Stokes Problems with FEniCS::DOLFIN

Keywords: Stokes, Uzawa, Hood-Taylor, Stabilized, DOLFIN, FENICS

Table of Contents

1 Generalized Stokes Problem in a square cylinder with an obstacle.

1.1 Description

We will consider the following 3D (Augmented Lagrangian) Stokes problems given by

where could be a function of the mesh size and is the deformation rate tensor given by .

The discretized domain is given by:

domain.png

xml mesh boundary marks

1.2 Examples,Tests, Benchmarks

In the following table,we present the results for some tests with different equation parameters and with different solving methods.

Direct Solver (H-T) (P2)3 × P1Param\MethodUzawa (H-T) (P2)3 × P1Direct Stabilized (P1)3 × P1
system dims 5924902system dims 5667692 + 257212system dims 1028842
time=?Test 1time=55.4mnts iter=19time=2.57mnts
Gmres Error=?Loop Error=10-4 Gmres Error=10-5Gmres Error=10-5
image: vel Bug?image: vel image: vel1image: vel
image: pressbound Bug?image: pressboundimage: pressbound
image: presscut Bug?image: presscutimage: presscut
code: dolfincode: dolfincode: dolfin
time= ?Test 2time=74.mnts iter=8 Note 1time=4.4mnts
Gmres Error=? Note 2Loop Error=10-4 Gmres Error=10-5Gmres Error=10-5
image: vel Bug?image: vel image: vel1image: vel
image: pressbound Bug?image: pressboundimage: pressbound
image: presscut Bug?image: presscutimage: presscut
code: dolfincode: dolfincode: dolfin
TODOTest 3TODOTODO
Note 1: In this example we can see the influence of the grad-div stabilization term on the number of Uzawa iterations.

Note 2: It seems difficult to fine tune the GMRES PETSc solver to get some acceptable results.

The test were made in a Ubuntu 8.04, Intel Duo Core 1.86GHz.


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Author: Nuno David Lopes <ndl (at) ptmat.fc.ul.pt>

Date: 2010-10-03 20:47:32 WEST

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