Model Order Reduction for Deforming Domain Problems in a Time-Continuous Space-Time Setting
arXiv:2303.16662 · doi:10.1002/nme.7342
Abstract
In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with changes in the domain topology, need to be tackled appropriately. The second challenge arises when computational resources and the time for evaluating the model become critical in so-called many query scenarios for parametric problems. For example, these problems occur in optimization, uncertainty quantification (UQ), or automatic control and using highly resolved full-order models (FOMs) may become impractical. To address both types of complexity, we present a novel projection-based model order reduction (MOR) approach for deforming domain problems that takes advantage of the time-continuous space-time formulation. We apply it to two examples that are relevant for engineering or biomedical applications and conduct an error and performance analysis. In both cases, we are able to drastically reduce the computational expense for a model evaluation and, at the same time, to maintain an adequate accuracy level. All in all, this work indicates the effectiveness of the presented MOR approach for deforming domain problems taking advantage of a time-continuous space-time setting.
References in corpus (5)
- A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to a Stokes Flow
- Boundary-Conforming Finite Element Methods for Twin-Screw Extruders using Spline-Based Parameterization Techniques
- Time-Continuous and Time-Discontinuous Space-Time Finite Elements for Advection-Diffusion Problems
- The Virtual Ring Shear-Slip Mesh Update Method
- Combining Boundary-Conforming Finite Element Meshes on Moving Domains Using a Sliding Mesh Approach