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

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

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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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