Research Group of Prof. Dr. D. Peterseim
Institute for Numerical Simulation

Dipl.-Math. Philipp Morgenstern

Dipl.-Math. Philipp Morgenstern
Address: Institut für Numerische Simulation
Wegelerstr. 6
53115 Bonn
Office: We4 0.024
Phone: +49 228 73-60153
Fax: +49 228 73-3979
PGP: Key data

Research Projects

DFG Priority Programme 1748: Reliable Simulation Techniques in Solid Mechanics. Development of Non-standard Discretisation Methods, Mechanical and Mathematical Analysis
Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials
Cooperation with Dr.-Ing. Markus Kästner, TU Dresden

Multi-material lightweight designs and smart devices with characteristic microscopic material structures are the key features for the development of innovative products. In this context, an adaptive isogeometric framework for the modeling and simulation of crack propagation in heterogeneous materials is to be developed, implemented, and mathematically analyzed in this project. The mechanical modeling of interface failure will be based on increasing knot multiplicities driven by cohesive zone models for crack propagation along material interfaces. In addition, a phase-field model will account for propagating cracks in the bulk material including interaction phenomena such as crack branching and coalescence. The spline-based discretization used offers higher efficiency compared to Lagrangian polynomials, control of regularity, accurate approximation of strong gradients in the phase-field order parameter, as well as the possibility to discretize higher-order phase-field equations. Local mesh adaptivity required for the resolution of material interfaces and the phase-field variables will be provided by T-splines as well as hierarchical spline approximations. In addition to the physical modeling, open mathematical problems include a practicable characterization of T-meshes suitable for IGA in 3D and clear understanding of the role of increased regularity in the approximation.



Journal Papers:

[1] P. Hennig, M. Kästner, P. Morgenstern, and D. Peterseim. Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison. Comp. Meth. Appl. Mech. Eng., 316:424–-448, 2017.
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[2] P. Morgenstern. Globally structured three-dimensional analysis-suitable t-splines: Definition, linear independence and $m$-graded local refinement. SIAM J. Numer. Anal., 54(4):2163-2186, May 2016. Also available as INS Preprint No. 1508.
bib | DOI | arXiv | http | .pdf 1 ]
[3] A. Buffa, C. Giannelli, P. Morgenstern, and D. Peterseim. Complexity of hierarchical refinement for a class of admissible mesh configurations. Computer Aided Geometric Design, 47:83-92, 2016.
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[4] P. Morgenstern and D. Peterseim. Analysis-suitable adaptive T-mesh refinement with linear complexity. Computer Aided Geometric Design, 34:50-66, 2015. Also available as INS Preprint No. 1409.
bib | DOI | http | .pdf 1 ]

Refereed Articles in Collections:

[1] P. Henning, P. Morgenstern, and D. Peterseim. Multiscale partition of unity. In M. Griebel and M. A. Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, volume 100 of Lecture Notes in Computational Science and Engineering, pages 185-204. Springer International Publishing, 2015.
bib | DOI | http | .pdf 1 ]