Project Title
MATHEON project C31: Numerical Minimization of Nonsmooth Energy Functionals in Multiphase Materials
This project is part of application area 'C' (Production) of the DFG Research Center Matheon.People
- Head: Prof. Dr. Michael Hintermüller [email], Prof. Andreas Griewank, Ph.D. [email], Prof. Dr. Carsten Carstensen [email]
- Assistants: Simon Rösel [email]
Project Description
In this project we consider the classical nonlinear elasticity poblem in variational form. Of particular interest is the examination of the semi-smoothness properties of typical energy densities and the corresponding effect of semi-convexification, discretization, and potential regularization.
Moreover, suitably adapted versions of generalized Newton, BFGS or bundle-type methods for the numerical solution of the semi-convexified energy minimization problem should be analyzed and implemented. Algorithmically, the goal is to cope with the limited smoothness and pointwise degeneracies while exploiting the semi-convex structure. Theoretically we are interested in local convergence results for semi-smooth Newton and BFGS-type solvers. The mesh (in)dependence behavior of these methods will be studied.
Potential new methods will find relevant applications in material science such as in case of compressible,non-Hookean materials.
Project [website] at MATHEON.
Selection of project-related references
Author | Title | Journal / Publisher |
---|---|---|
J. Kristensen | On the non-locality of quasiconvexity | Ann. Institut Henri Poincaré - Analyse non linéaire 16(1):1-13, 1999 |
B. Dacorogna, J. Haeberly |
Some numerical methods for the study of the convexity notions arising in the calculus of variations | RAIRO, Modélisation Math. Anal. Num. 32(2):153-175, 1998. |
L. Eneya | Pointwise evaluation of polyconvex envelopes | Ph.D. thesis, Humboldt-Universität zu Berlin, 2010 |
J.M. Ball, B. Kirchheim, J. Kristensen |
Regularity of quasiconvex envelopes | SIAM J. Numer. Anal. 43(1):363-385, 2000 |
M. Hintermüller, K. Ito, K. Kunisch |
The primal-dual active set strategy as a semismooth Newton method. | SIAM J. Optim. 17(1):159-187, 2003 |
K. Klatte B. Kummer |
Nonsmooth equations in optimization | Kluwer Academic Publishers, Dordrecht, 2002. |