Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11011124 | Applied Mathematics Letters | 2019 | 9 Pages |
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.
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Mads Mølholm Hejlesen, Grégoire Winckelmans, Jens Honoré Walther,