# BASIC NUMERICAL METHODS AND OPTIMIZATION TECHNIQUES FOR ELECTROMAGNETIC SYSTEMS

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Last update 02/07/2020 12:45
Code
101702
2020/2021
CREDITS
5 credits during the 2nd year of 8731 Electrical Engineering (LM-28) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
ING-IND/31
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Electrical Engineering)
semester
Annual
modules
This unit is a module of:
Teaching materials

OVERVIEW

Module of basic numerical methods, numerical techniques for the solution of field problems, and optimization techniques for applications to the design of electromagnetic devices and systems.

## AIMS AND CONTENT

LEARNING OUTCOMES

The module describes the main algorithms used for the numerical modeling of electromagnetic devices (interpolation, root search, derivation, integration, solution of linear equation systems), describes the basis of numerical solution of field problems (described by PDE) using the Finite Element Method, and gives an introduction to the techniques for the automatic design and operational optimization of industrial devices.

AIMS AND LEARNING OUTCOMES

At the end of the module, the Student shall have correctly understood the basic concepts enabling him/her to correctly choose from numerical libraries the most suitable algorithm to solve the problems of interest, shall be able to correctly solve, using the Finite Element Method, problems of quasi-stationary Electromagnetic Fields, and to correctly design a numerical optimization procedure, choosing the right optimization method.

Teaching methods

Theoric lectures and related exercises (4 credits) in the first semester, and further exercises developed autonomously by Students out of lecture hours, using free software in the second semester (1 credit, under Teacher’s tutoring) for a total of 5 credits.

SYLLABUS/CONTENT

1) Introductions on Numerical Methods and main Numerical Methods

• Root Search
• Interpolation
• Numerical Derivation and Integration
• Solution of Ordinary Differential Equations (O.D.E.)
• Solution of linear systems of algebraic equations

2) Numerical Solution of Field Problem (P.D.E.)

• The Finite Element Method (FEM)
• Two dimensional formulation in scalar and vector potential
• Static Two Dimensional Problems, with translation and rotation symmetry
• Linear and non-linear Problems
• Quasi-stationary Problems
• Coupled Problems
• Main Three Dimensional Formulations
• Brief introduction to other differential and integral methods
• The Finite Difference Method
• The Boundary Element Method (BEM)
• The Boundary Integral Method (BIM)

3) Optimization techniques

• deterministic
• stocastic
• hybrid ones

M. Nervi: “Dispense del corso”

Further Bibliography (for OPTIONAL study deepening on specific subjects):

• F. Scheid: “Analisi numerica” – collana SCHAUM, ETAS libri, 1975
• K. Atkinson: “An Introduction to Numerical Analysis”, 2nd ed., John Wiley & Sons, 1989
• K. Atkinson: http://www.math.uiowa.edu/~atkinson/ina_sem1.html
• K. Atkinson: http://www.math.uiowa.edu/~atkinson/ina_sem2.html
• W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery: “Numerical Recipes: The Art of Scientific Computing”, 3rd Edition, Cambridge University Press, 2007, http://numerical.recipes/
• O. C. Zienkiewicz: “The Finite Element Method in Engineering Science”, McGraw-Hill, 1971.
• P. P. Silvester, R. L. Ferrari: “Finite Elements for Electrical Engineers”, Cambridge University Press, 1983.
• J. Jin: “The finite Element Method in Electromagnetics”, John Wiley & Sons, 1993.
• G. Carey, J. T. Oden: “Finite Elements”, Vol. I-V, Prentice Hall, 1981.
• K. J. Binns, P. J. Lawrenson, C. W. Trowbridge: “The Analytical and Numerical Solution of Electric and Magnetic Fields”, John Wiley & Sons, 1994.

Recommended software:

• FEMM: http://www.femm.info/wiki/HomePage
• gmsh: http://onelab.info/
• GetDP: http://getdp.info/
• VisIt: https://wci.llnl.gov/simulation/computer-codes/visit/
• ParaView: https://www.paraview.org/

## TEACHERS AND EXAM BOARD

Ricevimento: Students in need of further clarifications are received via Teams, on appointment (tel. 010-353-2044, e-mail: mario.nervi@unige.it)

Exam Board

MARIO NERVI (President)

MANSUETO ROSSI

MATTEO SAVIOZZI

GIORGIO MOLINARI

PAOLO MOLFINO

MASSIMO BRIGNONE

PAOLA GIRDINIO

FRANCESCO CONTE (President Substitute)

## LESSONS

Teaching methods

Theoric lectures and related exercises (4 credits) in the first semester, and further exercises developed autonomously by Students out of lecture hours, using free software in the second semester (1 credit, under Teacher’s tutoring) for a total of 5 credits.

LESSONS START

According to the official teaching calendar

ORARI

L'orario di tutti gli insegnamenti è consultabile su EasyAcademy.

## EXAMS

Exam description

Oral only.

Assessment methods

The examination of Numerical Methods and Optimization for Electromagnetic Systems is based on an oral discussion, lasting about 30 minutes, normally about the solution of practical problems, and optional questions about the related theory.

The final marking of Numerical Methods and Optimization for Electrical Engineering is the average of the marks (rounded to the higher integer figure) of its modules (Numerical Methods and Optimization for Electromagnetic Systems and Optimization Techniques for Power Electric Systems).