Piotr Krzyżanowski, PhD


Supervision of doctoral theses
1.2021-05-27
co-supervisor
Wichrowski Michał Fluid-structure interaction problems: velocity-based formulation and monolithic computational methods1266
 

Recent publications
1.Wichrowski M., Krzyżanowski P., Heltai L., Stupkiewicz S., Exploiting high-contrast Stokes preconditioners to efficiently solve incompressible fluid-structure interaction problems, INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, ISSN: 0029-5981, DOI: 10.1002/nme.7350, Vol.124, pp.5446-5470, 2023
Abstract:

In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid-structure interaction problems using a matrix-free finite element method in arbitrary Lagrangian–Eulerian frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek-Hron benchmarks in two and three dimensions, and investigate timing and scalability results.

Keywords:

arbitrary Lagrangian-Eulerian, finite element method, fluid-structure interaction, geometric multigrid, matrix-free method, monolithic scheme

Affiliations:
Wichrowski M.-other affiliation
Krzyżanowski P.-other affiliation
Heltai L.-SISSA - International School for Advanced Studies (IT)
Stupkiewicz S.-IPPT PAN
2.Wichrowski M., Krzyżanowski P., A matrix-free multilevel preconditioner for the generalized Stokes problem with discontinuous viscosity, Journal of Computational Science, ISSN: 1877-7503, DOI: 10.1016/j.jocs.2022.101804, Vol.63, No.101804, pp.1-12, 2022
Abstract:

In this paper we present a matrix-free multilevel solver for the generalized Stokes problem with discontinuous viscosity. The algorithm is based on the FGMRES iteration preconditioned with a block-smoothed multigrid method. Numerical experiments on unstructured grids indicate that for a broad range of smoother parameters, the convergence speed is only weakly dependent on both the number of unknowns and the jumps of the viscosity coefficient.

Keywords:

Stokes problem, Discontinuous coefficients, Multigrid, Matrix-free, Parallel computing

Affiliations:
Wichrowski M.-IPPT PAN
Krzyżanowski P.-other affiliation