concretization of High Dimension PDE

[Song921012]

Appreciate your excellent works in SciML. I am struggling with a problem and really need help. Please !!! $$\mathcal{L} u = u_{xx} +u_{yy}, \quad \text{BCs:} \quad u(x+1,y)=u(x,y), u(x,y+1)= u(x,y).$$ I need the concretization of the operator with bcs and my codes are as follows:

using DiffEqOperators
const bc_p = PeriodicBC(Float64)
N = 4
dx = 0.1
Dxx = CenteredDifference(2,2,dx,N)
Dyy = CenteredDifference{2}(2,2,dx,N)
L0 = Dxx+Dyy
bc_px = MultiDimBC{1}(Dirichlet0BC(Float64), (4,4))
bc_py = MultiDimBC{2}(Dirichlet0BC(Float64), (4,4))
bc_co = compose(bc_px,bc_py)
L1 = L0*bc_co
Array(L1)
Array(L1,4)
Array(L1,(4,4))
using BlockBandedMatrices
BandedBlockBandedMatrix(L1)
BandedBlockBandedMatrix(L1,4)
BandedBlockBandedMatrix(L1,(4,4))

But neither of them works. It should be a $16 \times 16$ matrix. Someone can help me. Please

[eschnett]

This is probably the same as https://github.com/SciML/DiffEqOperators.jl/issues/491 .

[eschnett]

My comment above was wrong.

The matrices Dxx,Dyy, and L0 have the size (4, 6). They are not square because they expect two ghost points at the boundaries. You should expect at 16 x 36 matrix as result.