@Article{CiCP-24-1101,
author = {Xiang Ma and Chunxiong Zheng},
title = {Fast Finite Element Method for the Three-Dimensional Poisson Equation in Infinite Domains},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {4},
pages = {1101--1120},
abstract = {<p style="text-align: justify;">We aim at a fast finite element method for the Poisson equation in three-dimensional
infinite domains. Both the exterior and strip-tail problems are considered.
By introducing a suitable artificial boundary and imposing the exact boundary condition
of Dirichlet-to-Neumann (DtN) type, we reduce the original infinite domain problem
into a truncated finite domain problem. The point is how to efficiently implement
this exact artificial boundary condition. The traditional modal expansion method is
hard to apply for the strip-tail problem with a general cross section. We develop a fast
algorithm based on the Padé approximation for the square root function involved in
the exact artificial boundary condition. The most remarkable advantage of our method
is that it is unnecessary to compute the full eigen system associated with the Laplace-Beltrami
operator on the artificial boundary. Besides, compared with the modal expansion
method, the computational cost of the DtN mapping is significantly reduced.
We perform a complete numerical analysis on the fast algorithm. Some numerical examples
are presented to demonstrate the effectiveness of the proposed method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2018.hh80.04},
url = {http://global-sci.org/intro/article_detail/cicp/12320.html}
}