Numerical Techniques in Electromagnetics, Second Edition

Numerical Techniques in Electromagnetics, Second Edition

Author: Matthew N.O. Sadiku

Publisher: CRC Press

Published: 2000-07-12

Total Pages: 764

ISBN-13: 9780849313950

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As the availability of powerful computer resources has grown over the last three decades, the art of computation of electromagnetic (EM) problems has also grown - exponentially. Despite this dramatic growth, however, the EM community lacked a comprehensive text on the computational techniques used to solve EM problems. The first edition of Numerical Techniques in Electromagnetics filled that gap and became the reference of choice for thousands of engineers, researchers, and students. The Second Edition of this bestselling text reflects the continuing increase in awareness and use of numerical techniques and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite difference time domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. The author also added a chapter on the method of lines. Numerical Techniques in Electromagnetics continues to teach readers how to pose, numerically analyze, and solve EM problems, give them the ability to expand their problem-solving skills using a variety of methods, and prepare them for research in electromagnetism. Now the Second Edition goes even further toward providing a comprehensive resource that addresses all of the most useful computation methods for EM problems.


Book Synopsis Numerical Techniques in Electromagnetics, Second Edition by : Matthew N.O. Sadiku

Download or read book Numerical Techniques in Electromagnetics, Second Edition written by Matthew N.O. Sadiku and published by CRC Press. This book was released on 2000-07-12 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the availability of powerful computer resources has grown over the last three decades, the art of computation of electromagnetic (EM) problems has also grown - exponentially. Despite this dramatic growth, however, the EM community lacked a comprehensive text on the computational techniques used to solve EM problems. The first edition of Numerical Techniques in Electromagnetics filled that gap and became the reference of choice for thousands of engineers, researchers, and students. The Second Edition of this bestselling text reflects the continuing increase in awareness and use of numerical techniques and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite difference time domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. The author also added a chapter on the method of lines. Numerical Techniques in Electromagnetics continues to teach readers how to pose, numerically analyze, and solve EM problems, give them the ability to expand their problem-solving skills using a variety of methods, and prepare them for research in electromagnetism. Now the Second Edition goes even further toward providing a comprehensive resource that addresses all of the most useful computation methods for EM problems.


Numerical Methods for Engineering

Numerical Methods for Engineering

Author: Karl F. Warnick

Publisher: SciTech Publishing

Published: 2020-09-26

Total Pages: 376

ISBN-13: 9781839530739

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The revised and updated second edition of this textbook teaches students to create computer codes used to engineer antennas, microwave circuits, and other critical technologies for wireless communications and other applications of electromagnetic fields and waves. Worked code examples are provided for MATLAB technical computing software.


Book Synopsis Numerical Methods for Engineering by : Karl F. Warnick

Download or read book Numerical Methods for Engineering written by Karl F. Warnick and published by SciTech Publishing. This book was released on 2020-09-26 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The revised and updated second edition of this textbook teaches students to create computer codes used to engineer antennas, microwave circuits, and other critical technologies for wireless communications and other applications of electromagnetic fields and waves. Worked code examples are provided for MATLAB technical computing software.


Numerical Analysis for Electromagnetic Integral Equations

Numerical Analysis for Electromagnetic Integral Equations

Author: Karl F. Warnick

Publisher: Artech House

Published: 2008

Total Pages: 234

ISBN-13: 1596933348

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Introduction -- Surface integral equation formulations and the method of moments -- Error analysis of the EFIE / with W.C. Chew -- Error analysis of the MFIE and CFIE / with C.P. Davis -- Geometrical singularities and the flat strip -- Resonant structures -- Error analysis for 3D problems -- Higher-order basis functions / with A.F. Peterson -- Operator spectra and iterative solution methods.


Book Synopsis Numerical Analysis for Electromagnetic Integral Equations by : Karl F. Warnick

Download or read book Numerical Analysis for Electromagnetic Integral Equations written by Karl F. Warnick and published by Artech House. This book was released on 2008 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction -- Surface integral equation formulations and the method of moments -- Error analysis of the EFIE / with W.C. Chew -- Error analysis of the MFIE and CFIE / with C.P. Davis -- Geometrical singularities and the flat strip -- Resonant structures -- Error analysis for 3D problems -- Higher-order basis functions / with A.F. Peterson -- Operator spectra and iterative solution methods.


