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

Theoretical 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, second semester), 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

RECOMMENDED READING/BIBLIOGRAPHY

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, R. Taylor, J. Z. Zhu: “The Finite Element Method: Its Basis and Fundamentals”, Elsevier Science, 2005.
• P. P. Silvester, R. L. Ferrari: “Finite Elements for Electrical Engineers”, 3^ edn., Cambridge University Press, 1996.
• J. Jin: “The finite Element Method in Electromagnetics”, 3^ edn., John Wiley & Sons, 2014.
• 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.