Articles liés à Numerical Analysis of Electromagnetic Fields
Synopsis
1 Universal Concepts for Numerical Analysis of Electromagnetic Field Problems.- 1 Fundamental Concepts of Electromagnetic Field Theory.- 1.1 Maxwell's equations and boundary value problems.- 1.1.1 Potential equations in different frequency ranges.- 1.1.2 Boundary conditions of the interface.- 1.1.3 Boundary value problems.- 1.2 Green's theorem, Green's functions and fundamental solutions.- 1.2.1 Green's theorem.- 1.2.2 Vector analogue of Green's theorem.- 1.2.3 Green's function.- 1.2.3.1 Dirac-delta function.- 1.2.3.2 Green's function.- 1.2.4 Fundamental solutions.- 1.3 Equivalent sources.- 1.3.1 Single layer charge distribution.- 1.3.2 Double layer source distributions.- 1.3.3 Equivalent polarization charge and magnetization current.- 1.4 Integral equations of electromagnetic fields.- 1.4.1 Integral form of Poisson's equation.- 1.4.2 Integral equation for the exterior region.- 1.5 Summary.- References.- Appendix 1.1 The integral equation of 3-D magnetic fields.- 2 General Outline of Numerical Methods.- 2.1 Introduction.- 2.2 Operator equations.- 2.2.1 Hubert space.- 2.2.2 Definition and properties of operators.- 2.2.3 The relationship between the properties of the operators and the solution of operator equations.- 2.2.4 Operator equations of electromagnetic fields.- 2.3 Principles of error minimization.- 2.3.1 Principle of weighted residuals.- 2.3.2 Orthogonal projection principle.- 2.3.2.1 Projection operator.- 2.3.2.2 Orthogonal projection.- 2.3.2.3 Orthogonal projection methods.- 2.3.2.4 Non-orthogonal projection methods.- 2.3.3 Variational principle.- 2.4 Categories of various numerical methods.- 2.4.1 Methods of weighted residuals.- 2.4.1.1 Method of moments.- 2.4.1.2 Galerkin's finite element method.- 2.4.1.3 Collocation methods.- 2.4.1.4 Boundary element methods.- 2.4.2 Variational approach.- 2.5 Summary.- References.- 2 Domain Methods.- 3 Finite Difference Method (FDM).- 3.1 Introduction.- 3.2 Difference formulation of Poisson's equation.- 3.2.1 Discretization mode for 2-D problems.- 3.2.2 Difference equations in 2-D Cartesian coordinates.- 3.2.3 Discretization equation in polar coordinates.- 3.2.4 Discretization formula of axisymmetric fields.- 3.2.5 Discretization formula of the non-linear magnetic fields.- 3.2.6 Difference equations for time-dependent problems.- 3.3 Solution methods for difference equations.- 3.3.1 Properties of simultaneous equations.- 3.3.2 Successive over-relaxation (SOR) method.- 3.3.3 Convergence criterion.- 3.4. Difference formulations of arbitrary boundaries and interfacial boundaries between different materials.- 3.4.1 Difference formulations on the lines of symmetry.- 3.4.2 Difference equation of a curved boundary.- 3.4.3 Difference formulations for the interface of different materials.- 3.5 Examples.- 3.6 Further discussions about the finite difference method.- 3.6.1 Physical explanation of the finite difference method.- 3.6.2 The error analysis of the finite difference method.- 3.6.3 Difference equation and the principle of weighted residuals.- 3.6.4 Difference equation and the variational principle.- 3.7 Summary.- References.- 4 Fundamentals of Finite Element Method (FFM).- 4.1 Introduction.- 4.2 General procedures of the finite element method.- 4.2.1 Domain discretization and shape functions.- 4.2.2 Method using Galerkin residuals.- 4.2.2.1 Element matrix equations.- 4.2.2.2 System matrix equation.- 4.2.2.3 Storage of the system matrix.- 4.2.2.4 Treatment of the Dirichlet boundary condition.- 4.3 Solution methods of finite element equations.- 4.3.1 Direct methods.- 4.3.1.1 Gaussian elimination method.- 4.3.1.2 Cholesky's decomposition (triangular decomposition).- 4.3.2 Iterative methods.- 4.3.2.1 Method of over-relaxation iteration.- 4.3.2.2 Conjugate-gradient method (CGM).- 4.4 Mesh generation.- 4.4.1 Mesh generation of a triangular element.- 4.4.2 Automatic mesh generation.- 4.5 Examples.- 4.6 Summary.- References.- 5 Variational Finite Element Method.- 5.1 Introduction.-
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