Seminar by Simona Perotto

Speaker

Simona Perotto (Politecnico di Milano)

Title

Hierarchical model reduction: background, applications, recent progress, and future directions

Date

  • April 23, 2024 16:00 CEST+0200 (Europe/Rome)

  • April 23, 2024 10:00 EDT-0400 (US/Eastern)

  • April 23, 2024 09:00 CDT-0500 (US/Central)

  • April 23, 2024 07:00 PDT-0700 (US/Pacific)

Abstract

Hierarchical Model (HiMod) reduction is designed to describe phenomena where a primary dynamics is aligned with the dominant directionality of the domain, while secondary dynamics evolve along the transverse direction (Perotto, Ern, and Veneziani 2010). The modeling heterogenity along the different directions corresponds to diverse discretizations in correspondence with the mainstream and the transverse direction, following a separation of variables approach. Common choices involve using a finite element or an isogeometric approximation along the mainstream, which is enriched by a modal (Fourier) expansion to capture secondary dynamics. HiMod has demonstrated a substantial reduction in computational cost and simulation time, while delivering an informative solution.

The presentation will start by introducing the fundamental principles, theoretical outcomes, and tools associated with HiMod. Then, various applications will be showcased where HiMod reduction has been effectively applied, spanning from modeling blood flow in arteries impacted by conditions like severe stenosis or aneurysms (Brandes Costa Barbosa and Perotto 2020) to modeling acoustic wave propagation in deformed pipelines (Gentili et al. 2022). Following this, recent advances will be illustrated, including modeling flows in pipes with geometric settings inherently excluded by the theoretical formalization of HiMod, such as branches. Lastly, we’ll discuss the future directions of hierarchical model reduction, exploring potential challenges and the evolving landscape of research.

Brandes Costa Barbosa, Yves Antonio, and Simona Perotto. 2020. “Hierarchically Reduced Models for the Stokes Problem in Patient-Specific Artery Segments.” International Journal of Computational Fluid Dynamics 34 (2): 160–71. https://doi.org/10.1080/10618562.2020.1733537.

Gentili, G. G., M. Khosronejad, G. Bernasconi, S. Perotto, and S. Micheletti. 2022. “Efficient Modeling of Multimode Guided Acoustic Wave Propagation in Deformed Pipelines by Hierarchical Model Reduction.” Applied Numerical Mathematics 173: 329–44. https://doi.org/10.1016/j.apnum.2021.12.008.

Perotto, Simona, Alexandre Ern, and Alessandro Veneziani. 2010. “Hierarchical Local Model Reduction for Elliptic Problems: A Domain Decomposition Approach.” Multiscale Modeling & Simulation 8 (4): 1102–27. https://doi.org/10.1137/090756624.

Recording

Watch the recording on our YouTube channel.