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Fast algorithms for classical physics. (English) Zbl 1226.65116
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. Here we consider problems from diffusion, gravitation, and wave propagation.

MSC:
65Y20 Complexity and performance of numerical algorithms
70-08 Computational methods for problems pertaining to mechanics of particles and systems
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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