Computer Analysis of Low-Frequency EM Fields
Electromagnetic field equations (Laplace, Poisson, Diffusion, Helmholtz), choice of potentials in two and three dimensional geometries, gauge conditions (Coulomb, Lorentz), physical interpretation. Geometrical formulation of Maxwell’s equations. Γεωμετρική διατύπωση εξισώσεων Maxwell. Analytical Methods: method of separation of variables, coordinate system transformation, image theory, conformal transformation, other transformations. Numerical Methods: integral equation formulation, functional, Ritz’s projection theory, integral transformations. Discrete problem: space discretization (finite differences, finite elements – nodal and edge elements, boundary elements, equivalent single layer and double layer sources, Green’s function methodology. Automatic mesh generation. Time discretization (static analysis, harmonic time variation and complex variables, periodic and transient phenomena analysis by time stepping techniques, convergence in time, prediction – correction techniques). Numerical Techniques: nonlinear phenomena – iron saturation consideration (linearization methods, Newton-Raphson algorithm, spline functions. Numerical integration and finite elements of high order). Approximation error. Methods for solution of systems of equations (Gauss, Cholesky, Crout, Conjugate Gradient algorithms). Hybrid methods: coupling techniques of different methods, mesh edging techniques (absorbing boundaries, optimal mesh layer tuning). Applications: electrical machines, electrode configurations. Calculation of eddy currents, losses, self and mutual inductances, impact of iron saturation, forces and torques (Laplace forces, virtual work principle, Maxwell stress tensor), determination of equivalent circuit parameters, discharge condition analysis. Inverse problem and optimization (objective functions, evolution strategies, regularization techniques, sensitivity analysis, local and global extrema, simulated annealing, genetic algorithms).