Theory and Computation of Electromagnetic Fields

Theory and Computation of Electromagnetic Fields

Author: Jian-Ming Jin

Publisher: John Wiley & Sons

Published: 2015-08-10

Total Pages: 744

ISBN-13: 111910808X

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Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell’s equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: Provides the foundation necessary for graduate students to learn and understand more advanced topics Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates Covers computational electromagnetics in both frequency and time domains Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills.


Book Synopsis Theory and Computation of Electromagnetic Fields by : Jian-Ming Jin

Download or read book Theory and Computation of Electromagnetic Fields written by Jian-Ming Jin and published by John Wiley & Sons. This book was released on 2015-08-10 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell’s equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: Provides the foundation necessary for graduate students to learn and understand more advanced topics Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates Covers computational electromagnetics in both frequency and time domains Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills.


Computational Electromagnetics

Computational Electromagnetics

Author: Anders Bondeson

Publisher: Springer Science & Business Media

Published: 2006-02-07

Total Pages: 232

ISBN-13: 0387261605

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Describes most popular computational methods used to solve problems in electromagnetics Matlab code is included throughout, so that the reader can implement the various techniques discussed Exercises included


Book Synopsis Computational Electromagnetics by : Anders Bondeson

Download or read book Computational Electromagnetics written by Anders Bondeson and published by Springer Science & Business Media. This book was released on 2006-02-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes most popular computational methods used to solve problems in electromagnetics Matlab code is included throughout, so that the reader can implement the various techniques discussed Exercises included


Computational Electromagnetics with MATLAB, Fourth Edition

Computational Electromagnetics with MATLAB, Fourth Edition

Author: Matthew N.O. Sadiku

Publisher: CRC Press

Published: 2018-07-20

Total Pages: 687

ISBN-13: 1351365096

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This fourth edition of the text reflects the continuing increase in awareness and use of computational electromagnetics and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite-difference time-domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. It teaches the readers how to pose, numerically analyze, and solve EM problems, to give them the ability to expand their problem-solving skills using a variety of methods, and to prepare them for research in electromagnetism. Includes new homework problems in each chapter. Each chapter is updated with the current trends in CEM. Adds a new appendix on CEM codes, which covers commercial and free codes. Provides updated MATLAB code.


Book Synopsis Computational Electromagnetics with MATLAB, Fourth Edition by : Matthew N.O. Sadiku

Download or read book Computational Electromagnetics with MATLAB, Fourth Edition written by Matthew N.O. Sadiku and published by CRC Press. This book was released on 2018-07-20 with total page 687 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fourth edition of the text reflects the continuing increase in awareness and use of computational electromagnetics and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite-difference time-domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. It teaches the readers how to pose, numerically analyze, and solve EM problems, to give them the ability to expand their problem-solving skills using a variety of methods, and to prepare them for research in electromagnetism. Includes new homework problems in each chapter. Each chapter is updated with the current trends in CEM. Adds a new appendix on CEM codes, which covers commercial and free codes. Provides updated MATLAB code.


Numerical Electromagnetics

Numerical Electromagnetics

Author: Umran S. Inan

Publisher: Cambridge University Press

Published: 2011-04-07

Total Pages: 405

ISBN-13: 1139497987

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Beginning with the development of finite difference equations, and leading to the complete FDTD algorithm, this is a coherent introduction to the FDTD method (the method of choice for modeling Maxwell's equations). It provides students and professional engineers with everything they need to know to begin writing FDTD simulations from scratch and to develop a thorough understanding of the inner workings of commercial FDTD software. Stability, numerical dispersion, sources and boundary conditions are all discussed in detail, as are dispersive and anisotropic materials. A comparative introduction of the finite volume and finite element methods is also provided. All concepts are introduced from first principles, so no prior modeling experience is required, and they are made easier to understand through numerous illustrative examples and the inclusion of both intuitive explanations and mathematical derivations.


