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**FLEXMG: a new library of multigrid preconditioners for a spectral/finite element incompressible flow solver.**
*(English)*
Zbl 1188.76227

Summary: A new library called FLEXMG has been developed for a spectral/finite element incompressible flow solver called SFELES. FLEXMG allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods. Two families of algebraic multigrid preconditioners have been implemented, namely smooth aggregation-type and non-nested finite element-type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non-nested finite element-type multigrid so that our approaches can be considered as hybrid. Our aggregation-type multigrid is smoothed with either a constant or a linear least-square fitting function, whereas the non-nested finite element-type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand-alone solvers or coupled with a GMRES method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics, their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in the study.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76M22 | Spectral methods applied to problems in fluid mechanics |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

### Keywords:

algebraic multigrid; smooth aggregation; non-nested finite element interpolation; GMRES; CFD
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\textit{M. Rasquin} et al., Int. J. Numer. Methods Eng. 82, No. 12, 1510--1536 (2010; Zbl 1188.76227)

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