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Integral methods in low-frequency electromagnetics / / Pavel Solin, Ivo Dolezel, Pavel Karban
| Integral methods in low-frequency electromagnetics / / Pavel Solin, Ivo Dolezel, Pavel Karban |
| Autore | Solin Pavel |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hoboken, NJ, : Wiley, c2009 |
| Descrizione fisica | 1 online resource (418 p.) |
| Disciplina |
537
621.3 |
| Altri autori (Persone) |
DolezelIvo
KarbanP <1979-> (Pavel) |
| Soggetto topico |
ELF electromagnetic fields - Mathematical models
Integrals |
| ISBN |
1-282-25940-7
9786612259401 0-470-50273-8 0-470-50272-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Integral Methods in Low-Frequency Electromagnetics; Contents; List of Figures; List of Tables; Preface; Acknowledgments; 1 Electromagnetic Fields and their Basic Characteristics; 1.1 Fundamentals; 1.1.1 Maxwell's equations in integral form; 1.1.2 Maxwell's equations in differential form; 1.1.3 Constitutive relations and equation of continuity; 1.1.4 Media and their characteristics; 1.1.5 Conductors; 1.1.6 Dielectrics; 1.1.7 Magnetic materials; 1.1.8 Conditions on interfaces; 1.2 Potentials; 1.2.1 Scalar electric potential; 1.2.2 Magnetic vector potential; 1.2.3 Magnetic scalar potential
1.3 Mathematical models of electromagnetic fields 1.3.1 Static electric field; 1.3.2 Static magnetic field; 1.3.3 Quasistationary electromagnetic field; 1.3.4 General electromagnetic field; 1.4 Energy and forces in electromagnetic fields; 1.4.1 Energy of electric field; 1.4.2 Energy of magnetic field; 1.4.3 Forces in electric field; 1.4.4 Forces in magnetic field; 1.5 Power balance in electromagnetic fields; 1.5.1 Energy in electromagnetic field and its transformation; 1.5.2 Balance of power in linear electromagnetic field; 2 Overview of Solution Methods 2.1 Continuous models in electromagnetism 2.1.1 Differential models; 2.1.2 Integral and integrodifferential models; 2.2 Methods of solution of the continuous models; 2.2.1 Analytical methods; 2.2.2 Numerical methods; 2.2.3 Methods based on the stochastic approach; 2.2.4 Specific methods; 2.3 Classification of the analytical methods; 2.3.1 Methods built on the basic laws of electromagnetics; 2.3.2 Methods based on various transforms; 2.3.3 Direct solution of the field equations; 2.4 Numerical methods and their classification; 2.5 Differential methods; 2.5.1 Difference methods 2.5.2 Weighted residual methods 2.5.3 Variational and other related methods; 2.6 Finite element method; 2.6.1 Discretization of the definition area and selection of the approximate functions; 2.6.2 Computation of the functional and its extremization; 2.6.3 Further prospectives; 2.7 Integral and integrodifferential methods; 2.8 Important mathematical aspects of numerical methods; 2.8.1 Stability; 2.8.2 Convergence; 2.8.3 Accuracy; 2.9 Numerical schemes for parabolic equations; 2.9.1 Explicit scheme; 2.9.2 Implicit scheme; 3 Solution of Electromagnetic Fields by Integral Expressions 3.1 Introduction 3.2 1D integration area; 3.2.1 Review of typical problems; 3.2.2 Electric field generated by a solitary filamentary conductor of infinite length; 3.2.3 Electric field of charged thin circular ring; 3.2.4 Magnetic field generated by a solitary filamentary conductor of infinite length; 3.2.5 Magnetic field of thin circular current carrying loop; 3.2.6 Electric field generated by a system of uniformly charged parallel thin filaments of infinite length; 3.2.7 Magnetic field generated by a system of currents carrying parallel filamentary conductors of infinite length 3.3 2D integration area |
| Record Nr. | UNINA-9910808042003321 |
Solin Pavel
|
||
