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Improve poisson-pq2 example

Carsten Gräser requested to merge feature/improve-poisson-pq2-example into master

This introduces several improvements to the poisson-pq2 example:

  • Demonstrate usage of mixed grids if UGGrid is available. While there's no reason to use a mixed grid here, we should imho demonstrate that it simply works. This is done conditionally using HAVE_UG. However, we strictly speaking already depend on dune-uggrid, because it's used unconditionally in the tests.
  • Use symmetrized approach to incorporate Dirichlet data. While CG works on the non-symmetric approach to (because it stays in an appropriate subspace) it's unclear if this is still the case in the presence of a preconditioner (see below).
  • Use ILDL instead of ILU preconditioner. Since we use CG, the preconditioner should be s.p.d.. In fact it turnes out that ILDL and ILU generate exactly the same results once the problem is symmetrized (see above). However, we should still use ILDL since the ILU documentation does not guarantee this.
  • It turnes out that using ILDL/ILU for the properly symmetrized problem is much better that the old method (which was beyond any theory anyway).
Edited by Carsten Gräser

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