Next: Computational costs
Up: Numerical examples
Previous: Numerical examples
As discretization we use a five-point finite difference stencil with simple upwinding
to obtain stable discretizations already with respect to the finest grid

[
21].
This can be interpreted as a discretization which results from a Petrov-Galerkin FE method
with operator-dependent trial and test spaces

and

.
For reasons of numerical stability we scale the above operators in our computations by a
factor

for

.
If not stated differently we apply standard multiscale V- or W-cycles or improved
multiscale V-cycles together with a complete
decomposition of the spaces
and
.
Hence, the coarsest grid consists of one interior grid point only.
The approximation
of
used in our experiments is computed by a
forward- and backward-substitution from an
incomplete factorization (ILU(0)) of the blocks
(
).
We start our iterations with a normalized random vector
and consider without loss of generality the discrete solution
to a zero
right hand side
on the finest grid
[22].
Our measure for the speed of convergence is
 |
(2.1) |
i.e. the average error reduction within

steps with respect to the discrete

-norm [
22].
We start to measure after one initial iteration to be free of effects from the starting
vector.
The stopping criterion is

for the norm of the absolute error.
If this has not been reached with 30 iterations, the iteration is also stopped.
Next: Computational costs
Up: Numerical examples
Previous: Numerical examples
Frank Kiefer
2001-10-25