87328 - Modelling and Computation of Electric and Magnetic Fields M

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

Prerequisites/Recommended Preparatory Courses

A good understanding of the basics of differential and integral calculus is required. Additionally, basic knowledge of electromagnetism is necessary, typically acquired by passing the Physics exams in the Bachelor's degree courses in Engineering.

All lectures will be conducted in English. Therefore, comprehension of the English language is necessary to effectively follow the course and use the provided teaching materials.

Syllabus

• Electromagnetics: Electromagnetism Equations in differential and integral forms; Scalar and vector potentials; Interface conditions; Poynting theorem; Forces and energies; Maxwell's tensor; Harmonic functions; Green's formulas; Solution of Poisson's equation. Electrostatics; Magnetostatics. Quasistationary approximation.
• Fundamentals of Numerical Analysis: Floating-point representation, machine precision, algorithm stability. Numerical differentiation, numerical integration, interpolation.
• Elements of Numerical Analysis: Numerical errors, machine precision, error propagation; Finding zeros of a function; Interpolation; Numerical differentiation and integration. Solution of nonlinear systems: Newton-Raphson method.
• Numerical Methods for Electromagnetic Problems: Introduction; Finite difference method; Finite element method; Domain triangulation; Weighted residuals method; Magnetostatic and electrostatic problems; Nonlinear problems; Axisymmetric problems; Time-dependent problems in quasistationary approximation; Three-dimensional problems; Surface finite element method; Commercial codes for electromagnetic field analysis.

Readings/Bibliography

Course notes covering the lecture topics are available.

Additional recommended texts for further study:

• S.C. Chapra, R.P. Canale, "Numerical Methods for Engineers," 8th Edition, McGraw-Hill
• S.D. Conte, C. De Boor, "Elementary Numerical Analysis," McGraw-Hill
• 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 is held in the first cycle of the first year of the Master's Degree in Electrical Energy Engineering and is structured for 6 credits, equivalent to 60 hours of lectures, during which the instructor will cover the syllabus topics. Approximately 40 hours will be dedicated to the theoretical development of concepts and numerical methods related to Electrical Engineering. The remaining 20 hours will be dedicated to computer exercises. During these exercises, the student will develop some FDM (Finite Difference Method) and FEM (Finite Element Method) programs under the instructor's guidance.

Assessment methods

The student will have to take an oral exam. The exam is aimed at evaluating the student's acquisition of the main analytical and numerical methodologies for field calculation applied to electrical engineering. During the exam, the student will have to demonstrate knowledge of the foundational elements of the subject and the ability to apply analytical and numerical methods (finite differences, finite elements) to the study of common applications in electrical engineering. During the oral exam, the student will present a brief written report discussing the laboratory work carried out during the exercises and the results obtained. The student will also be invited to discuss some of the topics covered during the course. The discussion will aim to verify that the student has achieved an integrated view of the proposed topics, has gained a good command of the specific technical language, and has developed synthesis and analysis skills. The degree of satisfaction of the aforementioned requirements will contribute to the final grade.

Teaching tools

Teaching materials are available on the Virtual platform.

Office hours

See the website of Arturo Popoli