A Block Preconditioner for Scalable Large Scale Finite Element Incompressible Flow Simulations

Goik, Damian; Banaś, Krzysztof

doi:10.1007/978-3-030-50420-5_15

Cited by 2 publications

(3 citation statements)

References 17 publications

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“…In this paper, we present a solution procedure for the convective heat transfer problems that employ the preconditioner introduced in [16] as well as the results of its application to the well-known heat-driven (buoyancy) cavity-flow simulations. Implemented on the basis of the PETSC library, the preconditioner uses the block decomposition of the system of linear equations and Schur complement techniques to produce a three-step iterative procedure with separate linear subsystems.…”

Section: E a R L Y B I R Dmentioning

confidence: 99%

“…The main interface of the module allows for two main operations: the AMG-levels creation (set-up phase), and the execution of a single V-cycle on the created levels' structure. The exact form of each operation can be controlled by multiple parameters, including the number of levels, the number of pre-and post-smoothing steps, and the number of local and global iterations [16]. When tuning the solver, it is necessary to maintain good proportions among the level's set-up time, the number of iterations for the convergence, and the single iteration time.…”

Section: E a R L Y B I R Dmentioning

confidence: 99%

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Efficient Simulations of Large Scale Convective Heat Transfer Problems

Goik¹,

Banaś²,

Bielański³

et al. 2021

csci

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We describe an approach for efficient solution of large scale convective heat transfer problems, formulated as coupled unsteady heat conduction and incompressible fluid flow equations. The original problem is discretized in time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid flow problem uses Picard's iterations to solve the arising nonlinear equations. Both problems, heat transfer and Navier-Stokes quations, give rise to large sparse systems of linear equations. The systems are solved using iterative GMRES solver with suitable preconditioning. For the incompressible flow equations we employ a special preconditioner based on algebraic multigrid (AMG) technique. The paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned, especially for ill conditioned systems arising from discretizations of incompressible Navier-Stokes equations. We describe parallel implementation of the solver using MPI and elements of PETSC library. The scalability of the solver is favourably compared with other methods such as direct solvers and standard GMRES method with ILU preconditioning.

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Section: E a R L Y B I R Dmentioning

confidence: 99%

Section: E a R L Y B I R Dmentioning

confidence: 99%

Efficient Simulations of Large Scale Convective Heat Transfer Problems

Goik¹,

Banaś²,

Bielański³

et al. 2021

csci

Self Cite

View full text Add to dashboard Cite

show abstract

“…This approach turned out to be successful in various coupled multiphysics PDE simulations -e.g. in poroelasticity [1], geophysical electromagnetics [8], Cahn-Hilliard Navier-Stokes systems [9], multiphase poromechanics of heterogeneous media [11], linear elasticity in mixed form [13], incompressible (reduced) resistive magnetohydrodynamic [15], incompressible flow simulations [21], elliptic optimal control problems [22], fluid-structure interaction problems in hemodynamics [32], models of coupled magma/mantle dynamics [39] and incompressible Navier-Stokes problems [44]. For fully implicit discretisations of multidimensional radiation diffusion equations, An et al [2], Feng et al [18], and Mousseau et al [33] proposed various operator-based preconditioners in the Jacobian-free Newton-Krylov framework.…”

Section: Introductionmentioning

confidence: 99%

A New Relaxed Splitting Preconditioner for Multidimensional Multi-Group Radiation Diffusion Equations

Yue¹

2022

EAJAM

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Motivated by the ideas of Frigo et al. [SIAM J. Sci. Comput. 41 (2019) B694-B720], we develop a novel relaxed splitting preconditioner and consider its parallel implementation. Fully-coupled fully-implicit linearised algebraic systems arising from the multidimensional multi-group radiation diffusion equations are solved by using algebraic multigrid subsolvers. Spectral properties of the relaxed splitting rightpreconditioned matrix are studied. This allows to introduce an easily implementable algebraic selection strategy for finding the corresponding relaxation parameter. Numerical experiments show that the new preconditioner outperforms some existing popular preconditioners in robustness and efficiency and is well scalable both algorithmically and in parallel.

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A Block Preconditioner for Scalable Large Scale Finite Element Incompressible Flow Simulations

Cited by 2 publications

References 17 publications

Efficient Simulations of Large Scale Convective Heat Transfer Problems

Efficient Simulations of Large Scale Convective Heat Transfer Problems

A New Relaxed Splitting Preconditioner for Multidimensional Multi-Group Radiation Diffusion Equations

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