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
- Affiliation: College of Arts and Sciences, Department of Mathematics
- 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.
- Date of publication
- August 2010
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- Rights statement
- In Copyright
- "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics."
- Huang, Jingfang
- Place of publication
- Chapel Hill, NC
- Open access
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|Integral equation based fast algorithms and graph-theoretic methods for large-scale simulations||2019-04-10||Public||