Wavelet-Based Algorithms for Solving Neutron Diffusion Equations.

Nasif, Hesham; Omori, Ryota; Suzuki, Atsuyuki; Naguib, Mohamed; Nagy, Mohamed S.

doi:10.3327/jnst.38.161

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…Wavelets can build a basis for differential equation discretisation 4 and solving, [5][6][7] and the solvers have been developed and tested in various fields of science from diffusion to electromagnetic waves. [8][9][10][11] In electronic structure calculations, wavelet basis has been present since the early nineties, [12][13][14][15] and in the previous decade both a wavelet based 13,14,16 and a multiwavelet based [17][18][19] solver have been developed with chemical accuracy and massively parallel computational possibilities. These solvers mostly use two resolution levels, but adaptively refining solution schemes are also given for simpler systems.…”

Section: Introductionmentioning

confidence: 99%

An economic prediction of the finer resolution level wavelet coefficients in electronic structure calculations

Nagy

Pipek

2015

Phys. Chem. Chem. Phys.

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In wavelet based electronic structure calculations, introducing a new, finer resolution level is usually an expensive task, this is why often a two-level approximation is used with very fine starting resolution level. This process results in large matrices to calculate with and a large number of coefficients to be stored. In our previous work we have developed an adaptively refined solution scheme that determines the indices, where the refined basis functions are to be included, and later a method for predicting the next, finer resolution coefficients in a very economic way. In the present contribution, we would like to determine whether the method can be applied for predicting not only the first, but also the other, higher resolution level coefficients. Also the energy expectation values of the predicted wave functions are studied, as well as the scaling behaviour of the coefficients in the fine resolution limit.

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