Please use this identifier to cite or link to this item:
Title: Low‐rank linear fluid‐structure interaction discretizations
Author(s): Weinhandl, RomanLook up in the Integrated Authority File of the German National Library
Benner, PeterLook up in the Integrated Authority File of the German National Library
Richter, ThomasLook up in the Integrated Authority File of the German National Library
Issue Date: 2020
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-876915
Subjects: ChebyshevT
Parameter-dependent fluid-structure interaction
Abstract: Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for different solids and different fluids. For instance, a shipping company wants to know how the material, a ship's hull is made of, interacts with fluids at different Reynolds and Strouhal numbers before the building process takes place. Also, the behavior of such models for solids with different properties is considered before the prototype phase. A parameter-dependent linear fluid-structure interaction discretization provides approximations for a bundle of different parameters at one step. Such a discretization with respect to different material parameters leads to a big block-diagonal system matrix that is equivalent to a matrix equation as discussed in [1]. The unknown is then a matrix which can be approximated using a low-rank approach that represents the iterate by a tensor. This paper discusses a low-rank GMRES variant and a truncated variant of the Chebyshev iteration. Bounds for the error resulting from the truncation operations are derived. Numerical experiments show that such truncated methods applied to parameter-dependent discretizations provide approximations with relative residual norms smaller than 10−8 within a twentieth of the time used by individual standard approaches.
Open Access: Open access publication
License: (CC BY-NC-ND 4.0) Creative Commons Attribution NonCommercial NoDerivatives 4.0(CC BY-NC-ND 4.0) Creative Commons Attribution NonCommercial NoDerivatives 4.0
Sponsor/Funder: Projekt DEAL 2020
Journal Title: ZAMM
Publisher: Wiley-VCH
Publisher Place: Berlin
Volume: 100
Issue: 11
Original Publication: 10.1002/zamm.201900205
Page Start: 1
Page End: 28
Appears in Collections:Fakultät für Mathematik (OA)

Files in This Item:
File Description SizeFormat 
Weinhandl et al._Low‐rank linear_2020.pdfZweitveröffentlichung1.32 MBAdobe PDFThumbnail