MATHEON project C31: Numerical Minimization of Nonsmooth Energy Functionals in Multiphase MaterialsThis project is part of application area 'C' (Production) of the DFG Research Center Matheon.
- Head: Prof. Dr. Michael Hintermüller [email], Prof. Andreas Griewank, Ph.D. [email], Prof. Dr. Carsten Carstensen [email]
- Assistants: Simon Rösel [email]
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|
|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|
|Regularity of quasiconvex envelopes||SIAM J. Numer. Anal. 43(1):363-385, 2000|
|The primal-dual active set strategy as a semismooth Newton method.||SIAM J. Optim. 17(1):159-187, 2003|
|Nonsmooth equations in optimization||Kluwer Academic Publishers, Dordrecht, 2002.|