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

详细信息   

• 作者：Zhang ; Bo.
• 学历：Doctor
• 年：2010
• 导师：Huang, Jingfang,eadvisorMinion, Michael L.ecommittee memberMiller, Lauraecommittee memberPitsianis, Nikos P.ecommittee memberSun, Xiaobaiecommittee member
• 毕业院校：The University of North Carolina
• Department：Mathematics
• ISBN：9781124171449
• CBH：3418642
• Country：USA
• 语种：English
• FileSize：2294928
• Pages：112

文摘

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 FMM onto modern parallel computer architectures. We have particularly established 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.