Multiresolution Time Domain Scheme for Electromagnetic Engineering

Acknowledgments.

1. Introduction.

1.1 Prologue.

1.2 Objectives.

1.3 Overview.

2. Introduction to the Multiresolution Analysis.

2.1 Introduction.

2.2 Vectors and Signal Space.

2.3 Multiresolution Analysis.

2.4 Scaling Functions and Wavelets.

2.5 MRA in the Frequency Domain.

2.6 Examples.

2.7 Biorthogonal MRA and Wavelets.

2.8 Multidimensional Wavelets.

2.9 Field Expansions in the MRTD Analysis.

3. MRA Families in MRTD Analysis.

3.1 Introduction.

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.

4.1 Introduction.

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.

5.1 Introduction.

5.2 Method of Analysis.

5.3 Numerical Results.

5.4 Conclusions.

6. Open Boundary Truncation.

6.1 Introduction.

6.2 MRTD Update Equations in APML Regions.

6.3 Numerical Results.

6.4 Conclusion.

7. One-Dimensional MRTD Analysis.

7.1 Introduction.

7.2 MRTD Formulations.

7.3 Application Results.

7.4 Conclusion.

8. Two-Dimensional MRTD Analysis.

8.1 Introduction.

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.

8.6 Conclusions.

References.

9. Three-Dimensional MRTD Analysis.

9.1 Introduction.

9.2 Method of Analysis.

9.3 Application Results.

9.4 Conclusions.

10. MRTD Analysis for MMICs.

10.1 Introduction.

10.2 Microwave Networks.

10.3 Extraction of MMIC Characteristics.

10.4 Application Results.

10.5 Conclusions.

11. MRTD Scattering Analysis: 2D Cases.

11.1 Introduction.

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.

11.7 Conclusions.

12. MRTD Scattering Analysis: 3D Cases.

12.1 Introduction.

12.2 Governing Equations of MRTD.

12.3 MRTD Implementations.

12.4 Application Results.

12.5 Conclusions.

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.

Index.