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 Gene Golub SIAM Summer School 2014 Simulation, Optimization, and Identification in Solid Mechanics 4 August - 15 August 2014, Linz, Austria

## Courses

### Goals

The bulk of the summer school consists of the four topics:

1. Identification of material parameters from measurements (Identification and Inverse Problems, IIP),
2. Material- and topology optimization (Material optimization/Topology optimization, MO/TO),
3. Optimization subject to variational inequalities (Mathematical Programming with Complementarity Constraints, MPCC),

These topics complement each other in a natural way. In particular, topics 1 and 2, which will be covered during the first week, are connected by the following rationale

1. Any model needs identified parameters for reliable simulations and optimization of structures based upon such models.
2. Material optimization is a natural step beyond simulation.
3. Both, identification and optimization, can be written as minimization problems subject to the governing material model as a constraint.
4. In both disciplines regularization plays a crucial role. While in MO regularization is often a direct consequence of design requirements, a proper choice which would not alter the original material parameters is much more involved in identification.
5. Despite this similarity, both problems have a different goal and need some special arguments in their analysis.

To highlight these connections, as well as to show the differences, both topics will be covered during the first week.

During the second week, the topics 3 and 4 will be covered, as they are both very relevant extensions of the theory covered during the first week

1. In many practical applications, purely linear elastic material models may fail to predict the true deformation behavior of a loaded body. In the worst case this means that structure or component which is optimized on the basis of a purely linear elastic model may even break.
2. Hence, the incorporation of nonlinear material models, e.g., elastoplasticity, is mandatory to predict and optimize the behavior of materials outside of the linear elastic regime.
3. Accurate and efficient solution of the discretized material models requires adaptivity and error estimation.

### Daily Schedule and Program Details

Flyer: G2S3-Summerschool (PDF)

 Impress 2014-07-12, wwwmath (MJ)