| Hoboken, NJ, : Wiley, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Partial differential equations and the finite element method / / Pavel Solin
| Partial differential equations and the finite element method / / Pavel Solin |
| Autore | Solin Pavel |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2006 |
| Descrizione fisica | 1 online resource (505 p.) |
| Disciplina | 518/.64 |
| Collana | Pure and applied mathematics |
| Soggetto topico |
Differential equations, Partial - Numerical solutions
Finite element method |
| ISBN |
1-280-28697-0
9786610286973 0-470-35884-X 0-471-76410-8 0-471-76409-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Partial Differential Equations and the Finite Element Method; CONTENTS; List of Figures; LIST OF FIGURES; List of Tables; LIST OF TABLES; Preface; Acknowledgments; 1 Partial Differential Equations; 1.1 Selected general properties; 1.1.1 Classification and examples; 1.1.2 Hadamard's well-posedness; 1.1 Jacques Salomon Hadamard ( 1865-1963).; 1.2 Isolines of the solution u(x, t ) of Burger's equation.; 1.1.3 General existence and uniqueness results; 1.1.4 Exercises; 1.2 Second-order elliptic problems; 1.2.1 Weak formulation of a model problem
1.3 Johann Peter Gustav Lejeune Dirichlet (1805-1859).1.2.2 Bilinear forms, energy norm, and energetic inner product; 1.2.3 The Lax-Milgram lemma; 1.2.4 Unique solvability of the model problem; 1.2.5 Nonhomogeneous Dirichlet boundary conditions; 1.2.6 Neumann boundary conditions; 1.2.7 Newton (Robin) boundary conditions; 1.2.8 Combining essential and natural boundary conditions; 1.2.9 Energy of elliptic problems; 1.2.10 Maximum principles and well-posedness; 1.4 Maximum principle for the Poisson equation in 2D.; 1.2.11 Exercises; 1.3 Second-order parabolic problems 1.3.1 Initial and boundary conditions1.3.2 Weak formulation; 1.3.3 Existence and uniqueness of solution; 1.3.4 Exercises; 1.4 Second-order hyperbolic problems; 1.4.1 Initial and boundary conditions; 1.4.2 Weak formulation and unique solvability; 1.4.3 The wave equation; 1.4.4 Exercises; 1.5 First-order hyperbolic problems; 1.5.1 Conservation laws; 1.5.2 Characteristics; 1.5.3 Exact solution to linear first-order systems; 1.5.4 Riemann problem; 1.5 Georg Friedrich Bernhard Riemann (1826-1866).; 1.6 Propagation of discontinuity in the solution of the Riemann problem. 1.5.5 Nonlinear flux and shock formation1.5.6 Exercises; 1.7 Formation of shock in the solution u(x, t ) of Burger's equation.; 2 Continuous Elements for 1D Problems; 2.1 The general framework; 2.1.1 The Galerkin method; 2.1 Boris Grigorievich Galerkin (1871-1945).; 2.1.2 Orthogonality of error and Céa's lemma; 2.1.3 Convergence of the Galerkin method; 2.1.4 Ritz method for symmetric problems; 2.1.5 Exercises; 2.2 Lowest-order elements; 2.2.1 Model problem; 2.2.2 Finite-dimensional subspace Vn C V; 2.2.3 Piecewise-affine basis functions; 2.2.4 The system of linear algebraic equations 2.2 Example of a basis function vi of the space Vn2.2.5 Element-by-element assembling procedure; 2.3 Tridiagonal stiffness matrix Sn.; 2.2.6 Refinement and convergence; 2.2.7 Exercises; 2.3 Higher-order numerical quadrature; 2.3.1 Gaussian quadrature rules; 2.4 Carl Friedrich Gauss (1777-1855).; 2.3.2 Selected quadrature constants; 2.1 Gaussian quadrature on Ka, order 2k - 1 = 3.; 2.2 Gaussian quadrature on Ka, order 2k - 1 = 5.; 2.3 Gaussian quadrature on Ka, order 2k - 1 = 7.; 2.4 Gaussian quadrature on Ka, order 2k - 1 = 9.; 2.5 Gaussian quadrature on Ka, order 2k - 1 = 11. 2.3.3 Adaptive quadrature |
| Record Nr. | UNINA-9910876520603321 |
|
Solin Pavel
|
||
| Hoboken, N.J., : Wiley-Interscience, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||