Staff Dr. Philipp Morgenstern

Mr. Morgenstern has left the institute. This page is no longer maintained.

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Teaching

Summer semester 2015

See teaching activities of the whole group.

Completed Research Projects

Adaptive isogeometric modeling of propagating strong discontinuities in heterogeneous materials

DFG Priority Programme 1748.

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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.

Publications

  1. Mesh Refinement Strategies for the Adaptive Isogeometric Method. P. Morgenstern. PhD thesis, Institut für Numerische Simulation, Rheinische Friedrich-Wilhelms-Universität Bonn, 2017. BibTeX
  2. Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison. P. Hennig, M. Kästner, P. Morgenstern, and D. Peterseim. Comp. Meth. Appl. Mech. Eng., 316:424––448, 2017. BibTeX PDF DOI arXiv
  3. Complexity of hierarchical refinement for a class of admissible mesh configurations. A. Buffa, C. Giannelli, P. Morgenstern, and D. Peterseim. Computer Aided Geometric Design, 47:83–92, 2016. BibTeX PDF DOI
  4. Globally structured three-dimensional analysis-suitable T-splines: definition, linear independence and mm-graded local refinement. P. Morgenstern. SIAM J. Numer. Anal., 54(4):2163–2186, may 2016. Also available as INS Preprint No. 1508. BibTeX PDF DOI arXiv
  5. Multiscale partition of unity. P. Henning, P. Morgenstern, and D. Peterseim. 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. BibTeX PDF DOI
  6. Analysis-suitable adaptive T-mesh refinement with linear complexity. P. Morgenstern and D. Peterseim. Computer Aided Geometric Design, 34:50–66, 2015. Also available as INS Preprint No. 1409. BibTeX PDF DOI
  7. Lokale Verfeinerung regulärer Triangulierungen in Vierecke. P. Morgenstern. Master's thesis, Institut für Mathematik, Humboldt-Universität zu Berlin, 2013. BibTeX