A computational strategy for solving large generalized eigenvalue problems in fluid-structure interactions

Quentin Akkaoui (1) , Evangéline Capiez-Lernout (1) , Christian Soize (1) , Roger Ohayon (2)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 LMSSC - Laboratoire de Mécanique des Structures et des Systèmes Couplés

For constructing reduced-order models of large-scale fluid-structure systems, computations of generalized eigenvalue problems are required [1]. For linear, and a fortiori for nonlinear dynamical systems, reduced-order models are essential for reducing the computational costs of the simulation in terms of CPU time and memory use. The algorithms and mathematical libraries involved for solving such generalized eigenvalue problems have demonstrated their efficiency and are suitable for analyzing large-scale models using parallel computers and massively parallel computers such as LAPACK. However, when dealing with a large-scale fluid-structure system, a stop of the calculation due to an out of memory can be encountered on mid-power and moderate-memory computers. For instance, this case occured when trying to compute the generalized eigenvalue problems for a fluid-structure computational model with 2,000,000 degrees of freedom on a workstation with 264GB of RAM and 12 processors. For circumventing this problem, the present work is devoted to revisiting the algorithms in order to be able to compute these generalized eigenvalue problems on a midpower computer. The methods proposed [2] are algorithms based on double projection and subspace iteration methods [3], which efficiently allow for reducing the computational cost of these calculations and above all for avoiding the stop of the calculation due to an out of memory. In such context, after briefly recalling the existing algorithms used for solving the three generalized eigenvalue problems related to the displacement of the elastic structure, the pressure in the acoustic fluid, and the free-surface elevation of the fluid, a new adapted computational strategy [2] is described for reducing the numerical cost of each generalized eigenvalue problem. Finally, a detailed quantification of the computer resources required for computing the reduced-order projection basis with both classical and new method is presented, validating the efficiency of the proposed strategy. [1] R. Ohayon, C. Soize, Nonlinear model reduction for computational vibration analysis of structures with weak geometrical nonlinearity coupled with linear acoustic liquids in the presence of linear sloshing and capillarity, Computers & Fluids 141 (2016) 82–89. [2] Q. Akkaoui, E. Capiez-Lernout, C. Soize, R. Ohayon, Solving generalized eigenvalue problems for large scale fluid-structure computational models with mid-power computers, 205, 45-54 (2018) [3] K.-J. Bathe, The subspace iteration method–Revisited , Computers & Structures 126, 177–183 (2013).

Mots clés: Fluid-structure interactions; Generalized eigenvalue problem

Domaines: Mécanique [physics.med-ph]; Sciences de l'ingénieur [physics]; Analyse numérique [math.NA]

Quentin Akkaoui, Evangéline Capiez-Lernout, Christian Soize, Roger Ohayon. A computational strategy for solving large generalized eigenvalue problems in fluid-structure interactions. The 13th World Congress of Computational Mechanics (WCCM 2018) and Second Pan American Congress on Computational Mechanics (PANACM II), Jul 2018, New York, United States. ⟨hal-01876047⟩