##### Department of Mathematics,

University of California San Diego

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### Math 278 - Center for Computational Mathematics Seminar

## Rolf Krause

#### Universitaet Bonn

## From Molecular Dynamics to Biomechanics: Multiscale Methods for strongly Non-linear Problems

##### Abstract:

The mathematical modeling of complex problems in, e.g., mechanics, often gives rise to heterogeneous and strongly non-linear models, whose numerical treatment is far from trivial. For example, the numerical simulation of (bio-)mechanical problems based on realistic geometries and material models puts high demands on the efficiency and reliability of the simulation methods, the handling of the geometries, and the design of the numerical software. In this talk, we discuss different non-linear multiscale approaches for the efficient simulation of constrained and non-linear minimization problems and their efficient and problem-open implementation. Within our multiscale approach, different models (or energy functionals) on different scales are used concurrently in order to resolve scale-dependent non-linear effects. Only a proper synchronization of the scale dependent models on the different scales will lead to an increase in convergence speed and robustness. Thus, particular emphasis has to be put on the transfer between the different scales as well as on the convergence properties of the non-linear multilevel iteration process. Examples from (bio-)mechanics including large deformations, strongly non-linear materials, frictional contact problems, and coupled multiscale simulations will illustrate the efficiency and robustness of our approach.

Host: Randy Bank

### November 25, 2008

### 10:00 AM

### AP&M 2402

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