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Low‐rank linear fluid‐structure interaction discretizations
Author(s) -
Weinhandl Roman,
Benner Peter,
Richter Thomas
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900205
Subject(s) - discretization , mathematics , fluid–structure interaction , rank (graph theory) , matrix (chemical analysis) , tensor (intrinsic definition) , reynolds number , block matrix , mathematical analysis , finite element method , geometry , physics , mechanics , materials science , combinatorics , turbulence , composite material , thermodynamics , eigenvalues and eigenvectors , quantum mechanics
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.