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Solving Elliptical PDEs in Arbitrarily Shaped Regions

Richard Gass
Organization: University of Cincinnati
Department: Department of Physics

Wolfram Technology Conference 2012
Conference location

Champaign, Illinois, USA

I will discuss some recent work on eigenfunction rescaling which provides a fast and efficient method for solving eigenvalue problems on essentially arbitrary domains. This work generalizes the earlier work of Lijnen, Chibotaru and Ceulemans [1]. The technique has a host of physical applications including quantum billiards, quantum dots, waves in electromagnetic cavities and the expansion of functions over arbitrary regions. Mathematica is ideally suited for implementing an eigenfunction rescaling algorithm since the integrated symbolic/numerical capabilities of Mathematica allow easy calculation of the rescaling functions. Calculation of the resulting matrix elements can then be done on a GPU. OpenCL link and CUDA link allow this to be done with minimal effort. I will present a complete Mathematica/GPU based implementation of the algorithm and discuss some physically interesting applications.

*Wolfram Technology