Friederich, Jan, Dipl.-Math.

Dipl.-Math. Jan Friederich

Department of Mechanical Engineering
Institute of Applied Mechanics (LTM, Prof. Steinmann)

Egerlandstraße 5
91058 Erlangen
Deutschland

Phone number: +49 9131 85-28502
Fax number: +49 9131 85-28503
Email: ltm-sekretariat@fau.de
Website: https://www.ltm.tf.fau.de/person/dipl-math-jan-friederich/

Adaptive finite elements based on sensitivities for topological mesh changes

(Own Funds)

Project leader: Paul Steinmann
Start date: 16. March 2012
End date: 15. March 2018

Abstract:

We consider local refinements of finite element triangulations as continuous graph operations, for instance by splitting nodes and inflating edges to elements. This approach allows for the derivation of sensitivities for functionals depending on the finite element solution, which may in turn be used to define local refinement indicators. Thereby, we develop adaptive algorithms exploiting sensitivities for both hierarchical and non-hierarchical mesh changes, and analyze their properties and performance in comparison with established methods.

Publications:

2016

Schmitt O., Friederich J., Riehl S., Steinmann P.:
On the formulation and implementation of geometric and manufacturing constraints in node-based shape optimization
In: Structural and Multidisciplinary Optimization 53 (2016), p. 881 - 892
ISSN: 1615-147X
DOI: 10.1007/s00158-015-1359-0

2015

Friederich J., Pfaller S., Steinmann P.:
A web-based tool for the interactive visualization of stresses in an infinite plate with an elliptical hole under simple tension: www.ltm.fau.de/plate .
In: Archive of Applied Mechanics (2015), p. 1-9
ISSN: 0939-1533
DOI: 10.1007/s00419-015-1049-9

2014

Leugering G., Friederich J., Steinmann P.:
Adaptive finite elements based on sensitivities for topological mesh changes
In: Control and Cybernetics 43 (2014), p. 279-306
ISSN: 0324-8569
URL: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85018838294&origin=inward
Riehl S., Friederich J., Scherer M., Meske R., Steinmann P.:
On the discrete variant of the traction method in parameter-free shape optimization
In: Computer Methods in Applied Mechanics and Engineering 278 (2014), p. 119-144
ISSN: 0045-7825
DOI: 10.1016/j.cma.2014.05.009
Riehl S., Friederich J., Steinmann P.:
On regularization in parameter-free shape optimization
85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) (Erlangen, 10. March 2014 - 14. March 2014)
In: Proc. Appl. Math. Mech., Weinheim: 2014
DOI: 10.1002/pamm.201410375
Schmitt O., Friederich J., Steinmann P.:
Manufacturing constraints in parameter-free sensitivity-based shape optimization
1st International Conference on Engineering and Applied Sciences Optimization (OPT-i) (Kos Island, Greece, 4. June 2014 - 6. June 2014)
In: Proceedings of 1st International Conference on Engineering and Applied Sciences Optimization 2014
Schmitt O., Friederich J., Steinmann P.:
Manufacturing constraints in parameter-free shape optimization
GAMM 2014 (Erlangen, Germany, 10. March 2014 - 14. March 2014)
In: PAMM, Erlangen, Germany: 2014
DOI: 10.1002/pamm.201410376

2012

Friederich J., Leugering G., Steinmann P.:
An adaptive finite element method based on sensitivities for node insertion
In: GAMM-Mitteilungen 35 (2012), p. 175-190
ISSN: 0936-7195
DOI: 10.1002/gamm.201210012
URL: http://onlinelibrary.wiley.com/doi/10.1002/gamm.201210012/full
Leugering G., Friederich J., Steinmann P.:
Adaptive refinement based on asymptotic expansions of finite element solutions for node insertion in 1d
In: GAMM-Mitteilungen 35 (2012), p. 175-190
ISSN: 0936-7195
DOI: 10.1002/gamm.201210012