Solving Elliptic Problems with Singular Sources using Singularity Splitting Deep Ritz Method. (arXiv:2209.02931v1 [math.NA])

In this work, we develop an efficient solver based on deep neural networks
for the Poisson equation with variable coefficients and singular sources
expressed by the Dirac delta function $\delta(\mathbf{x})$. This class of
problems covers general point sources, line sources and point-line
combinations, and has a broad range of practical applications. The proposed
approach is based on decomposing the true solution into a singular part that is
known analytically using the fundamental solution of the Laplace equation and a
regular …

arxiv math singularity