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# 101.978 AKNUM Modeling of Nonlinear Coupled Field Problems 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"});}); 2022W

2022W, UE, 1.0h, 1.5EC

## Properties

• Semester hours: 1.0
• Credits: 1.5
• Type: UE Exercise
• Format: Hybrid

## Learning outcomes

After successful completion of the course, students are able to

• formulate coupled nonlinear partial differential equations for multiphysics problems,
• determine the differential geometric character physical fields that is decisive for appropriate finite element discretizations and
• recognize essential invariants of various (multi)physics problems.

## Subject of course

Theory

• Selected concepts of differential geometry for the formulation and description of partial differential equations (vectors, differential forms, exteriror derivative, Lie derviative)
• Lokal and global invariants and stationary conditions
• Geometrically consistent discretization of (pyhsical) fields
• Formalisms for thermodynamically consistent nonlinear coupled material equations (coupled material laws)

Applications

• Fundamentals of the geometrically nonlinear theory of elasticity
• Fundamentals of the electro- and magnetostatics
• Selected magnetoelectromechanical coupling mechanisms
• Multiscale modeling and numerical homogenization

## Teaching methods

The exercise part fosters the understanding of the theory presented in the lecture. For the theoretical and formal content, the students carry out derivations and prove identities where details have been deliberately omitted in the lecture. Concepts and techniques introduced in the lecture part are applied to practically relevant examples and by that help the students to master their new tools.

After a brief introduction to the software NGSolve, the students perform numerical Simulation that connect coupled partial differential equations with phenomenological models and physical effects.

Immanent

## Lecturers

• Rambausek, Matthias

## Course dates

DayTimeDateLocationDescription
Tue13:00 - 14:0011.10.2022 - 24.01.2023 Seminar room DA03 (green) CExercise
AKNUM Modeling of Nonlinear Coupled Field Problems - Single appointments
DayDateTimeLocationDescription
Tue11.10.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue18.10.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue25.10.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue08.11.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue22.11.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue29.11.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue06.12.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue13.12.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue20.12.202213:00 - 14:00 Seminar room DA03 (green) CExercise
Tue10.01.202313:00 - 14:00 Seminar room DA03 (green) CExercise
Tue17.01.202313:00 - 14:00 Seminar room DA03 (green) CExercise
Tue24.01.202313:00 - 14:00 Seminar room DA03 (green) CExercise

## Examination modalities

Active participation in weekly exercises as well as the solution of exercise sheets.

## Course registration

Begin End Deregistration end
01.09.2022 00:00 17.10.2022 23:59 28.02.2023 23:59

## Curricula

Study CodeObligationSemesterPrecon.Info
860 GW Optional Courses - Technical Mathematics Mandatory elective

## Literature

No lecture notes are available.

## Miscellaneous

• Attendance Required!

English