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

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

7 Nov 2019, 15:00

2h

Main/groundfloor-none - Magistrale (Max Planck Institute for Dynamics of Complex Technical Systems)

Poster Posters 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

$(A_0+{\mu }_i{A}_1+A_2(x_i))x_i=b\text{for}i\in \{1,...,m\}$,

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.