Integral-equation-based fast algorithms and graph-theoretic methods for large-scale simulations Public Deposited

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  • Integral equation based fast algorithms and graph-theoretic methods for large-scale simulations
Last Modified
  • March 21, 2019
Creator
  • Zhang, Bo
    • Affiliation: College of Arts and Sciences, Department of Mathematics
Abstract
  • In this dissertation, we extend Greengard and Rokhlin's seminal work on fast multipole method (FMM) in three aspects. First, we have implemented and released open-source new-version of FMM solvers for the Laplace, Yukawa, and low-frequency Helmholtz equations to further broaden and facilitate the applications of FMM in different scientific fields. Secondly, we propose a graph-theoretic parallelization scheme to map the FMM onto modern parallel computer architectures. We have particularly established the critical path analysis, exponential node growth condition for concurrency-breadth, and a spatio-temporal graph partition strategy. Thirdly, we introduce a new kernel-independent FMM based on Fourier series expansions and discuss how information can be collected, compressed, and transmitted through the tree structure for a wide class of kernels.
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  • In Copyright
Note
  • "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics."
Advisor
  • Huang, Jingfang
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Place of publication
  • Chapel Hill, NC
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  • Open access
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