Citation:
M. M. Hejlesen, G. Winckelmans, and J. H. Walther, “Non-singular green’s functions for the unbounded poisson equation in one, two and three dimensions,” Applied Mathematics Letters, vol. 89, pp. 28–34, 2019.
Abstract:
In this paper, we derive the non-singular Green’s functions for the unbounded Poisson equation in one, two and three dimensions using a spectral cut-off function approach to impose a minimum length scale in the homogeneous solution. The resulting non-singular Green’s functions are relevant to applications which are restricted to a minimum resolved length scale (e.g. a mesh size h) and thus cannot handle the singular Green’s function of the continuous Poisson equation. We furthermore derive the gradient vector of the non-singular Green’s function, as this is useful in applications where the Poisson equation represents potential functions of a vector field.
Full Text
DOI
BibTeX
@article{hejlesen2019a,
author = {Mads M{\o}lholm Hejlesen and Gr{\'{e}}goire Winckelmans and Jens Honor{\'{e}} Walther},
doi = {10.1016/j.aml.2018.09.012},
journal = {{Appl. Math.}},
month = {mar},
pages = {28--34},
publisher = {Elsevier {BV}},
title = {Non-singular Green's functions for the unbounded Poisson equation in one, two and three dimensions},
url = {https://cse-lab.seas.harvard.edu/files/cse-lab/files/hejlesen2019a.pdf},
volume = {89},
year = {2019}
}