Aim
The course presents methods for solving physical problems that are described by partial differential equations. The student should be given a physical insight and be able to use this in order to mathematically formulate the problems. The course gives an introduction to electromagnetic field theory and to areas where the theory is applied. The projects in the course aim at giving the student an experience in solving comprehensive physical problems.

Knowledge and understanding
For a passing grade the student must

• know and understand the basics of field theory, electromagnetism, and the finite element method.

• be able to apply Maxwell’s equations to simple electrostatic, magnetostatic, and electrodynamic problems.

• be able to apply the finite element method to problems in electrostatics, magnetostatics and heat conduction

Skills and abilities
For a passing grade the student must

• know how to use basic vector analysis in Cartesian and curvilinear coordinate systems.

• be able to determine the electric and magnetic fields and forces in simple problems.

• be able to determine induced currents and voltages in simple cases.

• be able to treat plane electromagnetic waves mathematically.

• know how to make the transformation from strong to weak form.

• know how to establish the finite element formulation from the weak form.

• be able to write a finite element method program.

Judgement and approach
For a passing grade the student must

• have the ability to analyse and simulate physical problems, and to interpret and present the results.

• understand that technical and physical problems from different areas can be analysed and simulated with the same methods.

Contents
Basic field theory

• Physical phenomena that are describe by partial differential equations.

• Fundamental laws and constitutive relations.

• The nabla operator as an invariant vector operator.

• Gauss’s and Stoke’s theorems.

• The continuity equation and constitutive relations.

• Cylindrical and spherical coordinates.

• Applications to heat transfer.

• Electrostatic fields. The scalar electric potential. Coulomb’s law. Polarisation.

• Magnetostatic fields. Vector potential. Magnetisation.

• The induction law.

• Electromagnetic waves.

• The direct element method. Strong and weak formulation.

• Approximating functions. The weighted residual method. Galerkin’s method.

• Finite element formulation of heat transfer.

• Elastic bodies and their deformation. Isoparametric elements.

• Numerical integration.

Literature
Griffiths, D J: Introduction to Electrodynamics. Prentice Hall 1999. Ottosen, N and Petersson, H: Introduction to the Finite Element Method. Prentice Hall 1992. Olsson, K-G and Heyden, S: Introduction to the Finite Element methods-Problems. CALFEM-manual.

Code: 0105. Name: Elementary Field Theory, Electromagnetic Field Theory 1.
Higher education credits: 6. Grading scale: UG. Assessment: Written exam. Contents: Vector analysis, electrostatics, magnetostatics, induction, electromagnetic waves, antennas.

Code: 0205. Name: Electromagnetsic Field Theory 2, Finite Element Method.
Higher education credits: 6. Grading scale: UG. Assessment: Writen exam. Contents: Heat equation. Finite element method.

Code: 0305. Name: Discussion Exercises.
Higher education credits: 1,5. Grading scale: UG. Assessment: Oral and written presentation. Contents: The exercises are discussed in a group on sessions in the presence of teachers. The reports and preparations for the oral presentations are done as home work.

Code: 0405. Name: Project.
Higher education credits: 3. Grading scale: UG. Assessment: Written report. Contents: An applied problem in heat conduction or electromagnetic theory is solved by the finite element method.