The efficient solution of the Helmholtz equation
Jok Tang

Site of the project:
Hoekstede Building
Visseringlaan 26
2280AB Rijswijk
The Netherlands

start of the project: November 2003

In February 2004 the Interim Thesis has been appeared.

The Master project has been finished in August 2004 ( Masters Thesis). For working address etc. we refer to our alumnipage.

Summary of the master project:
The efficient solution of the Helmholtz equation on very large grids (1000 x 1000 x 1000) is very important for Shell and a challenge for numerical linear algebra research. The Helmholtz equation is used for seismic investigations of the earth's crust. The results can be used to determine the position of various layers. Thereafter, possible locations of oil or gas reservoirs can be predicted.


At this moment a number of solvers are known:
  1. ILU preconditioners
  2. multigrid preconditioners
  3. shifted Laplace preconditioners
  4. separation of variable preconditioners
  5. Gander and Nataf preconditioners
Some of these preconditioners work for certain applications, but fail for other ones (some of which are interesting for Shell). During the master thesis work literature about these preconditioners should be studied. A comparison of these methods for realistic problems is important. Investigation of the properties of the preconditioners can lead to an understanding of their success or failure. Probably a combination of different preconditioners can lead to a robust and efficient solver.

To be more specific the following topics can be studied:

Contact information: Kees Vuik

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