Hauptseminar Moderne Simulationsmethoden WS 2009/Langreichweitige Wechselwirkungen II

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Langreichweitige Wechselwirkungen in periodischen Geometrien II: MMM und schnelle Multipol Methoden (FMM)
Alexey Neelov

Literatur, FMM (Fast Multipole Method)

A simpler version of the algorithm, to get the idea: H.-Q. Ding, N. Karasawa, and W. Goddard, J. Chem Phys, 97, 4309-4315, 1992.

Recent review: J. Kurzak, B.M. Pettitt, Mol. Simul. 32(10-11), pp.775-790 (2006).

A good paper: C. A. White and M. Head-Gordon, J. Chem. Phys. 101, 6593 (1994).

Book: S. Pfalzner and P. Gibbon, Many-body tree methods in physics (Cambridge University Press, 1996).

The paper where FMM was introduced: L. Greengard and V. Rokhlin, J. Comput. Phys. 73, pp. 325-348 (1987).

FMM is so famous that it is in the Wikipedia: http://en.wikipedia.org/wiki/Fast_multipole_method

..and considered to be one of 10 greatest algorithms of the 20th century: http://amath.colorado.edu/resources/archive/topten.pdf

Literatur, MMM (M-Body Method) (optional?)

Review by Arnold and Holm (good starting point): http://springerlink.com/content/965j2ev8rc9wlld3/?p=a413f88a65324fd9bf31cc0d04e171d2&pi=1

The MMM2D method: A. Arnold, C. Holm, Comput. Phys. Commun. 148(3), pp. 327-348 (2002)

The MMM1D method: A. Arnold, C. Holm, J. Chem. Phys. 123, 144103 (2005)

PhD thesis of Axel Arnold: http://deposit.ddb.de/cgi-bin/dokserv?idn=975904000&dok_var=d1&dok_ext=pdf&filename=975904000.pdf

The MMM method:

R. Sperb, Mol. Simul. 20, pp.179-200 (1998)

R. Sperb, Mol. Simul. 22, pp.199-212 (1999)

R. Strebel and R. Sperb, Mol. Simul. 27, pp.61 -74 (2001)

PhD thesis of the author of MMM algorithm: ftp://ftp.inf.ethz.ch/pub/publications/diss/th13504.pdf