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Introduction to the Fast Multipole Method

Introduction to the Fast Multipole Method

          
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About the Book

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


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Product Details
  • ISBN-13: 9780429541216
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: CRC Press
  • Language: English
  • ISBN-10: 042954121X
  • Publisher Date: 17 Dec 2019
  • Binding: Digital (delivered electronically)
  • No of Pages: 456


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