Fast Algorithms for Classical Physics

Some of the recently developed fast summation methods that have arisen in scientific computing are described. These methods require an amount of work proportional to N or N log N to evaluate all pairwise interactions in an ensemble of N particles. Traditional methods, by contrast, require an amount...

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Bibliographic Details
Published in:Science (American Association for the Advancement of Science) Vol. 265; no. 5174; pp. 909 - 914
Main Author: Greengard, Leslie
Format: Journal Article
Language:English
Published: Washington, DC American Society for the Advancement of Science 12.08.1994
American Association for the Advancement of Science
The American Association for the Advancement of Science
Subjects:
990200 - Mathematics & Computers
Algorithm
ALGORITHMS
Algorithms for functional approximation
Classical and quantum physics: mechanics and fields
Classical mechanics of discrete systems: general mathematical aspects
Climate
Company systems management
Computation
Computing in Science
Elementary particle interactions
Exact sciences and technology
Far fields
Function theory, analysis
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
General relativity and gravitation
Gravitational fields
Gravitational interaction
Information management
Innovations
MANY-BODY PROBLEM
Mathematical functions
MATHEMATICAL LOGIC
Mathematical methods in physics
Mathematics
Multipole expansion
Multipoles
N-body problem (Celestial mechanics)
Number Concepts
Numerical approximation and analysis
Particle interactions
Physics
Science
Scientific Concepts
Sequences, series, and summability
Simulation
Classical mechanics
Wave equations
Gravitational fields
Diffusion equation
Fast algorithm
Summation
Calculation methods
ISSN:0036-8075, 1095-9203
Online Access:Get full text
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Description
Summary:Some of the recently developed fast summation methods that have arisen in scientific computing are described. These methods require an amount of work proportional to N or N log N to evaluate all pairwise interactions in an ensemble of N particles. Traditional methods, by contrast, require an amount of work proportional to N$^2$. As a result, large-scale simulations can be carried out using only modest computer resources. In combination with supercomputers, it is possible to address questions that were previously out of reach. Problems from diffusion, gravitation, and wave propagation are considered.
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ISSN:0036-8075
1095-9203
DOI:10.1126/science.265.5174.909