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 ) 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.
Original language | English |
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Journal | Applied Mathematics Letters |
Volume | 89 |
Pages (from-to) | 28-34 |
ISSN | 0893-9659 |
DOIs | |
Publication status | Published - 2019 |
Keywords
- Partial differential equations
- Poisson equation
- Green’s function
- Unbounded domain