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
Journal of Parallel and Distributed Computing
The evolution of size and shape
Advances in genetic programming
Size Fair and Homologous Tree Crossovers for Tree Genetic Programming
Genetic Programming and Evolvable Machines
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
Size Control Via Size Fair Genetic Operators In The PushGP Genetic Programming System
GECCO '02 Proceedings of the Genetic and Evolutionary Computation Conference
Introduction to Evolutionary Computing
Introduction to Evolutionary Computing
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
A New Parallel Kernel-Independent Fast Multipole Method
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
Short note: A kernel independent fast multipole algorithm for radial basis functions
Journal of Computational Physics
Balancing accuracy and parsimony in genetic programming
Evolutionary Computation
Evolutionary induction of sparse neural trees
Evolutionary Computation
Effects of code growth and parsimony pressure on populations in genetic programming
Evolutionary Computation
An Accelerated Kernel-Independent Fast Multipole Method in One Dimension
SIAM Journal on Scientific Computing
GECCO '96 Proceedings of the 1st annual conference on Genetic and evolutionary computation
A simple but theoretically-motivated method to control bloat in genetic programming
EuroGP'03 Proceedings of the 6th European conference on Genetic programming
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
Hi-index | 0.00 |
This paper introduces an automatic learning algorithm 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(Nlog N) operations, while direct multiplication requires O(N2) operations. Soon after its invention, the FMM algorithm was applied successfully in many scientific fields such as simulation of physical systems Electromagnetic, Stellar clusters, Turbulence, Computer Graphics and Vision Light scattering and Molecular dynamics. However, FMM relies on the analytical expansions of the underlying kernel function defining the interactions between particles, which are not obvious to derive. This is a major factor that severely limits the application of the FMM to many interesting problems. Thus, the proposed automatic technique in this article can be regarded as a very useful tool helping practitioners to apply FMM to their own problems. Here, we have implemented a prototype system and tested it on various types of kernels. The preliminary results are very promising, and so we hope that the proposed method can be applied successfully to other problems in different application domains.