# 325.099 Finite Element Methods for Multi-Physics II This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2024S 2023S 2022S 2021S 2020S 2019S

2023S, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• Format: Hybrid

## Learning outcomes

After successful completion of the course, students are able to:

• explain the physics of mechanical, electromagnetic, mechanical, thermal and acoustic fields and their couplings;
• explain the modelling assumptions necessary in the derivation of the governing partial differential equations (PDEs);
• understand the mathematics of the Finite Element (FE) method and sketch their computer implementation;
• describe advanced FEM topics and study scientific Literature;
• identify and work on relevant topics in research.

## Subject of course

The accurate modelling of mechatronic systems leads to so-called multi-field problems, which are described by a system of non-linear partial differential equations. These systems cannot be solved analytically and thus numerical calculation schemes have to be applied. Thereby, the finite element (FE) method has been established as the standard method for numerically solving the coupled system of partial differential equations describing the physical fields including their couplings.

In detail, the course will teach the physical / mathematical modelling and its FE formulations of the following coupled fields

Acoustics

• Viscous and thermal effects in oscillationg flows
• Perturbation ansatz to obtain a linearised formulation
• FE formulation for the radiated sound
• Approximation of free field conditions by absorbing boundary conditions and the Perfectly Matched Layer (PML) technique
• Non-conforming finite elements

Electromagnetics-mechanics

• Maxwell's equations
• Vector potential formulation for magneto-dynamics
• Nonlinear finite elements (Newton method) using edge finite elements
• Coupling mechanism (electromagnetic forces, motional electromotive force)
• FE formulation for the coupled field problem including moving / deforming solid bodies

Electromagnetics-Heat

• Multi-harmonic ansatz for the solution of the nonlinear electromagnetic partial differential equations in the frequency domain
• Finite elements of higher order to efficiently resolve eddy currents in electric conductive structures
• Coupling mechanism (Joule's losses due to currents, temperature dependent material parameters)
• FE formulation of the coupled field problem

## Teaching methods

The lecture contant (recordings) will be interactively discussed in calss to strengthen the understanding of the crucial points. Thereby, a high priority is placed on the physical understanding. The acomponying exercise session focuses on the practical application.

Written and oral

## Course dates

DayTimeDateLocationDescription
Wed13:00 - 15:0001.03.2023 - 28.06.2023Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Finite Element Methods for Multi-Physics II - Single appointments
DayDateTimeLocationDescription
Wed01.03.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed08.03.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed15.03.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed22.03.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed29.03.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed19.04.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed26.04.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed03.05.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed10.05.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed17.05.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed24.05.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed31.05.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed07.06.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed14.06.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed21.06.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)
Wed28.06.202313:00 - 15:00Seminarraum BA 05 - MB Lecture / Q&A (also via zoom, see TUWEL)

## Examination modalities

Work out questions / exercises and perform an oral exam

## Course registration

Begin End Deregistration end
13.02.2023 00:00 30.07.2023 23:55 30.07.2023 23:00

## Curricula

Study CodeObligationSemesterPrecon.Info
066 445 Mechanical Engineering Mandatory elective
Course requires the completion of the introductory and orientation phase
066 482 Mechanical Engineering - Management Mandatory elective
Course requires the completion of the introductory and orientation phase
066 646 Computational Science and Engineering Not specified
066 646 Computational Science and Engineering Not specified

## Literature

M. Kaltenbacher. Numerical Simulation of Mechatronic Sensors and Actuators. Finite Elements for Computational Multiphysics. Springer-Verlag, Heidelberg, 2015, ISBN: 978-3-642-40169-5

## Previous knowledge

The cours Finite Element for Multi-Physics I (325.095, VU) is recommended.

English