Model Order Reduction for Complex Domain Problems in the Time-Continuous Space-Time Setting


Tuesday, 4 July, 2023 - 16:00

by Dr Fabian Key (TU Wien)

In scientific and engineering applications, simulation-based methods can provide insight and
prediction capabilities with respect to the problem under investigation. They are used today,
for example, in the context of component analysis, product design, optimization, uncertainty
quantification (UQ), or to support ongoing operations as digital twins as well as through optimal
When using simulation-based methods, one faces many challenges, two of which are relevant
to this work. The first challenge is applications that involve transient phenomena and complex
domain deformations, possibly including topology changes. Thus, the computational model
needs to appropriately handle both the corresponding mesh and the unsteady solution field.
As a second challenge, the computational resources and the time required for evaluating the
model can be critical. On the one hand, this is relevant when many different configurations or
operating points need to be studied; for example, in optimization or uncertainty quantification
(UQ) scenarios. On the other hand, the fast feedback times of the model are essential in in-
line procedures, such as automatic control. All these cases have in common that (1) they can
be characterized as so-called many query scenarios, in which one needs to perform a great
number of model evaluations, and (2) that the problems involved are formulated in a
parametric manner. Here, employing highly resolved or full-order models (FOMs) may be
infeasible due to insufficient resources. As a remedy, parametric reduced-order models
(ROMs) are constructed to lower the computational demands while maintaining a desired level
of accuracy.
We address both types of complexity here and present a model order reduction (MOR)
approach for transient problems, including deforming domains with topological changes. The
underlying FOM is constructed using the time-continuous space-time finite element method.
Building on this FOM, we follow a projection-based MOR approach using proper orthogonal
decomposition (POD). This particular combination of the resulting FOM and the MOR
approach chosen here comes with the benefit that a ROM can be obtained in a straightforward
manner, which otherwise would be quite involved for transient deforming domain problems,
including changes in the spatial topology.
We will present results for two examples of transient fluid flow in complex geometries as
representatives for problems present in engineering or biomedical applications. The geometric
complexity is caused by the movement of a valve plug or the deformation of flexible artery
walls. For both cases, an error and performance analysis of the respective ROM is performed
to demonstrate the reduction concerning the computational expense as well as the
preservation of an adequate accuracy level.