Publication

Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo
2019
Journal Articles

Abstract

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (MSRB) preconditioning method proposed in Dal Santo et al. (2018); it combines an approximated block (fine grid) preconditioner with a reduced basis (RB) solver which plays the role of coarse component. A sequence of RB spaces, constructed either with an enriched velocity formulation or a Petrov - Galerkin projection, is built. Each RB coarse component is defined to perform a single iteration of the iterative method at hand. The flexible GMRES (FGMRES) algorithm is employed to solve the resulting preconditioned system and targets small tolerances with a very small iteration count and in a very short time. Numerical test cases for Stokes flows in three dimensional parameter-dependent geometries are considered to assess the numerical properties of the proposed technique in different large scale computational settings. (C) 2018 Elsevier Ltd. All rights reserved.

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Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo
2019
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/79bbefff-f094-413d-b4f0-d324b624e063

About this result

Related concepts (28)

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In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems.

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