References for Math 671, Winter 2007
FFT
Briggs, W.L. & Henson, V.E. (1995)
The DFT : an Owner's Manual for the Discrete Fourier Transform,
SIAM
Sedgewick, R. (1988)
Algorithms,
by R. Sedgewick, Addison-Wesley
Wickerhauser, V. (1994)
Adapted Wavelet Analysis from Theory to Software,
A.K. Peters
potential theory
MacRobert, T.M. (1967)
Spherical Harmonics; An Elementary Treatise on Harmonic Functions,
with Applications,
Pergamon Press
Sternberg, W.J. & Smith, T.L. (1961)
The Theory of Potential and Spherical Harmonics,
University of Toronto Press
Wallace, P.R. (1984)
Mathematical Analysis of Physical Problems,
Dover
treecode/Fast Multipole Method/panel clustering
Anderson, C.R. (1992)
An implementation of the fast multiple method without multipoles,
SIAM J. Sci. Stat. Comput. 13, 923-947.
Appel, A.W. (1985)
An efficient program for many-body simulation,
SIAM J. Sci. Stat. Comput. 6, 85-103.
Barnes, J. & Hut, P. (1986)
A hierarchical O(NlogN) force-calculation algorithm,
Nature 324, 446-449.
Beatson, R. & Greengard, L. (1997)
A short course on fast multipole methods,
in Wavelets, Multilevel Methods and Elliptic PDEs,
M. Ainsworth, J. Levesley, W. Light and M. Marletta (eds.), pp. 1-37,
Oxford University Press.
Cheng, H., Greengard, L. & Rokhlin, V. (1999)
A fast adaptive multipole algorithm in three dimensions,
J. Comput. Phys. 155, 468-498.
Draghicescu, C.I. & Draghicescu, M. (1995)
A fast algorithm for vortex blob interactions,
J. Comput. Phys. 116, 69-78.
Duan, Z.-H. & Krasny, R. (2001)
An adaptive treecode for computing nonbonded potential energy
in classical molecular systems,
J. Comput. Chem. 22, 184-195.
Greengard, L. (1988)
The Rapid Evaluation of Potential Fields in Particle Systems, MIT Press
Greengard, L. & Rokhlin, V. (1987)
A fast algorithm for particle simulations,
J. Comput. Phys. 73, 325-348.
Greengard, L. & Rokhlin, V. (1988)
The rapid evaluation of potential fields in three dimensions,
in Vortex Methods,
Lecture Notes in Mathematics 1360,
pp. 121-141, Springer-Verlag.
Greengard, L. & Rokhlin, V. (1997)
A new version of the fast multipole method for the Laplace equation
in three dimensions,
Acta Numerica, 229-269.
Hackbusch, W. & Nowak, Z.P. (1989)
On the fast matrix multiplication in the boundary element method by
panel clustering,
Numer. Math. 54, 463-491.
Lindsay, K. & Krasny, R. (2001)
A particle method and adaptive treecode for vortex sheet motion
in three-dimensional flow,
J. Comput. Phys. 172, 879-907.
Rokhlin, V. (1984)
Rapid solution of integral equations of classical potential theory,
J. Comput. Phys. 60, 187-207.
Ewald summation
Darden, T., York, D. and Pedersen, L.G. (1993)
Particle mesh Ewald: An Nlog(N) method for Ewald sums in large systems,
J. Chem. Phys. 98, 10089-10092.
Duan, Z.-H. & Krasny, R. (2000)
An Ewald summation based multipole method,
J. Chem. Phys. 113, 3492-3495.
Essmann, U., Perera, L., Berkowitz, M.L., Darden, T., Lee, H. and Pedersen, L.G. (1995)
A smooth particle mesh Ewald method,
J. Chem. Phys. 103, 8577-8593.
Fincham, D. (1993)
Optimisation of the Ewald sum,
CCP5 Newsletter 38.
Perram, J.W., Petersen, H.G. and de Leeuw, S.W. (1988)
An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles,
Molec. Phys. 65 (1988) 875-893.
Tosi, M.P. (1964)
Evaluation of electrostatic lattice potentials by the Ewald method,
in Solid State Physics, Advances in Research and Applications
16, F. Seitz and D. Turnbull (eds.), Appendix A, 107-113.
Toukmaji, A.Y. & Board Jr., J.A. (1996)
Ewald summation techniques in perspective: a survey,
Comput. Phys. Commun. 95, 73-92.
particle-in-cell
Hockney, R.W. & Eastwood, J.W. (1988)
Computer Simulation Using Particles,
Taylor & Francis
radial basis functions
Buhmann, M.D. (2003) Radial Basis Functions,
Cambridge University Press
Larsson, E. & Fornberg, B. (2003)
A numerical study of some radial basis function based solution methods for
elliptic PDEs,
Comp. Math. Appl. 46, 891-902.
multigrid
Briggs, W.L., Emson, V.E. & McCormick, S.F. (2000)
A Multigrid Tutorial,
SIAM
applications
Allen, M.P. & Tildesley, D.J. (1987)
Computer Simulation of Liquids,
Clarendon Press, Oxford
Birdsall, C.K. & Langdon, A.B. (1991)
Plasma Physics via Computer Simulation,
IOP Publishing
Cottet, G.-H. & Koumoutsakos, P.D. (2000)
Vortex Methods Theory and Practice,
Cambridge University Press
Koumoutsakos, P.D. (2005)
Multiscale flow simulations using particles,
Annu. Rev. Fluid Mech. 37, 457-487.
Li, S & Liu, W.K. (2004)
Meshfree Particle Methods,
Springer
Liu, G.R. & Liu, M.B. (2003)
Smoothed Particle Hydrodynamics. A Meshfree Particle Method,
World Scientific Publishing
Pfalzner, S. & Gibbon, P. (1996)
Many-Body Tree Methods in Physics,
Cambridge University Press
Potter, D. (1973)
Computational Physics,
John Wiley & Sons
Schlick, T. (2002)
Molecular Modeling and Simulation:
An Interdisciplinary Guide,
Springer
websites
FFTW :
www.fftw.org
FMM :
www.madmaxoptics.com