34614 - CAD of Electrical and Magnetic Fields (Graduate Course)

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 Italian. It is therefore necessary to understand the Italian language to successfully attend the course and to be able to use the educational material provided.

Course Contents

Equations of electromagnetism in differential and integral form; scalar and vector potentials; Clebsch theorem; Poynting theorem; forces and energies; uniqueness condition for the solution to an electromagnetic problem; Green's identities; harmonic functions; uniqueness conditions for the solution of the Poisson equation. Solution of the Poisson equation. Electrostatics; Magnetostatics. Quasistationary approximation


Fundamentals of numerical analysis: floating point representation, machine precision, stability of an algorithm. Numerical derivative, numerical integration, interpolation; calculation of the zeros of a function; Solution of nonlinear systems: Newton-Raphson method.


Numerical analysis methods for electromagnetic problems: introduction; finite difference method; finite element method; domain triangulation; Weighted residue method; Magnetostatic and electrostatic problems; Nonlinear problems; Axisymmetric problems; Time-dependent problems in quasi-stationary approximation; Three-dimensional problems; Commercial codes for electromagnetic field analysis. 
 

 

Readings/Bibliography

The teaching material covering the whole course is available from the Insegnamentonline plaform.

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 second 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 students, 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.

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Students with specific learning disorders (SLD) or temporary/permanent disabilities:

We recommend contacting the University Office responsible for support services in a timely manner (https://site.unibo.it/studenti-con-disabilita-e-dsa/it) [https://site.unibo.it/studenti-con-disabilita-e-dsa/it):] ). The office will evaluate the students' needs and, where appropriate, propose possible accommodations. These must in any case be submitted for approval at least 15 days in advance to the course instructor, who will assess their suitability also in relation to the learning objectives of the course.

 

Assessment methods

The examination is designed to assess the student's understanding of the main analytical and numerical methods for electromagnetic field computation in electrical engineering applications. During the examination, students are expected to demonstrate knowledge of the fundamental concepts of the subject and the ability to apply analytical and numerical techniques (finite difference and finite element methods) to the analysis of common electrical engineering problems.

Students may choose one of the following examination formats.

Option 1: Oral Examination

During the oral examination, students will be asked to discuss selected topics covered during the course. The discussion aims to assess their overall understanding of the subject, their command of the appropriate technical terminology, and their ability to analyze and synthesize the course material.

Students are also required to submit a short written report describing the laboratory activities carried out during the course and discussing the results obtained. The report may be prepared in groups of up to three students. Group members are not required to take the examination during the same examination session. However, once the first member of a group takes the examination, both the composition of the group and the submitted report are considered final and may no longer be modified.

Option 2: Project

Under this option, students work in groups of up to three members to complete a project. The project consists of developing or modifying computational codes (preferably in MATLAB, although other programming languages may be used upon approval by the instructor) implementing one of the numerical methods studied during the course.

Throughout the project, periodic meetings with the instructor will be held to monitor progress and provide guidance and feedback. At the end of the project, each group must submit a written report describing the work carried out, the engineering problem addressed, the numerical methods employed, and the results obtained.

The final examination consists of the discussion of both the project report and the laboratory report. Students will also be asked to discuss one topic selected by the instructor from the following list:

• Electromagnetic field equations in differential and integral form;
• Scalar and vector potentials;
• Poynting's theorem and the uniqueness theorem in electromagnetics;
• Green's formulas;
• Harmonic functions;
• Solution of Poisson's equation and uniqueness theorems;
• Volume, single-layer and double-layer potentials.

Whenever possible, it is recommended that all members of the same project group take the examination during the same examination session.

 

Option 3:midterm tests

The examination may also be completed through continuous assessment. During the course, two or more midterm tests will be scheduled, each covering the topics taught during the corresponding period. Each test will consist of a written assessment based on a set of open-ended and/or multiple-choice questions designed to evaluate the students' understanding of the material covered up to that point. The specific format of the midterm tests and the assessment criteria will be explained by the instructor at the beginning of the course.

The final grade will be determined on the basis of the scores obtained in the midterm tests and the outcome of a final oral examination, which will focus on the discussion of the laboratory reports prepared during the course.

 

Teaching tools

Computer Lab

Educational material on the Virtuale platform

Office hours

See the website of Andrea Cristofolini