Affiliation:
1. Institute of Lightweight Design and Structural Biomechanics (ILSB) TU Wien Vienna Austria
2. Institute for Mathematics and Computer‐Based Simulation (IMCS) Universität der Bundeswehr München Neubiberg Germany
3. Department of Mathematics and Physics Università Cattolica del Sacro Cuore Brescia Italy
4. Mathematics Area, mathLab Scuola Internazionale Superiore di Studi Avanzati (SISSA) Trieste Italy
Abstract
AbstractIn 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 to 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, maintain an adequate accuracy level, each compared to the original time‐continuous space‐time full‐order model (FOM). All in all, this work indicates the effectiveness of the presented MOR approach for deforming domain problems by taking advantage of a time‐continuous space‐time setting.
Funder
Gruppo Nazionale per il Calcolo Scientifico
MSCA
Technische Universität Wien Bibliothek
Università Cattolica del Sacro Cuore
Subject
Applied Mathematics,General Engineering,Numerical Analysis