engineering, physics, and applied mathematics who wish to know more about the MRA concepts and MRTD applications in efficient computational electromagnetics.
2. Introduction to the Multiresolution Analysis.
2.2 Vectors and Signal Space.
2.3 Multiresolution Analysis.
2.4 Scaling Functions and Wavelets.
2.5 MRA in the Frequency Domain.
2.7 Biorthogonal MRA and Wavelets.
2.8 Multidimensional Wavelets.
2.9 Field Expansions in the MRTD Analysis.
3. MRA Families in MRTD Analysis.
3.2 Basic Spline MRA Family.
3.3 Battle Lemari´e Spline MRA Family.
3.4 Cubic Spline Battle Lemari´e MRA An Example.
3.5 Daubechies Procedure of MRA Construction.
3.6 Daubechies Original Family.
3.7 Coiflet Family.
3.8 Biorthogonal MRA.
3.9 Biorthogonal Cohen Daubechies Feauveau Family.
4. Kernel of Multiresolution Time Domain Scheme.
4.2 Relationships Among the FDTD, MoM, and MRTD.
4.3 The MRTD Scheme.
4.4 Stability Criteria.
4.5 Computation of Total Fields.
4.6 Orthogonal and Integral Relations.
5. PEC Boundary Truncations.
5.2 Method of Analysis.
5.3 Numerical Results.
6. Open Boundary Truncation.
6.2 MRTD Update Equations in APML Regions.
6.3 Numerical Results.
7. One–Dimensional MRTD Analysis.
7.2 MRTD Formulations.
7.3 Application Results.
8. Two–Dimensional MRTD Analysis.
8.2 MRTD Analysis for Printed Transmission Lines.
8.3 Application Results for Printed Transmission Lines.
8.4 MRTD Analysis for Parallel Waveguide Structures.
8.5 Application Results for Parallel–Waveguide Structures.
9. Three–Dimensional MRTD Analysis.
9.2 Method of Analysis.
9.3 Application Results.
10. MRTD Analysis for MMICs.
10.2 Microwave Networks.
10.3 Extraction of MMIC Characteristics.
10.4 Application Results.
11. MRTD Scattering Analysis: 2D Cases.
11.2 Scattering Fundamentals.
11.3 Governing Equations of MRTD.
11.4 MRTD Scattering Algorithm for TMz Wave.
11.5 MRTD Scattering Algorithm for TEz Wave.
11.6 Application Results.
12. MRTD Scattering Analysis: 3D Cases.
12.2 Governing Equations of MRTD.
12.3 MRTD Implementations.
12.4 Application Results.
APPENDIX A: Generalized Differential Matrix Operators.
A.1 Generalized Differential Matrix Operators.
A.2 GDMO Representation of Maxwell and Wave Equations.
A.3 GDMOs for Differential and Integral Formulations.
APPENDIX B: MRTD Orthogonal and Integral Relations.
B.1 Orthogonal and Integral Relations.
B.2 Orthogonal Relations.
B.3 Integral Relations of the Pulse Function.
B.4 Integral Relations for the Scaling Functions.
B.5 Integral Relations for Mixed Functions.
B.6 Integral Relations for Wavelet Functions.
B.7 Integral Coefficients.
APPENDIX C: Update Equations in APML Regions.
C.1 Maxwell Equations in APML Regions.
C.2 Field Expansions.
C.3 Update Equations for Face–APML Regions.
C.4 Update Equations for Edge–APML Regions.
C.5 Update Equations for Corner–APML Regions.
APPENDIX D: Expressions and Properties of the Cubic Battle Lemari´e Functions.
D.1 Expression for the B–Spline Function in the Frequency Domain.
D.2 Orthogonality Condition in the Frequency Domain.
D.3 Expression of B–Spline Functions in the Frequency and Space Domains.
D.4 Cubic Spline Battle Lemari´e Wavelet Function in the Frequency Domain.