MADNESS  0.10.1
Solves heat equation using the Green's function

The source is here.

Points of interest
  • use of a functor to compute the solution at an arbitrary future time
  • convolution with the Green's function
Background

Solves the 3D time-dependent heat equation

\[ \frac{\partial u}{\partial t} = c \nabla^2 u(r,t) \]

by direct convolution with the Green's function,

\[ \frac{1}{\sqrt{4 \pi c t}} \exp \frac{-x^2}{4 c t} \]