ICCE 2024

Ghent University, Ghent, Belgium

Title: Recent advances in quasi-Newton methods for partitioned simulation of fluid-structure interaction

Abstract: Quasi-Newton methods can be used in partitioned fluid-structure interaction simulations if there are coupling iterations between the solvers and the convergence needs to be stabilized and accelerated. Recently, it has been shown how surrogate models of the actual solvers can be included in these algorithms to further accelerate their convergence. This also led to the reformulation of several existing quasi-Newton methods in the generalized Broyden framework and to more emphasis on the necessity of linear scaling with the number of degrees of freedom on the coupling interface. Furthermore, numerical experiments have demonstrated that limiting the amount of work in each solver per coupling iteration can be beneficial for the total duration of the simulation, outweighing the increase in number of coupling iterations up to a certain point. Finally, the additional coupling tolerance can be avoided if some information about the convergence of the solvers is accessible to the coupling framework. Individually or combined, these recent evolutions can lead to a meaningful reduction in simulation time.

Joris Degroote (1),(3); Nicolas Delaissé (1); Thomas Spenke (2) and Norbert Hosters (2)

(1) Department of Electromechanical, Systems and Metal Engineering, Faculty of Engineering and Architecture, Ghent University – Ghent, Belgium

(2) Chair for Computational Analysis of Technical Systems (CATS), Center for Simulation and Data Science (JARA-CSD), RWTH Aachen University – Aachen, Germany

(3) Core Lab MIRO, Flanders Make – Ghent, Belgium

Brown University, Providence (Rhode Island), USA

Title: Employing Machine Learning Approaches to solve PDEs in “Mechanics” within Big-data Regime

Abstract: A new paradigm in scientific research has been established with the integration of data-driven and physics-informed methodologies in the domain of deep learning, and it is certain to have an impact on all areas of science and engineering. This field, popularly termed “scientific machine learning,” relies on an over-parametrized deep learning model trained with (or without) high-fidelity data (simulated or experimental) to be able to generalize the solution field across multiple input instances. The neural operator framework fulfills this promise by learning the mapping between infinite dimensional functional spaces. The application of neural operators’ techniques within the context of operator regression to resolve efficiently and accurately time-dependent and -independent PDEs in mechanics will be the major focus of this presentation. The approaches' extrapolation ability, accuracy, and computing efficiency when integrated with traditional numerical solvers will be discussed.