How Dirichlet boundary conditions are imposed about diffeqoperators.jl HOT 5 CLOSED

From the Gitter:

I don't think it's a big task
and I think it's just the Dirichlet BCs
https://github.com/JuliaDiffEq/DiffEqOperators.jl/blob/master/src/derivative_operators/boundary_operators.jl#L305
https://github.com/JuliaDiffEq/DiffEqOperators.jl/blob/master/src/derivative_operators/boundary_operators.jl#L353
you'd just have to modify these two in order to have them take into account the fact that the last point should just have the BC imposed.
https://github.com/JuliaDiffEq/DiffEqOperators.jl/blob/master/src/derivative_operators/boundary_operators.jl#L181
this is what ends up callin them
so from that you can look at the whole logic pretty quick

from diffeqoperators.jl.

But Dirichlet is a little weird, with that implementation what should we do if the BCs don't match what you put on the ends of the vector?

from diffeqoperators.jl.

From Gitter:

the left BC for Dirichlet is here: https://github.com/JuliaDiffEq/DiffEqOperators.jl/blob/master/src/derivative_operators/boundary_operators.jl#L53
for i in 1 : A.boundary_point_count[1]
for each point where the boundary would go over the edge
(so for 2nd order that's just the last point)
it calls dirichlet_1!(x_temp, x, A.stencil_coefs, mid, i)
https://github.com/JuliaDiffEq/DiffEqOperators.jl/blob/master/src/derivative_operators/boundary_operators.jl#L353
so that's the function to find out
x_temp[i] is the output
coeffs is the stencil [-1 2 1]
x is the initial vector
i is the current location, so at the edge it's 1
need to find out what mid is

function dirichlet_1!(x_temp::AbstractVector{T}, x::AbstractVector{T}, coeffs::SVector, mid::Int, i::Int) where T<:Real
    stencil_length = length(coeffs)
    N = length(x)
    #=
        Here we are taking the weighted sum of a window of the input vector to calculate the derivative
        at the middle point. Once the stencil goes out of the edge, we assume that it's has a constant
        value outside for all points.
    =#
    xtempi = zero(T)
    @inbounds for idx in 1:stencil_length
        xtempi += coeffs[idx] * x[limit(i - (mid-idx), N)]
    end
    x_temp[i] = xtempi
end

so something about x[limit(i - (mid-idx), N)] is making the x's all do something
but whatever it is, that's a weird line of code and should be changed.
it should have the user's BC there
and basically if i-idx<1, it's a point over the boundary and should use the BC value.

so my guess is it needs to be something like

     @inbounds for idx in 1:stencil_length
        loc = i - idx
        if loc < 0
           xtempi += coeffs[idx]*bc_right
        else
           xtempi += coeffs[idx] * x[i-idx]
         end
    end

then the function needs to get passed bc_right
err, left
mb
so the function call dirichlet_1!(x_temp, x, A.stencil_coefs, mid, i)
needs to change
the type is defined here: https://github.com/JuliaDiffEq/DiffEqOperators.jl/blob/master/src/derivative_operators/derivative_operator.jl#L57
so you can see that A.boundary_condition is where that tuple is stored
so it should be passed
dirichlet_1!(x_temp, x, A.stencil_coefs, mid, i,A.boundary_condition[1])
the function should be expanded
and it should replace the loop to put in the BC like that

from diffeqoperators.jl.

Example problem: https://github.com/francispoulin/DiffEqOperators.jl/blob/master/docs/DiffusionEqTutorial.ipynb

from diffeqoperators.jl.

Here's a review of the BCs:

• Dirichlet0 assumes the boundary points are the first points off the boundary
• Dirichet assumes the last points are the boundary points and fixes them
• Neumann0 assumes the boundary points are the last points on the vector
• Neumann assumes the boundary points are the last points on the vector
• Periodic assumes the first point is a BC and the last point is not (since they would be the same.

We should make these all CenterPeriodic, etc., and then have Periodic be the case where the boundary is included in the ends (and do error checks).

from diffeqoperators.jl.