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.
Saved in:
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Nature
2013
Springer Berlin / Heidelberg Springer Berlin Heidelberg Springer |
| Edition: | 1 |
| Series: | Lecture Notes in Electrical Engineering |
| Subjects: | |
| ISBN: | 9783642361012, 3642361013, 3642434509, 9783642434501, 3642361005, 9783642361005 |
| ISSN: | 1876-1100, 1876-1119 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- 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