The 7th Annual Meeting on High Performance Computing and Infrastructure in Norway

NOTUR2008 - ABSTRACTS

The multiwavelet approach in quantum chemistry

Luca Frediani

The Kohn-Sham equations of Density Functional Theory can can be cast in an integral equation form that is suited for a multiwavelet representation involving separable operators and functions defined on adaptive meshes We have developed and implemented a formalism for the application of separable integral operators in d > 1 dimensions using the so-called Non-Standard (NS) form of separable operators.

The proposed formalism is general, compact and oriented towards the practical implementation into a working code using multiwavelets. For the case of Poisson and Helmholtz operators, which are the basis for a DFT implementation, we also propose a simple scheme for the generation of an approximate separated representation of the corresponding kernels with finite arbitrary precision. Such a representation, combined with the NS-form, allows us to build a sparse, banded representation of the operator. We have implemented a code for the application of the Poisson and Helmholtz operators on a separated Non-Standard form. The implemented code computes explicitly all the 2^(2d) components of the $d$-dimensional operator. We finally demonstrate the performance of our implementation on some test cases.

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