## Weak coupling between scales and models: a frequency oriented approach for transferring information in heterogeneous models

#### Rolf KrauseUniversity of Lugano

For discrete heterogeneous or multiscale models, the information transfer between the different scales or models is of crucial importance for the accuracy of the obtained results. Examples are micro/macro scale coupling, multidimensional models (Coupling of $1D$ and $3D$ models), or simply the coupling of different finite element discretizations.
As a matter of fact, within these heterogeneous models, an efficient and stable information transfer at the model or scale interfaces requires some filtering'' of the information passed from one model or scale to another. By means of this filtering'', only the information which can be used in both of the interfacing models or scales should be passed, thus avoiding possible spurious interface or coupling effects.
In this talk, we will present frequency oriented coupling concepts for concurrent multiscale simulations and will discuss their relation with recent coupling concepts as mortar methods.

The discussing will be done along benchmarking results from Lattice mechanics (wave propagation). As an illustrative example, we will consider the coupling of different models as Molecular Dynamics and Finite Elements. We will show that the effects on different scales can be captured efficiently by means of a concurrent multiscale simulation.
The most demanding problem of this concurrent multiscale coupling, however, is the aspect of information transfer between these different length scales and models. Frequencies not representable by the coarse scale model of the employed hierarchy might be reflected at the coupling interface, thus leading to spurious oscillations. Using constraints which only incorporate the low frequent part of the fine scale model, we are able to separate the scale-coupling from the necessary damping of the high frequent waves. The construction of the corresponding discrete constraints, which is based on a discrete $L^2$-projection, will be discussed in detail (including parallelism), since it is the most important ingredient for a stable information transfer.

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