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## Forward simulation methods

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This book chapter presents methods for simulation of electromagnetic problems related to MIECT. The main purpose of the presented methods is their application to development of the general LET systems. Furthermore, the main objective is the calculation the Lorentz forces which result from the interaction between permanent magnets and moving, nonmagnetic and electrically conductive objects. In general, numerical simulations of LET problems can be relatively time-consuming. Therefore, an additional emphasis was put on the development of fast semi-analytical and simplified numerical methods that allow solving general LET problems with satisfactory accuracy.

Chapter Contents:

• 2.1 Moving coordinate systems—transformations
• 2.2 Semianalytical methods used in LET systems
• 2.2.1 Calculation of forces in 2D LET systems
• 2.2.2 Lorentz forces acting on 3D permanent magnets above moving conducting plate without defects
• 2.2.3 Calculation of forces in 3D LET systems
• 2.2.4 Oscillatory motion of permanent magnets above a conducting plate
• 2.2.4.1 Introduction and motivation
• 2.2.4.2 Mathematical formulation of the problem
• 2.2.4.2.1 The governing equations and its solutions
• 2.2.4.2.2 Fourier transform of the source current
• 2.2.4.2.3 Force calculation
• 2.2.4.3 Comparison to numerical simulations
• 2.2.4.3.1 The 2D numerical model
• 2.2.4.3.2 The 2D analytical model
• 2.2.4.3.3 Comparison of analytical and numerical results
• 2.2.4.4 Results and discussion
• 2.2.4.4.1 Constant rectilinear motion
• 2.2.4.4.2 Harmonic motion
• 2.2.4.4.3 Constant rectilinear motion superimposed by harmonic oscillations
• 2.2.4.4.4 Conclusions
• 2.2.5 The simplest approach to calculate DRS
• 2.2.6 A hole in a thin, large, conductive sheet
• 2.2.7 An extended area approach in the calculation of DRS
• 2.3 Surface charge simulation method
• 2.4 Numerical simulations with FEM
• 2.4.1 Introduction and motivation
• 2.4.2 Computation of eddy current distributions including moving parts
• 2.4.3 Numerical modeling of conductivity anomalies
• 2.4.3.1 Benchmark problem definition
• 2.4.3.2 Logical expression approaches
• 2.4.3.2.1 Moving magnet approach
• 2.4.3.2.2 Moving defect approach
• 2.4.3.3 Quasi-static approach
• 2.4.3.4 Weak reaction approaches
• 2.4.3.4.1 Extended weak reaction approach
• 2.4.3.4.2 Direct weak reaction approach
• 2.4.3.5 Summary and overview
• 2.4.4 Comparison of numerical approaches

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