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Comparison of accelerated recursive polynomial expansions for electronic structure calculations
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In electronic structure calculations the computational cost is of great importance because large systems can contain a huge number of electrons. One effective method to make such calculations is by density matrix purification. Although, the cost for this method is relatively low compared to other existing methods there is room for improvements. In this paper one method proposed by Emanuel Rubensson and one method proposed by Jaehoon Kim & Yousung Jung was compared to each other with respect to efficiency, simplicity and robustness. Both are improved methods to compute the density matrix by accelerated polynomial expansion. Rubensson’s method consists of two different algorithms and results showed that both performed better than Kim & Jung’s method in terms of efficiency, which is the property both methods directs their main focus on. The major differences between them was identified in terms of adaptivity. The methods require different inputs that demands separate levels of knowledge about the system. Kim & Jung’s method which require less knowledge can however benefit efficiency-wise from more information in order to optimize the algorithm for the system. Results also showed that both methods were stable, but since they only were tested with arbitrarily assumed input arguments no conclusion about their general stability could be drawn.

Place, publisher, year, edition, pages
2015. , 36 p.
TVE, 15 058
Keyword [en]
Electronic structure calculations, Density matrix, Polynomial expansion, Purification
National Category
Computational Mathematics
URN: urn:nbn:se:uu:diva-256377OAI: oai:DiVA.org:uu-256377DiVA: diva2:826137
Educational program
Master Programme in Engineering Physics
Available from: 2015-09-02 Created: 2015-06-23 Last updated: 2015-09-02Bibliographically approved

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Computational Mathematics

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