A fast algorithm for particle simulations
Journal of Computational Physics
A rapid hierarchical radiosity algorithm
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Guest Editors' Introduction: The Top 10 Algorithms
Computing in Science and Engineering
Using Schema Theory To Explore Interactions Of Multiple Operators
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Introduction to Evolutionary Computing
Introduction to Evolutionary Computing
Short note: A kernel independent fast multipole algorithm for radial basis functions
Journal of Computational Physics
An Accelerated Kernel-Independent Fast Multipole Method in One Dimension
SIAM Journal on Scientific Computing
A Field Guide to Genetic Programming
A Field Guide to Genetic Programming
A Fourier-series-based kernel-independent fast multipole method
Journal of Computational Physics
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This paper introduces an automatic learning method based on genetic programming to derive local and multipole expansions required by the Fast Multipole Method (FMM). FMM is a well-known approximation method widely used in the field of computational physics, which was first developed to approximately evaluate the product of particular N ×N dense matrices with a vector in O(N log N) operations. Later, it was applied successfully in many scientific fields such as simulation of physical systems, Computer Graphics and Molecular dynamics. However, FMM relies on the analytical expansions of the underlying kernel function defining the interactions between particles, which are not always obvious to derive. This is a major factor limiting the application of the FMM to many interesting problems. Thus, the proposed method here can be regarded as a useful tool helping practitioners to apply FMM to their own problems such as agent-based simulation of large complex systems. The preliminary results of the implemented system are very promising, and so we hope that the proposed method can be applied to other problems in different application domains.