References for Math 671 (particle methods)

Green's functions
Greenberg, M.D. (2015) Applications of Green's Functions in Science and Engineering, Dover

Briggs, W.L. and Henson, V.E. (1995) The DFT : an Owner's Manual for the Discrete Fourier Transform, SIAM
Sedgewick, R. (1988) Algorithms, Addison-Wesley
Wickerhauser, V. (1994) Adapted Wavelet Analysis from Theory to Software, A.K. Peters
Edelman, A., McCorquodale, P. and Toledo, S. (1999) The future Fast Fourier Transform?, SIAM J. Sci. Comput. 20, 1094-1114.

potential theory
Folland, G.B. (1992) Fourier Analysis and its Applications, Wadsworth & Brooks/Cole
Hildebrand, F.B. (1962) Advanced Calculus for Applications, Prentice-Hall
MacRobert, T.M. (1967) Spherical Harmonics; An Elementary Treatise on Harmonic Functions, with Applications, Pergamon Press
Sternberg, W.J. and 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

multipole methods (fast multipole method, treecode, 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. and Hut, P. (1986) A hierarchical O(NlogN) force-calculation algorithm, Nature 324, 446-449.
Beatson, R. and 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. and Rokhlin, V. (1999) A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys. 155, 468-498.
Draghicescu, C.I. and Draghicescu, M. (1995) A fast algorithm for vortex blob interactions, J. Comput. Phys. 116, 69-78.
Duan, Z.-H. and 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. and Rokhlin, V. (1987) A fast algorithm for particle simulations, J. Comput. Phys. 73, 325-348.
Greengard, L. and 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. and Rokhlin, V. (1997) A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numerica, 229-269.
Hackbusch, W. and Nowak, Z.P. (1989) On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math. 54, 463-491.
Li, P., Johnston, H. and Krasny, R. (2009) A Cartesian treecode for screened Coulomb interactions, J. Comput. Phys. 228, 3858-3868.
Lindsay, K. and 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. and 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. and Board Jr., J.A. (1996) Ewald summation techniques in perspective: a survey, Comput. Phys. Commun. 95, 73-92.

Hockney, R.W. and Eastwood, J.W. (1988) Computer Simulation Using Particles, Taylor and Francis

radial basis functions
Buhmann, M.D. (2003) Radial Basis Functions, Cambridge University Press
Larsson, E. and Fornberg, B. (2003) A numerical study of some radial basis function based solution methods for elliptic PDEs, Comp. Math. Appl. 46, 891-902.
Krasny, R. and Wang, L. (2011) Fast evaluation of multiquadric RBF sums by a Cartesian treecode, SIAM J. Sci. Comput. 33, 2341-2355.

iterative methods
Ciarlet, P.G. (1989) Introduction to Numerical Linear Algebra and Optimisation, Cambridge University Press

Brandt, A. (1977) Multi-level adaptive solutions to boundary-value problems, Math. Comp. 31, 333-390.
Briggs, W.L., Henson, V.E. and McCormick, S.F. (2000) A Multigrid Tutorial, SIAM

Allen, M.P. and Tildesley, D.J. (1987) Computer Simulation of Liquids, Clarendon Press, Oxford
Birdsall, C.K. and Langdon, A.B. (1991) Plasma Physics via Computer Simulation, IOP Publishing
Cottet, G.-H. and 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 and Liu, W.K. (2004) Meshfree Particle Methods, Springer
Liu, G.R. and Liu, M.B. (2003) Smoothed Particle Hydrodynamics. A Meshfree Particle Method, World Scientific Publishing
Pfalzner, S. and Gibbon, P. (1996) Many-Body Tree Methods in Physics, Cambridge University Press
Potter, D. (1973) Computational Physics, John Wiley and Sons
Sagui, C. and Darden, T.A. (1999) Molecular dynamics simulations of biomolecules: Long-range electrostatic effects, Annu. Rev. Biophys. Biomol. Struct. 28, 155-179.
Schlick, T. (2002) Molecular Modeling and Simulation: An Interdisciplinary Guide, Springer