Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method

Abstract

In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be done efficiently thanks to the Fast Diagonalization method. These preconditioners are robust with respect to both the spline degree and mesh size. By incorporating information on the geometry parametrization and equation coefficients, we maintain efficiency on non-trivial computational domains and for variable kinematic viscosity. In our numerical tests we compare to a standard approach, showing that the overall iterative solver based on our preconditioners is significantly faster.

31 pages, 4 figures

References in corpus (4)

• Fast formation of isogeometric Galerkin matrices by weighted quadrature
• Matrix-free weighted quadrature for a computationally efficient isogeometric $k$-method
• Robust Multigrid for Isogeometric Analysis Based on Stable Splittings of Spline Spaces
• Robust multigrid methods for isogeometric discretizations of the Stokes equations

Cited by in corpus (5)

• Matrix-free weighted quadrature for a computationally efficient isogeometric $k$-method
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• Fast multigrid solvers for conforming and non-conforming multi-patch Isogeometric Analysis
• An efficient solver for space-time isogeometric Galerkin methods for parabolic problems
• Space-time least-squares isogeometric method and efficient solver for parabolic problems