Introduction to the Fast Multipole Method

This book introduces the reader to the theory and computer implementation of the Fast Multipole Method. It covers the topics of Laplace’s equation, spherical harmonics, angular momentum, the Wigner matrix, the addition theorem for solid harmonics, and lattice sums for periodic boundary conditions, along with providing a complete, self-contained explanation of the math of the method, so that anyone having an undergraduate grasp of calculus should be able to follow the material presented. The authors derive the Fast Multipole Method from first principles and systematically construct the theory connecting all the parts. Key Features: Introduces each topic from first principles Derives every equation presented, and explains each step in its derivation Builds the necessary theory in order to understand, develop, and use the method Describes the conversion from theory to computer implementation Guides through code optimization and parallelization Autho Biography Victor Anisimov is an Application Performance Engineer at the Argonne National Laboratory James J. P. Stewart is the author of the MOPAC program developed by Stewart Computational Chemistry, LLC

Table of Contents:
Introduction to Biomolecular Simulations Dawn of Quantum Biology What Makes Biomolecules Special Matching Computational and Experimental Conditions Mathematical Preliminaries Linear Algebra Spherical Coordinates Internal Coordinates Coordinate Transformation Differential and Integral Calculus Dirac Delta Function Linear Operators Function Minimization Mathematical Statistics Classical Mechanics The Newton Laws The Lagrange Equation Classical Electrostatics Electrostatic Potential Electric Field Curl and Divergence Gauss' Law Poisson and Laplace Equations The Legendre Polinomials Spherical Harmonics Multipole Expansion Fourier Series Many-Electron Systems The Schrodinger Equation The Born-Oppenheimer Approximation Variation Principle Perturbation Theory The Hartree-Fock Approximation Geometry Optimization Constrained Optimization using Lagrange Multipliers Coupled Perturbed Hartree-Fock Theory Vibrational Analysis The Semiempirical Theory The NDDO Approximation Energy Derivatives Linear Scaling Methods Initial Guess VFL Approximation and LocalSCF Method Multiple-Layer QM Models Implicit Solvent Model COSMO Classical Biomolecular Force Fields Mean Field Approximation Simulation of Bulk Liquids Determination of Electrostatic and Lennard-Jones Parameters Biomolecular Force Fields and Programs Long-Range Electrostatics Fast Multipole Method Ewald Sums Method Condensed Phase Translational Symmetry Periodic Structures Hartree-Fock Method for Periodic Systems Statistical Mechanics Statistical Ensembles Configuration Space Entropy Time-Correlation Function Radial Distribution Function Molecular Dynamics Hamiltonian Dynamics Langevin Dynamics Non-Hamiltonian Dynamics Constrained Dynamics Free Energy Calculations Free Energy Problem Potential of Mean Force Free Energy Pe11urbation Thermodynamic Integration The Weighted Histogram Analysis Method Sample Applications Structure Preconditioning Water Solvation Adding Ions Structure Relaxation by Using Force Fields Quantum Mechanical Molecular Dynamics Chemical Reactions Conformational Sampling Protein-Ligand Binding Free Energy High Performance Computing MPI Basics Submitting Multiple Jobs on Multiple Processors

About the Author :
Victor M. Anisimov is a Postdoctoral Fellow at the School of Health Information Science at the University of Texas, Houston. James J. P. Stewart is the Owner of Stewart Computational Chemistry, Colorado Springs.