# METT VIII - 8th Workshop on Matrix Equations and Tensor Techniques

Nov 6 – 8, 2019
MPI Magdeburg
Europe/Berlin timezone

## Matrix Equations Appearing in Parameter-dependent Fluid-structure Interaction Discretizations

Nov 7, 2019, 3:00 PM
2h
Main/groundfloor-none - Magistrale (Max Planck Institute for Dynamics of Complex Technical Systems)

200
Poster Posters

### Speaker

Roman Weinhandl (Otto von Guericke University Magdeburg)

### Description

In the first place, the poster presented will give an overview on the matrix equations that appear in the low-rank parameter-dependent fluid-structure interaction (FSI) framework. In contrast to linear FSI problems, the equations that result after finite element discretization of parameter-dependent nonlinear FSI problems are not translatable to a single matrix equation. Such a discretization with respect to $m \in N$ shear moduli given by the set $\{\mu_i\}_{i \in \{1,...,m\}} \subset R$ and a number of $n \in N$ degrees of freedom yields equations of the form

$(A_0+\mu_iA_1+A_2(x_i) )x_i=b \quad \text{for} \quad i \in \{1,...,m\}$,

with $A_0$, $A_1$, $A_2(x_i) \in R^{n \times n}$, $b \in R^n$ and the finite element solution $x_i \in R^n$. $A_2(\cdot)$ is a discretization matrix of nonlinear operators and depends on the unknown. An equivalent translation of the $m$ equations above to a matrix equation, similar to the linear case, is not possible anymore. The poster will, in addition, illustrate how such parameter-dependent nonlinear FSI discretizations can be tackled on the basis of the Newton iteration.

### Primary author

Roman Weinhandl (Otto von Guericke University Magdeburg)

### Co-authors

Peter Benner (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg) Thomas Richter (Otto von Guericke University Magdeburg)

### Presentation materials

There are no materials yet.