467 research outputs found
Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations
An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids
An algebraic multigrid method for mixed discretizations of the Navier-Stokes equations
Algebraic multigrid (AMG) preconditioners are considered for discretized
systems of partial differential equations (PDEs) where unknowns associated with
different physical quantities are not necessarily co-located at mesh points.
Specifically, we investigate a mixed finite element discretization of
the incompressible Navier-Stokes equations where the number of velocity nodes
is much greater than the number of pressure nodes. Consequently, some velocity
degrees-of-freedom (dofs) are defined at spatial locations where there are no
corresponding pressure dofs. Thus, AMG approaches leveraging this co-located
structure are not applicable. This paper instead proposes an automatic AMG
coarsening that mimics certain pressure/velocity dof relationships of the
discretization. The main idea is to first automatically define coarse
pressures in a somewhat standard AMG fashion and then to carefully (but
automatically) choose coarse velocity unknowns so that the spatial location
relationship between pressure and velocity dofs resembles that on the finest
grid. To define coefficients within the inter-grid transfers, an energy
minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific
coarsening schemes and grid transfer sparsity patterns, and so it is applicable
to the proposed coarsening. Numerical results highlighting solver performance
are given on Stokes and incompressible Navier-Stokes problems.Comment: Submitted to a journa
h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems
In this work we exploit agglomeration based -multigrid preconditioners to
speed-up the iterative solution of discontinuous Galerkin discretizations of
the Stokes and Navier-Stokes equations. As a distinctive feature -coarsened
mesh sequences are generated by recursive agglomeration of a fine grid,
admitting arbitrarily unstructured grids of complex domains, and agglomeration
based discontinuous Galerkin discretizations are employed to deal with
agglomerated elements of coarse levels. Both the expense of building coarse
grid operators and the performance of the resulting multigrid iteration are
investigated. For the sake of efficiency coarse grid operators are inherited
through element-by-element projections, avoiding the cost of numerical
integration over agglomerated elements. Specific care is devoted to the
projection of viscous terms discretized by means of the BR2 dG method. We
demonstrate that enforcing the correct amount of stabilization on coarse grids
levels is mandatory for achieving uniform convergence with respect to the
number of levels. The numerical solution of steady and unsteady, linear and
non-linear problems is considered tackling challenging 2D test cases and 3D
real life computations on parallel architectures. Significant execution time
gains are documented.Comment: 78 pages, 7 figure
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