The Cell Method for Electrical Engineering and Multiphysics Problems An Introduction
This book describes the main components of the cell method technique: space-time discretization, problem formulation, solution and representation of the resulting physical fields. Offers solved problems in electromagnetism, elasticity and thermo-elasticity.
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| Hlavní autor: | |
|---|---|
| Médium: | E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Berlin, Heidelberg
Springer Nature
2013
Springer Berlin / Heidelberg Springer Berlin Heidelberg Springer |
| Vydání: | 1 |
| Edice: | Lecture Notes in Electrical Engineering |
| Témata: | |
| ISBN: | 9783642361012, 3642361013, 3642434509, 9783642434501, 3642361005, 9783642361005 |
| ISSN: | 1876-1100, 1876-1119 |
| On-line přístup: | Získat plný text |
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| Abstract | This book describes the main components of the cell method technique: space-time discretization, problem formulation, solution and representation of the resulting physical fields. Offers solved problems in electromagnetism, elasticity and thermo-elasticity. |
|---|---|
| AbstractList | This book presents a numerical scheme for the solution of field problems governed by partial differential equations: the cell method. The technique lends itself naturally to the solution of multiphysics problems with several interacting phenomena. The Cell Method, based on a space-time tessellation, is intimately related to the work of Tonti and to his ideas of classification diagrams or, as they are nowadays called, Tonti diagrams: a graphical representation of the problem's equations made possible by a suitable selection of a space-time framework relating physical variables to each other. The main features of the cell method are presented and links with many other discrete numerical methods (finite integration techniques, finite difference time domain, finite volumes, mimetic finite differences, etc.) are discussed. After outlining the theoretical basis of the method, a set of physical problems which have been solved with the cell method is described. These single and multiphysics problems stem from the authors' research experience in the fields of electromagnetism, elasticity, thermo-elasticity and others. Finally, the implementation of the numerical technique is described in all its main components: space-time discretization, problem formulation, solution and representation of the resulting physical fields. This book describes the main components of the cell method technique: space-time discretization, problem formulation, solution and representation of the resulting physical fields. Offers solved problems in electromagnetism, elasticity and thermo-elasticity. |
| Author | Alotto, Piergiorgio Rosso, Carlo Freschi, Fabio Repetto, Maurizio |
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| Copyright | Springer-Verlag Berlin Heidelberg 2013 |
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| DOI | 10.1007/978-3-642-36101-2 |
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| EISSN | 1876-1119 |
| Edition | 1 2013 |
| Editor | Rosso, Carlo Repetto, Maurizio Freschi, Fabio |
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| PublicationYear | 2013 |
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| Snippet | This book describes the main components of the cell method technique: space-time discretization, problem formulation, solution and representation of the... This book presents a numerical scheme for the solution of field problems governed by partial differential equations: the cell method. The technique lends... |
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| SubjectTerms | Electrical Engineering Engineering Engineering & allied operations Engineering mathematics Mathematical and Computational Engineering Mathematical physics Numerical and Computational Physics, Simulation |
| Subtitle | An Introduction |
| TableOfContents | Title Page -- Preface -- Contents -- Tonti Diagrams -- Classification of the Physical Variables -- Local and Global Variables -- Cell Complexes -- Variables and Orientation -- A Note on Time -- Tonti Diagrams -- References -- Topological Equations -- The Numerical Scheme -- Cell Complexes -- Basic Definitions of Algebraic Topology and Cell Complexes -- Coboundary Process -- Topological Equations -- Incidence Numbers and Incidence Matrices -- The Cell Method for Stationary Heat Conduction -- A Note for Practitioners -- Links with Other Numerical Methods -- References -- Constitutive Equations -- Introduction -- Example of a Constitutive Equation for a Simple Problem -- Constitutive Equations for Orthogonal Grids -- Case 1 -- Case 2 -- Constitutive Matrix Set-Up -- Constitutive Equations on Tetrahedral Grids -- Uniform Field -- Non-uniform Field -- Whitney Interpolation -- Thermal Mass Matrix -- Boundary Conditions -- References -- Classical Physical Problems -- Electrostatics and Electric Current Flow -- Magnetostatics -- Sources of the Magnetostatic Field -- TEAM Problem 20 -- Force Computation -- Elastostatics -- Elastostatics Definition -- Finite Formulation of Elastostatics -- Application of Elastostatic Formulation -- Thermal Transient -- Elastodynamics -- Eigenmode Analysis -- References -- Multiphysics Problems -- Coupled Problems -- Electro-thermo-mechanical Coupling -- Electro-thermal Coupling Term -- Thermo-mechanical Coupling Term -- Complete System of Equations -- Example: MEMS Microbeam -- Induction Heating -- Eddy Current Numerical Formulation -- Unstationary Thermal Problem -- Test Case: Heating Inductor -- Thermo-mechanical Coupling -- Thermal Model -- Structural Model -- References -- Implementation -- Development Environment -- Anatomy of the Code -- Phase 1: Data Structures -- Phase 2: Material Properties Phase 3: Constitutive and Stiffness Matrices -- Phase 4: Sources -- Phase 5: Boundary Conditions -- Phase 6: Solution -- 6.9 Phase 7: Plotting Maps -- Example -- Discussion -- References |
| Title | The Cell Method for Electrical Engineering and Multiphysics Problems |
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