5 ms·
> In each time step, the solver performs an "advection" update followed by a "pressure projection" step. This "pressure projection" step involves solving a "Poi
by santaclaus 10y ago
> In each time step, the solver performs an "advection" update followed by a "pressure projection" step. This "pressure projection" step involves solving a "Poisson equation," which is computationally intensive and usually requires an iterative solver. Instead of directly solving the Poisson equation, they train a ConvNet regression model to infer these "pressure projections."
Yea, I mean, for applications like solving a Poisson equation, it seems like it would be cheaper to just solve the damn linear system. The system is going to be fairly sparse with a nice, well understood distribution of non-zeros and one should be able to make the linear solve fly. I'm curious where the tipping point is, however, between just solving the linear system and pushing everything through a CNN.
- gnipgnip 10y agoMoreover Poisson equation, being a Linear PDE, is essentially solved using convolutions. The crux of the problem seems to be in the handling of boundaries - once FEM-ized the nice grid like structure gets replaced by an irregular graph (with similar topological dimension). Can someone please shed some light on this ?