Book Synopsis Numerical Electromagnetics by : Umran S. Inan

Download or read book Numerical Electromagnetics written by Umran S. Inan and published by Cambridge University Press. This book was released on 2011-04-07 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: Beginning with the development of finite difference equations, and leading to the complete FDTD algorithm, this is a coherent introduction to the FDTD method (the method of choice for modeling Maxwell's equations). It provides students and professional engineers with everything they need to know to begin writing FDTD simulations from scratch and to develop a thorough understanding of the inner workings of commercial FDTD software. Stability, numerical dispersion, sources and boundary conditions are all discussed in detail, as are dispersive and anisotropic materials. A comparative introduction of the finite volume and finite element methods is also provided. All concepts are introduced from first principles, so no prior modeling experience is required, and they are made easier to understand through numerous illustrative examples and the inclusion of both intuitive explanations and mathematical derivations.


Numerical Methods in Electromagnetism

Numerical Methods in Electromagnetism

Author: M. V.K. Chari

Publisher: Academic Press

Published: 2000

Total Pages: 783

ISBN-13: 012615760X

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Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. Numerical Methods in Electromagnetism will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students. Comprehensive descriptions of numerical methods In-depth introduction to finite differences, finite elements, and integral equations Illustrations and applications of linear and nonlinear solutions for multi-dimensional analysis Numerical examples to facilitate understanding of the methods Appendices for quick reference of mathematical and numerical methods employed


Book Synopsis Numerical Methods in Electromagnetism by : M. V.K. Chari

Download or read book Numerical Methods in Electromagnetism written by M. V.K. Chari and published by Academic Press. This book was released on 2000 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. Numerical Methods in Electromagnetism will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students. Comprehensive descriptions of numerical methods In-depth introduction to finite differences, finite elements, and integral equations Illustrations and applications of linear and nonlinear solutions for multi-dimensional analysis Numerical examples to facilitate understanding of the methods Appendices for quick reference of mathematical and numerical methods employed


The Method of Moments in Electromagnetics

The Method of Moments in Electromagnetics

Author: Walton C. Gibson

Publisher: CRC Press

Published: 2021-09-06

Total Pages: 510

ISBN-13: 1000412482

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The Method of Moments in Electromagnetics, Third Edition details the numerical solution of electromagnetic integral equations via the Method of Moments (MoM). Previous editions focused on the solution of radiation and scattering problems involving conducting, dielectric, and composite objects. This new edition adds a significant amount of material on new, state-of-the art compressive techniques. Included are new chapters on the Adaptive Cross Approximation (ACA) and Multi-Level Adaptive Cross Approximation (MLACA), advanced algorithms that permit a direct solution of the MoM linear system via LU decomposition in compressed form. Significant attention is paid to parallel software implementation of these methods on traditional central processing units (CPUs) as well as new, high performance graphics processing units (GPUs). Existing material on the Fast Multipole Method (FMM) and Multi-Level Fast Multipole Algorithm (MLFMA) is also updated, blending in elements of the ACA algorithm to further reduce their memory demands. The Method of Moments in Electromagnetics is intended for students, researchers, and industry experts working in the area of computational electromagnetics (CEM) and the MoM. Providing a bridge between theory and software implementation, the book incorporates significant background material, while presenting practical, nuts-and-bolts implementation details. It first derives a generalized set of surface integral equations used to treat electromagnetic radiation and scattering problems, for objects comprising conducting and dielectric regions. Subsequent chapters apply these integral equations for progressively more difficult problems such as thin wires, bodies of revolution, and two- and three-dimensional bodies. Radiation and scattering problems of many different types are considered, with numerical results compared against analytical theory as well as measurements.


Book Synopsis The Method of Moments in Electromagnetics by : Walton C. Gibson

Download or read book The Method of Moments in Electromagnetics written by Walton C. Gibson and published by CRC Press. This book was released on 2021-09-06 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Method of Moments in Electromagnetics, Third Edition details the numerical solution of electromagnetic integral equations via the Method of Moments (MoM). Previous editions focused on the solution of radiation and scattering problems involving conducting, dielectric, and composite objects. This new edition adds a significant amount of material on new, state-of-the art compressive techniques. Included are new chapters on the Adaptive Cross Approximation (ACA) and Multi-Level Adaptive Cross Approximation (MLACA), advanced algorithms that permit a direct solution of the MoM linear system via LU decomposition in compressed form. Significant attention is paid to parallel software implementation of these methods on traditional central processing units (CPUs) as well as new, high performance graphics processing units (GPUs). Existing material on the Fast Multipole Method (FMM) and Multi-Level Fast Multipole Algorithm (MLFMA) is also updated, blending in elements of the ACA algorithm to further reduce their memory demands. The Method of Moments in Electromagnetics is intended for students, researchers, and industry experts working in the area of computational electromagnetics (CEM) and the MoM. Providing a bridge between theory and software implementation, the book incorporates significant background material, while presenting practical, nuts-and-bolts implementation details. It first derives a generalized set of surface integral equations used to treat electromagnetic radiation and scattering problems, for objects comprising conducting and dielectric regions. Subsequent chapters apply these integral equations for progressively more difficult problems such as thin wires, bodies of revolution, and two- and three-dimensional bodies. Radiation and scattering problems of many different types are considered, with numerical results compared against analytical theory as well as measurements.


