An Automatic Learning System to Derive Multipole and Local Expansions for the Fast Multipole Method

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  author =       "Seyed Naser Razavi and Nicolas Gaud and 
                 Abderrafiaa Koukam and Nasser Mozayani",
  title =        "An Automatic Learning System to Derive Multipole and
                 Local Expansions for the Fast Multipole Method",
  booktitle =    "Third International Conference on Swarm Intelligence
  year =         "2012",
  editor =       "Ying Tan and Yuhui Shi and Zhen Ji",
  volume =       "7332",
  series =       "Lecture Notes in Computer Science",
  pages =        "1--10",
  address =      "Shenzhen, China",
  month =        jun,
  publisher =    "Springer",
  keywords =     "genetic algorithms, genetic programming, agent-based
                 simulation, complex systems, fast Multipole Method",
  isbn13 =       "978-3-642-31019-5",
  DOI =          "doi:10.1007/978-3-642-31020-1_1",
  size =         "10 pages",
  abstract =     "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 by 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.",
  notes =        "See \cite{Razavi:2012:AIc} Also known as

Genetic Programming entries for Seyed Naser Razavi Nicolas Gaud Abderrafiaa Koukam Nasser Mozayani