maximize

Dipl.-Math. Benedict Geihe

 

I am now at the German Aerospace Center, Institute of Propulsion Technology.

E-Mail: benedict DOT geihe AT dlr DOT de

 

Research Interests

Microstructures in elastic materials

  • Risk-averse elastic shape optimization

  • Two-scale shape optimization using simple, constructible geometries

  • Optimal microstructures

  • A posteriori estimates and adaptivity for shape optimization problems

  • Numerics for rate independent effective damage models

Publications

[1] S. Conti, B. Geihe, M. Lenz, and M. Rumpf. A posteriori modeling error estimates in the optimization of two-scale elastic composite materials. ESAIM: Mathematical Modelling and Numerical Analysis, 2017. to appear. [ bib | arXiv | .pdf | Abstract ]
[2] B. Geihe and M. Rumpf. A posteriori error estimates for sequential laminates in shape optimization. Discrete and Continuous Dynamical Systems - Series S, 9(5):1377-1392, 2016. [ bib | DOI | arXiv | http | .pdf | Abstract ]
[3] S. Conti, B. Geihe, M. Rumpf, and R. Schultz. Two-stage stochastic optimization meets two-scale simulation. In G. Leugering, P. Benner, S. Engell, A. Griewank, H. Harbrecht, M. Hinze, R. Rannacher, and S. Ulbrich, editors, Trends in PDE Constrained Optimization, volume 165 of International Series of Numerical Mathematics, pages 193-211. Springer International Publishing, 2014. [ bib | DOI | http | .pdf | Abstract ]
[4] B. Geihe, M. Lenz, M. Rumpf, and R. Schultz. Risk averse elastic shape optimization with parametrized fine scale geometry. Mathematical Programming, 141(1-2):383-403, 2013. [ bib | DOI | http | .pdf | Abstract ]
[5] P. Atwal, S. Conti, B. Geihe, M. Pach, M. Rumpf, and R. Schultz. On shape optimization with stochastic loadings. In G. Leugering, S. Engell, A. Griewank, M. Hinze, R. Rannacher, V. Schulz, M. Ulbrich, and S. Ulbrich, editors, Constrained Optimization and Optimal Control for Partial Differential Equations, volume 160 of International Series of Numerical Mathematics, chapter 2, pages 215-243. Springer, Basel, 2012. [ bib | DOI | http | .pdf | Abstract ]

Talks

May 20th, 2014 SIAM Conference on Optimization in San Diego, California, USA
Two-Stage meets Two-Scale in Stochastic Shape Optimization
September 9th, 2013 26th IFIP TC7 Conference on System Modelling and Optimization at Alpen-Adria Universität Klagenfurt, Austria
Error Estimates for Sequential Laminates in Elastic Shape Optimization
March 20th, 2013 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics in Novi Sad, Serbia
A Posteriori Error Estimates for Nested Laminates in Shape Optimization
March 12th, 2013 Workshop on Numerical Methods for Optimal Control and Inverse Problems at Technische Universität München, Garching
A Posteriori Error Estimates for Nested Laminates in Shape Optimization
August 24th, 2012 21st International Symposium on Mathematical Programming at Technische Universität Berlin
A Two-Scale Approach for Risk Averse Shape Optimization
March 12th, 2012 Workshop on Numerical Methods for Optimal Control and Inverse Problems at Technische Universität München, Garching
Elastic Shape Optimization of Fine Scale Geometry
May 19th, 2011 SIAM Conference on Optimization in Darmstadt
A Two-Scale Approach for Optimization of Fine Scale Geometry in Elastic Macroscopic Shapes
March 15th, 2011 Workshop on Numerical Methods for Optimal Control and Inverse Problems at Technische Universität München, Garching
Risk Averse Elastic Shape Optimization with Parametrized Fine Scale Geometry
July 21st, 2010 Workshop on Analysis and Numerics of PDE Constrained Optimization in Lambrecht
Optimization of Fine Scale Geometry in Elastic Macroscopic Shapes
March 23rd, 2010 81st Annual Meeting of the International Association of Applied Mathematics and Mechanics in Karlsruhe
Risk Averse Elastic Shape Optimization with Fine Scale Geometries