# 87328 - Modelling and Computation of Electric and Magnetic Fields M

• Campus: Bologna
• Corso: Second cycle degree programme (LM) in Electrical Energy Engineering (cod. 9066)
• from Sep 18, 2023 to Dec 19, 2023

## Learning outcomes

The course deal with the analytical and numerical calculation methods for the analysis of electric and magnetic fields in the stationary and quasi-stationary regimes for specific applications of electrical engineering. In particular, at the end of the course the student: • has become familiar with the main concepts regarding numerical analysis (machine precision, truncation errors and round off); • will know the main basic numerical techniques (derivation, integration, solution of differential equations); • knows how to apply the main numerical methodologies available in the field of electrical engineering (FEM, FDM, BEM) with full knowledge.

## Course contents

Requirements/Prior knowledge

A basic knowledge of electromagnetisms is requires. This knowledge is usually given by the Physics courses of the Bachelor degree in Engineering. The student should also have gained a good knowledge of the fundamentals of differential and integral calculation, provided in the Mathematical Analysis courses.

All lectures will be held in English. It is therefore necessary to understand the english language to successfully attend the course and to be able to use the educational material provided.

Course Contents

Electromagnetics formulation in differential and integral form , scalar and vector potentials, interface conditions, Poynting's theorem, power and energy, the Maxwell tensor, harmonic functions, Green formula, solution of the Poisson equation. Electrostatics; Magnetostatics. Quasi-steady approximation.

Elements of Numerical Analysis: numerical errors, machine precision, error propagation, calculation of the zeros of a function, interpolation, numerical derivation and integration. Numerical methods for solving systems of equations: direct algorithms, iterative algorithms, Jacobi, Gauss-Siedel, SOR, conjugate gradient method and biconiugato, GMRES; solution of nonlinear systems: the method of Newton-Raphson. Preconditioning.

Fundamentals of numerical analysis: floating point representation, machine accuracy, stability of an algorithm. Numerical derivative, numerical integration, interpolation.

Numerical methods of analysis for electromagnetic problems: introduction, finite differences method, finite element method; domain triangulation, method of weighted residuals; magnetostatic and electrostatic problems, nonlinear problems, axisymmetric problems, problems in time-dependent approximation quasistazionaria; Problems three-dimensional, finite element surface; commercial codes for the analysis of electromagnetic field.

Algorithms for the solution of linear algebraic systems: generalities. Direct methods, method of Gaussian elimination. Sparse systems, iterative methods. Fixed point methods, Gauss Seidel, SOR, conjugate gradient method

Constrained optimization and non-constrained: optimal conditions, deterministic and stochastic search methods: gradient method, conjugate gradient. Genetic and Evolutionary Algorithms.Readings/Bibliography

The teaching material covering the course is available from insegnamenti online- University of Bologna platform.

For further reading, we recommend the following books:

SD Conte, C. De Boor, Elementary numerical analisys, McGraw-Hill

V Comincioli Analisi numerica: metodo, modelli, applicazioni. Mc Graw Hill Italia Ed

Zienkiewcz, Taylor The Finite Element Method, Mc Graw Hill Altri testi di consultazione:

K. J. Binns, P. J. Lawrenson, C. W. Trowbridge: “The Analytical and Numerical Solution of Electric and Magnetic Fields”. J. Wiley and Sons.

## Teaching methods

The course takes place on the first cycle of the first year of the master degree course in "Ingegneria dell'Energia Elettrica", and consists of 6 credits corresponding to 60 hours of lectures, during which the teacher will explain in classroom the topics covered in the program. About 40 hours will be devoted to the theoretical development of the fundamental concepts and methodologies of electrical engineering. The remaining 20 hours will be spent in lab. During the lab classes the student, using the theoretical notions treated in the previous lessons, will develop under the teacher guidance some numerical tools FDM and FEM for the analysis of problem of interest in the field of electrical engineering.

## Assessment methods

The exam is aimed to assess the acquisition by the student of the basic analytical and numerical methodologies in electrical engineering for the calculation of electric and magnetic fields.

During the examination the student must demonstrate the knowledge of the fundamentals enabling to apply the analytical and numerical methods (finite difference methods, finite element methods) to the study of the most common applications of electrical engineering. The student must pass an oral examination. During the examination, the student will present a brief report on the activities he has carried out during the lab classes, and will discuss the obtained results. The student will also be invited to discuss some of the topics taught during the course. The discussion will be aimed at confirming that the student has reached an organic view of the proposed topic, that he has achieved a good grasp of the specific technical language and has acquired capacity for synthesis and analysis. The degree of satisfaction of the above mentioned requirements will be used to formulate the final score.

## Teaching tools

Computer Lab

Educational material is available on the Virtuale platform

## Office hours

See the website of Andrea Cristofolini

### SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.