BSce Advanced Studies project: Using wavelet transforms to assist the solution of van der Waals forces

During my undergraduate studies I was invited to join the “Advanced Studies” stream of my Bachelor of Science. This involved doing a few reports on assorted research topics, culminating in a final project as an introduction to participating in scientific research. I did my project under Prof. John Dobson, investigating the potential suitability of using wavelet transforms to enhance the speed of numerical solutions of van der Waals forces in solid materials.

I took several wavelet transform families and types, and examined the outcomes of their application to the matrix representations of the two operators involved in the force calculations. This was only a preliminary study, so it's uncertain how applicable the results ultimately are. That said, I found that certain wavelet transformations make the matrices less dense and, thus, possibly easier to solve. The PDF of my project report can be found here.

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