Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method
This work provides robust and efficient preconditioners for solving Stokes problems in isogeometric analysis, benefiting computational fluid dynamics simulations.
The paper introduces a new class of preconditioners for isogeometric Stokes discretizations that are robust to spline degree and mesh size, using the Fast Diagonalization method for efficient Sylvester-like equation solves. Numerical tests show the iterative solver is significantly faster than standard approaches.
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.