Constructing projection vectors for DICCG
Gjalt Wijma

Plaats van afstuderen:
Shell Research
Volmerlaan 8
2280 AB Rijswijk
start van afstuderen: oktober 1997

De afstudeeropdracht is augustus 1998 afgerond met het schrijven van het afstudeerverslag. Huidige adresgegevens etc. zijn te vinden op onze alumnipagina.

Korte omschrijving van de afstudeeropdracht:
Shell wants to use CG for solving pressure problems in the upper three to six kilometers of the earth. Due to large contrasts in permeability the usual scaling methods like Incomplete Choleski are not powerful enough to ensure a smooth convergence behaviour. The mathematical reason for this is that Incomplete Choleski does not remove all of the small eigenvalues in the original system. There are a few eigenvalues left of order of the low permeability.

A projection method is introduced to remove these small eigenvalues. The projection method transforms the preconditioned system into a new one which kernel contains the eigenvectors belonging to the small eigenvalues. The new system can be solved and has a much better convergence bahviour than the preconditioned system. The projection method is practical in this case because the projection vectors have a clear link to the physical problem. Therefore it is possible to estimate them upfront. My research is focussed on the prediction and construction of these eigenvectors. The resulting method is implemented in SEPRAN.

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