31 research outputs found
A p-multigrid method enhanced with an ILUT smoother and its comparison to h-multigrid methods within Isogeometric Analysis
Over the years, Isogeometric Analysis has shown to be a successful
alternative to the Finite Element Method (FEM). However, solving the resulting
linear systems of equations efficiently remains a challenging task. In this
paper, we consider a p-multigrid method, in which coarsening is applied in the
approximation order p instead of the mesh width h. Since the use of classical
smoothers (e.g. Gauss-Seidel) results in a p-multigrid method with
deteriorating performance for higher values of p, the use of an ILUT smoother
is investigated. Numerical results and a spectral analysis indicate that the
resulting p-multigrid method exhibits convergence rates independent of h and p.
In particular, we compare both coarsening strategies (e.g. coarsening in h or
p) adopting both smoothers for a variety of two and threedimensional
benchmarks
Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method
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.Comment: 31 pages, 4 figure