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Record Nr. |
UNINA9910139496003321 |
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Titolo |
The finite element method for electromagnetic modeling [[electronic resource] /] / edited by Gerard Meunier |
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Pubbl/distr/stampa |
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London, : ISTE |
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Hoboken, NJ, USA, : Wiley, 2008 |
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ISBN |
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1-282-16504-6 |
9786612165047 |
0-470-61117-0 |
0-470-39380-7 |
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Descrizione fisica |
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1 online resource (618 p.) |
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Collana |
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Altri autori (Persone) |
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Disciplina |
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621.301/51825 |
621.30151825 |
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Soggetti |
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Electromagnetic devices - Mathematical models |
Electromagnetism - Mathematical models |
Engineering mathematics |
Finite element method |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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The Finite Element Method for Electromagnetic Modeling; Table of Contents; Chapter 1. Introduction to Nodal Finite Elements; 1.1. Introduction; 1.1.1. The finite element method; 1.2. The 1D finite element method; 1.2.1. A simple electrostatics problem; 1.2.2. Differential approach; 1.2.3. Variational approach; 1.2.4. First-order finite elements; 1.2.5. Second-order finite elements; 1.3. The finite element method in two dimensions; 1.3.1. The problem of the condenser with square section; 1.3.2. Differential approach; 1.3.3. Variational approach |
1.3.4. Meshing in first-order triangular finite elements1.3.5. Finite element interpolation; 1.3.6. Construction of the system of equations by the Ritz method; 1.3.7. Calculation of the matrix coefficients; 1.3.8. Analysis of the results; 1.3.9. Dual formations, framing and convergence; 1.3.10. Resolution of the nonlinear problems; 1.3.11. Alternative to the variational method: the weighted residues method; |
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1.4. The reference elements; 1.4.1. Linear reference elements; 1.4.2. Surface reference elements; 1.4.3. Volume reference elements; 1.4.4. Properties of the shape functions |
1.4.5. Transformation from reference coordinates to domain coordinates.1.4.6. Approximation of the physical variable; 1.4.7. Numerical integrations on the reference elements; 1.4.8. Local Jacobian derivative method; 1.5. Conclusion; 1.6. References; Chapter 2. Static Formulations: Electrostatic, Electrokinetic, Magnetostatics; 2.1. Problems to solve; 2.1.1. Maxwell's equations; 2.1.2. Behavior laws of materials; 2.1.3. Boundary conditions; 2.1.4. Complete static models; 2.1.5. The formulations in potentials; 2.2. Function spaces in the fields and weak formulations |
2.2.1. Integral expressions: introduction2.2.2. Definitions of function spaces; 2.2.3. Tonti diagram: synthesis scheme of a problem; 2.2.4. Weak formulations; 2.3. Discretization of function spaces and weak formulations; 2.3.1. Finite elements; 2.3.2. Sequence of discrete spaces; 2.3.3. Gauge conditions and source terms in discrete spaces; 2.3.4. Weak discrete formulations; 2.3.5. Expression of global variables; 2.4. References; Chapter 3. Magnetodynamic Formulations; 3.1. Introduction; 3.2. Electric formulations; 3.2.1. Formulation in electric field |
3.2.2. Formulation in combined potentials α - Ψ3.2.3. Comparison of the formulations in field and in combined potentials; 3.3. Magnetic formulations; 3.3.1. Formulation in magnetic field; 3.3.2. Formulation in combined potentials t - Φ; 3.3.3. Numerical example; 3.4. Hybrid formulation; 3.5. Electric and magnetic formulation complementarities; 3.5.1. Complementary features; 3.5.2. Concerning the energy bounds; 3.5.3. Numerical example; 3.6. Conclusion; 3.7. References; Chapter 4. Mixed Finite Element Methods in Electromagnetism; 4.1. Introduction; 4.2. Mixed formulations in magnetostatics |
4.2.1. Magnetic induction oriented formulation |
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Sommario/riassunto |
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Written by specialists of modeling in electromagnetism, this book provides a comprehensive review of the finite element method for low frequency applications. Fundamentals of the method as well as new advances in the field are described in detail.Chapters 1 to 4 present general 2D and 3D static and dynamic formulations by the use of scalar and vector unknowns and adapted interpolations for the fields (nodal, edge, face or volume).Chapter 5 is dedicated to the presentation of different macroscopic behavior laws of materials and their implementation in a finite element context: anisotrop |
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