Iterative approaches to the solution of large scale non-linear eigen problems.

Picture of rhys-hawkins.md Rhys Hawkins

7 Dec 2023

This project is intended as a full year Honours project and a scholarship is available to the right candidate.

In many fields of science and engineering, the eigen solutions of physical equations have important applications in many fields.

Examples from structural analysis include the Tacoma Narrows bridge where a relatively mild wind excited torsional vibration modes of a bridge that subsequently resulted in its eventual collapse.

An example from seismology include using passive techniques that ``listen’’ for fundamental eigen modes at different frequencies. From this information, the subsurface structure and its likelihood to shake severely during an Earthquake can be inferred.

The traditional calculation of eigen solutions is well established but scales very poorly and cannot be used for large scale problems. Fortunately, in many cases, we only require a small number of eigen solutions rather than the whole spectrum and there have been many algorithms developed over the years that efficiently compute a small subset of eigen solutions. A recent advance is the so called FEAST algorithm with its additional benefit being that it can also operate on polynomial and non-linear eigen problems.

This honours project would examine the application of High Performance Computing strategies for solving larger scale non-linear eigen problems.

More information is available on my homepage

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The Australian National University acknowledges, celebrates and pays our respects to the Ngunnawal and Ngambri people of the Canberra region and to all First Nations Australians on whose traditional lands we meet and work, and whose cultures are among the oldest continuing cultures in human history.

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