@Article{CiCP-18-808,
author = {},
title = {PVFMM: A Parallel Kernel Independent FMM for Particle and Volume Potentials},
journal = {Communications in Computational Physics},
year = {2018},
volume = {18},
number = {3},
pages = {808--830},
abstract = {<p style="text-align: justify;">We describe our implementation of a parallel fast multipole method for evaluating
potentials for discrete and continuous source distributions. The first requires
summation over the source points and the second requiring integration over a continuous
source density. Both problems require&nbsp;$\mathcal{O}$($N^2$) complexity when computed directly;
however, can be accelerated to <span style="text-align: justify;">$\mathcal{O}$</span>($N$) time using FMM. In our PVFMM software
library, we use kernel independent FMM and this allows us to compute potentials for
a wide range of elliptic kernels. Our method is high order, adaptive and scalable. In
this paper, we discuss several algorithmic improvements and performance optimizations
including cache locality, vectorization, shared memory parallelism and use of
coprocessors. Our distributed memory implementation uses space-filling curve for
partitioning data and a hypercube communication scheme. We present convergence
results for Laplace, Stokes and Helmholtz (low wavenumber) kernels for both particle
and volume FMM. We measure efficiency of our method in terms of CPU cycles per
unknown for different accuracies and different kernels. We also demonstrate scalability
of our implementation up to several thousand processor cores on the Stampede
platform at the Texas Advanced Computing Center.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.020215.150515sw},
url = {http://global-sci.org/intro/article_detail/cicp/11049.html}
}