Different Boundary Conditions under Spectral DEC

To validate the code and ensure that it does what is expected of it, we start off with a simple example of a linear wave travelling in one direction.

The checkerboard that the surface is shaded with corresponds to the actual cellular complex.

Periodic

Dirichlet

Neumann

Having validated the code with a simple example, now we can consider a more complicated wave form. In the examples, below we will start off with a Gaussian bump in the middle of the domain and see how it spreads out under different boundary conditions.