Electromagnetic Analysis Using Transmission Line Variables

Electromagnetic Analysis Using Transmission Line Variables

Author: Maurice Weiner

Publisher: World Scientific

Published: 2001

Total Pages: 536

ISBN-13: 9789812810472

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V. Boundary conditions and dispersion. 5.1. Dielectric-dielectric interface. Node coupling: nearest node and multi-coupled node approximations. 5.2. Nearest nodes for ID interface. 5.3. Nearest nodes at 2D interface. 5.4. Truncated cell and oblique interface. 5.5. Single index cell notation. 5.6. Simplified iteration neglecting the nearest node approximation. 5.7. Non-uniform dielectric. Use of cluster cells. Other boundary conditions. 5.8. Dielectric- open circuit interface. 5.9. Dielectric - conductor interface. 5.10. Input/output conditions. 5.11. Composite transmission line. 5.12. Determination of initial static field by TLM method. 5.13. Time varying source voltage and antenna simulation. Dispersion. 5.14. Dispersion sources. 5.15. Dispersion example. 5.16. Propagation velocity in terms of wave number. 5.17. Dispersive properties of node resistance. 5.18. Node resistance in terms of wave number. 5.19. Anomalous dispersion. Incorporation of dispersion into TLM formulation. 5.20. Dispersion approximations. 5.21. Outline of dispersion calculation using the TLM method. 5.22. One dimensional dispersion iteration. 5.23. Initial conditions with dispersion present. 5.24. Stability of initial profiles with dispersion present. 5.25. Replacement of non-uniform field in cell with effective uniform field -- VI. Cell discharge properties and integration of transport phenomena into the TLM matrix. 6.1. Charge transfer between cells. 6.2. Relationship between field and cell charge. 6.3. Dependence of conductivity on carrier properties. Integration of carrier transport using TLM notation. Changes in cell occupancy and its effect on TLM iteration. 6.4. General continuity equations. 6.5. Carrier generation due to light activation. 6.6. Carrier generation due to avalanching: identical hole and electron drift velocities. 6.7. Avalanching with differing hole and electron drift velocities. 6.8. Two step generation process. 6.9. Recombination. 6.10. Limitations of simple exponential recovery model. 6.11. Carrier drift. 6.12. Cell charge iteraction.equivalence of drift and inter-cell currents. 6.13. Carrier diffusion. 6.14. Frequency of transport iteration. 6.15. Total contribution to changes in carrier cell occupancy -- VII. Description of TLM iteration. 7.1. Specification of geometry. 7.2. Description of inputs and TLM iteration outline. 7.3. Output format. Output simulation data. 7.4. Conditions during simulation. 7.5. Behavior during charge-up.establishment of static field profile. 7.6. Node resistance R(n,m) during activation. 7.7. Output pulse when semiconductor is activated. 7.8. Node recovery and its effect on output pulse. 7.9. Steady state and transient field profiles. 7.10. Partial activation of nodes and effect on profiles and output. 7.11. Cell charge following recovery. 7.12. Role ofTLM waves at charged boundary. 7.13. Comparison of possible boundary conditions at the semiconductor/dielectric interface. 7.14. Simulation results for boundary with non-integral nearest nodes. 7.15. Comparison of output with and without matched input /output lines. 7.16. Simulation of plane wave effects. Effect of alternating input -- VIII. Spice solutions. 8.1. Photoconductive switch. 8.2. Traveling wave Marx generator. 8.3. Traveling Marx wave in a layered dielectric. 8.4. Simulation of a traveling Marx wave in a layered dielectric. Pulse transformation and generation using non-uniform transmission lines. 8.5. Use of cell chain to simulate pulse transformer. 8.6. Pulse transformer simulation results. 8.7. Pulse sources using non-uniform TLM lines (switch at output). 8.8. Radial pulse source (switch at output). 8.9. Pulse sources with gain (PFXL sources). Darlington pulser. 8.10. TLM formulation of Darlington pulser. 8.11. SPICE simulation of Lossy Darlington Pulser.


