BC when stencil reaches out of grid about diffeqoperators.jl HOT 7 CLOSED

Yeah this is slightly decoupled from the BC overhaul. What should be happening is the uncentered discretization should be used. For example, a 4th order discretization of the 2nd derivative one away from the boundary should use the stencil that is 2 to the left and 1 to the right. So basically you need to adapt which derivative you're using near the boundary to make sure it only ever goes to the boundary point. I don't believe we are properly doing all of this though.

from diffeqoperators.jl.

Okay, yes. I didn't really read into the BC overhaul. Do you think if I put some work into this now it is easily adaptable to the new way of putting together the linear operators?

from diffeqoperators.jl.

Yes, getting this done would be very helpful. Basically what we to start BC overhaul is to just get very solid the "BC-less" operators, i.e. an operator whose stencil is correct (i.e. does this de-centering).

from diffeqoperators.jl.

As I understand, the stencils of the Dirichlet boundary condition should essentially be equal to those of the None condition? Except for the boundary column, which can be set to 0.

from diffeqoperators.jl.

No, the stencils and the BCs should be kept separate.

from diffeqoperators.jl.

I see, you mean the stencils influenced by the boundary are computed and stored anyways and the BC is applied ontop.

from diffeqoperators.jl.

The stencil is always a mapping from the full domain to the interior. The mapping from the interior to the full domain is what holds the BCs.

from diffeqoperators.jl.