Computational electromagnetism variational formulations, complementarity, edge elements
Computational Electromagnetism refers to the modern concept of computer-aided analysis, and design, of virtually all electric devices such as motors, machines, transformers, etc., as well as of the equipment inthe currently booming field of telecommunications, such as antennas, radars, etc.The prese...
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
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San Diego :
Academic Press
c1998.
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| Edición: | 1st edition |
| Colección: | Electromagnetism.
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| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009627151406719 |
Tabla de Contenidos:
- Front Cover; Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements; Copyright Page; Contents; Preface; Chapter 1. Introduction: Maxwell Equations; 1.1 Field Equations; 1.2 Constitutive Laws; 1.3 Macroscopic Interactions; 1.4 Derived Models; Exercises; Solutions; References; Chapter 2. Magnetostatics: ""Scalar Potential"" Approach; 2.1 Introduction: A Model Problem; 2.2 Honing Our Tools; 2.3 Weak Formulations; 2.4 Modelling: The Scalar Potential Formulation; Exercises; Solutions; References; Chapter 3. Solving for the Scalar Magnetic Potential
- 3.1 The ""Variational"" Formulation3.2 Existence of a Solution; 3.3 Discretization; Exercises; Solutions; References; Chapter 4. The Approximate Scalar Potential: Properties and Shortcomings; 4.1 The ""m-weak"" Properties; 4.2 The Maximum Principle; 4.3 Convergence and Error Analysis; Exercises; Solutions; References; Chapter 5. Whitney Elements; 5.1 A Functional Framework; 5.2 The Whitney Complex; 5.3 Trees and Cotrees; Exercises; Solutions; References; Chapter 6. The ""Curl Side"": Complementarity; 6.1 A Symmetrical Variational Formulation; 6.2 Solving the Magnetostatics Problem
- 6.3 Why Not Standard Elements?Exercises; Solutions; References; Chapter 7. Infinite Domains; 7.1 Another Model Problem; 7.2 Formulation; 7.3 Discretization; 7.4 The ""Dirichlet-to-Neumann"" Map; 7.5 Back to Magnetostatics; Exercises; Solutions; References; Chapter 8. Eddy-Current Problems; 8.1 The Model in H; 8.2 Infinite Domains: ""Trifou""; 8.3 Bounded Domains: Trees, H-?; 8.4 Summing Up; Exercises; Solutions; References; Chapter 9. Maxwell's Model in Harmonic Regime; 9.1 A Concrete Problem: The Microwave Oven; 9.2 The ""Continuous"" Problem; 9.3 The ""Discrete"" Problem; References
- APPENDIX A. Mathematical BackgroundA.1 Basic Notions; A.2 Important Structures; A.3 Our Framework for Electromagnetism: E3; A.4 Glimpses of Functional Analysis; References; APPENDIX B. LDL t Factorization and Constrained Linear Systems; B.1 Nonnegative Definite Matrices; B.2 A Digression about Programming; B.3 The LDL t Factorization; B.4 Application to Constrained Linear Systems; References; APPENDIX C. A Cheaper Way to Complementarity; C.1 Local Corrections; C.2 Solving Problem (14); C.3 Conclusion and Speculations; Author Index; Subject Index
