Lecturer: Paolo Di Barba   Maria Evelina Mognaschi  

Course name: Field theory and computation
Course code: 503066
Degree course: Ingegneria Elettrica
Disciplinary field of science: ING-IND/31
L'insegnamento è caratterizzante per: Ingegneria Elettrica
University credits: ECTS 12
Course website: n.d.

Specific course objectives

Advanced knowledge of electric, magnetic and electromagnetic fields. Base knowledge of commercial codes for finite element simulations. Knowledge of inverse problems and optimization methods.

Course programme

Vector fields
Basic operators and equations, electrostatic field, magnetostatic field, steady conduction field.

Analytical methods for solving boundary-value problems
Method of Green's function. Method of images. Method of separation of variables.

Numerical methods for solving boundary-value problems
Variational formulation in two-dimensional magnetostatics. Finite elements for two-dimensional magnetostatics. Finite elements for three-dimensional magnetostatics.

Time-varying electromagnetic field
Maxwell's equation in differential form. Poynting's vector. Maxwell's equations in the frequency domain. Plane waves in an infinite domain. Wave and diffusion equations in terms of vectors E and H.Wave and diffusion equations in terms of scalar and vector potentials. Electromagnetic field radiated by an oscillating dipole. Diffusione equation in terms of dual potentials. Weak eddy current in a conducting plane under AC conditions. Strong eddy current in a conducting plane under AC conditions. Eddy current in a cylindrical conductor under step excitation current. Electromagnetic field equations in different reference frames (a relativistic example and Galileian and Lorentzian transformations).

Computer aided design
Introduction to computer aided design by means of commercial software e.g. Magnet by Infolytica or Comsol Multiphysics. Finite element analysis of a simple case study.

Inverse problems
Direct and inverse problems. Well-posed and ill-posed problems. Fredholm's integral equation of the first kind. Under- and over-determined systems of equations. Least-squares solution. Classification of inverse problems.

Optimization
Solutions of inverse problems by the minimization of a functional. Constrained optimization. Multiobjective optimization. Gradient-free and gradient-based methods. Deterministic vs non-deterministic search. Numerical case studies.

Industrial electromagnetic compatibility
Field in low and high frequency, wave propagation, reflection and refraction. Near- and far-field. Biological effects of electromagnetic field. ICNIRP, Italian and European laws. Sources in low and high frequency. Antennas: properties (gain, directivity and polarization), kind of antennas, signal modulation. Theory of measurements of electric, magnetic and electromagnetic fields. Instruments for field measurements. Measurements of electromagnetic field radiated by microwave antennas and devices, radiofrequency antennas and fields produced by electric-power transmission plants.

Course entry requirements

Base knowledge of electric and magnetic field in low frequency, elementary vector analysis and operators as curl, divergence and gradient.

Course structure and teaching

Lectures (hours/year in lecture theatre): 90
Practical class (hours/year in lecture theatre): 0
Practicals / Workshops (hours/year in lecture theatre): 0

Suggested reading materials

P. Di Barba, A. Savini, S. Wiak. Field models in electricity and magnetism. Springer, 2008.

Slides shown during the lessons. .

Testing and exams

The final examination consists in developing two case studies: a finite element simulation and an inverse problem. These works will be discussed in an interview. During the interview some questions about the environmental electromagnetic compatibility will be done.