@Article{CiCP-20-1381,
author = {},
title = {A Novel Efficient Numerical Solution of Poisson's Equation for Arbitrary Shapes in Two Dimensions},
journal = {Communications in Computational Physics},
year = {2018},
volume = {20},
number = {5},
pages = {1381--1404},
abstract = {<p style="text-align: justify;">Even though there are various fast methods and preconditioning techniques
available for the simulation of Poisson problems, little work has been done for solving
Poisson&#39;s equation by using the Helmholtz decomposition scheme. To bridge this
issue, we propose a novel efficient algorithm to solve Poisson&#39;s equation in irregular
two dimensional domains for electrostatics through a quasi-Helmholtz decomposition
technique&nbsp;–&nbsp;the loop-tree basis decomposition. It can handle Dirichlet, Neumann or
mixed boundary problems in which the filling media can be homogeneous or inhomogeneous.
A novel point of this method is to first find the electric flux efficiently by
applying the loop-tree basis functions. Subsequently, the potential is obtained by finding
the inverse of the gradient operator. Furthermore, treatments for both Dirichlet
and Neumann boundary conditions are addressed. Finally, the validation and efficiency are illustrated by several numerical examples. Through these simulations, it
is observed that the computational complexity of our proposed method almost scales
as $\mathcal{O}$$(N)$, where $N$ is the triangle patch number of meshes. Consequently, this new
algorithm is a feasible fast Poisson solver.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.230813.291113a},
url = {http://global-sci.org/intro/article_detail/cicp/11194.html}
}