I encountered a problem with the LDLt factorization in the finite-difference solution of a 2D Poisson equation: u_xx + u_yy = -1 on 0 < x < 1 and 0 < y < 1 with u = 0 Dirichlet boundary conditions. The factorization works fine for small problems (e.g. nx = ny = 64), but I get told my matrix has one or more zero pivots for bigger problems (e.g. nx = ny = 128). If I instead use an LU factorization, the solution works fine also for bigger problems. Any idea what could be going on?

Here’s the code:

```
# grid points
nx = 128
ny = 128
# grid spacing
dx = 1/(nx+1)
dy = 1/(ny+1)
# setup matrix
idx(j,i) = (i-1)*ny+j
B = spzeros(nx*ny,nx*ny)
for i = 1:nx
for j = 1:ny
# x-derivative
if i < nx
B[idx(j,i),idx(j,i+1)] += 1/dx^2
end
B[idx(j,i),idx(j,i)] -= 1/dx^2
B[idx(j,i),idx(j,i)] -= 1/dx^2
if i > 1
B[idx(j,i),idx(j,i-1)] += 1/dx^2
end
# y-derivative
if j < ny
B[idx(j,i),idx(j+1,i)] += 1/dy^2
end
B[idx(j,i),idx(j,i)] -= 1/dy^2
B[idx(j,i),idx(j,i)] -= 1/dy^2
if j > 1
B[idx(j,i),idx(j-1,i)] += 1/dy^2
end
end
end
# solve
u = -reshape(B\ones(ny*nx), (ny,nx))
```

And here is the error I’m getting:

```
ERROR: LoadError: ArgumentError: matrix has one or more zero pivots
in #ldltfact!#10(::Float64, ::Function, ::Base.SparseArrays.CHOLMOD.Factor{Float64}, ::Base.SparseArrays.CHOLMOD.Sparse{Float64}) at ./sparse/cholmod.jl:1350
in (::Base.LinAlg.#kw##ldltfact!)(::Array{Any,1}, ::Base.LinAlg.#ldltfact!, ::Base.SparseArrays.CHOLMOD.Factor{Float64}, ::Base.SparseArrays.CHOLMOD.Sparse{Float64}) at ./<missing>:0
in #ldltfact#12(::Float64, ::Array{Int64,1}, ::Function, ::Base.SparseArrays.CHOLMOD.Sparse{Float64}) at ./sparse/cholmod.jl:1386
in #ldltfact#13(::Array{Any,1}, ::Function, ::Hermitian{Float64,SparseMatrixCSC{Float64,Int64}}) at ./sparse/cholmod.jl:1426
in \(::SparseMatrixCSC{Float64,Int64}, ::Array{Float64,1}) at ./sparse/linalg.jl:871
in include_from_node1(::String) at ./loading.jl:488
```