Book Synopsis Electromagnetic Analysis Using Transmission Line Variables by : Maurice Weiner

Download or read book Electromagnetic Analysis Using Transmission Line Variables written by Maurice Weiner and published by World Scientific. This book was released on 2001 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: V. Boundary conditions and dispersion. 5.1. Dielectric-dielectric interface. Node coupling: nearest node and multi-coupled node approximations. 5.2. Nearest nodes for ID interface. 5.3. Nearest nodes at 2D interface. 5.4. Truncated cell and oblique interface. 5.5. Single index cell notation. 5.6. Simplified iteration neglecting the nearest node approximation. 5.7. Non-uniform dielectric. Use of cluster cells. Other boundary conditions. 5.8. Dielectric- open circuit interface. 5.9. Dielectric - conductor interface. 5.10. Input/output conditions. 5.11. Composite transmission line. 5.12. Determination of initial static field by TLM method. 5.13. Time varying source voltage and antenna simulation. Dispersion. 5.14. Dispersion sources. 5.15. Dispersion example. 5.16. Propagation velocity in terms of wave number. 5.17. Dispersive properties of node resistance. 5.18. Node resistance in terms of wave number. 5.19. Anomalous dispersion. Incorporation of dispersion into TLM formulation. 5.20. Dispersion approximations. 5.21. Outline of dispersion calculation using the TLM method. 5.22. One dimensional dispersion iteration. 5.23. Initial conditions with dispersion present. 5.24. Stability of initial profiles with dispersion present. 5.25. Replacement of non-uniform field in cell with effective uniform field -- VI. Cell discharge properties and integration of transport phenomena into the TLM matrix. 6.1. Charge transfer between cells. 6.2. Relationship between field and cell charge. 6.3. Dependence of conductivity on carrier properties. Integration of carrier transport using TLM notation. Changes in cell occupancy and its effect on TLM iteration. 6.4. General continuity equations. 6.5. Carrier generation due to light activation. 6.6. Carrier generation due to avalanching: identical hole and electron drift velocities. 6.7. Avalanching with differing hole and electron drift velocities. 6.8. Two step generation process. 6.9. Recombination. 6.10. Limitations of simple exponential recovery model. 6.11. Carrier drift. 6.12. Cell charge iteraction.equivalence of drift and inter-cell currents. 6.13. Carrier diffusion. 6.14. Frequency of transport iteration. 6.15. Total contribution to changes in carrier cell occupancy -- VII. Description of TLM iteration. 7.1. Specification of geometry. 7.2. Description of inputs and TLM iteration outline. 7.3. Output format. Output simulation data. 7.4. Conditions during simulation. 7.5. Behavior during charge-up.establishment of static field profile. 7.6. Node resistance R(n,m) during activation. 7.7. Output pulse when semiconductor is activated. 7.8. Node recovery and its effect on output pulse. 7.9. Steady state and transient field profiles. 7.10. Partial activation of nodes and effect on profiles and output. 7.11. Cell charge following recovery. 7.12. Role ofTLM waves at charged boundary. 7.13. Comparison of possible boundary conditions at the semiconductor/dielectric interface. 7.14. Simulation results for boundary with non-integral nearest nodes. 7.15. Comparison of output with and without matched input /output lines. 7.16. Simulation of plane wave effects. Effect of alternating input -- VIII. Spice solutions. 8.1. Photoconductive switch. 8.2. Traveling wave Marx generator. 8.3. Traveling Marx wave in a layered dielectric. 8.4. Simulation of a traveling Marx wave in a layered dielectric. Pulse transformation and generation using non-uniform transmission lines. 8.5. Use of cell chain to simulate pulse transformer. 8.6. Pulse transformer simulation results. 8.7. Pulse sources using non-uniform TLM lines (switch at output). 8.8. Radial pulse source (switch at output). 8.9. Pulse sources with gain (PFXL sources). Darlington pulser. 8.10. TLM formulation of Darlington pulser. 8.11. SPICE simulation of Lossy Darlington Pulser.