Error when dependent variables depend on different independent spatial variables

[valentinsulzer]

@parameters t x y
@variables u(..) v(..)
Dt = Differential(t)
Dxx = Differential(x)^2
Dyy = Differential(y)^2
eqs  = [Dt(u(t,x)) ~ Dxx(u(t,x)), 
        Dt(v(t,y)) ~ Dxx(v(t,y))]
bcs = [u(0,x) ~ - x * (x-1) * sin(x),
       v(0,y) ~ - y * (y-1) * sin(y),
       u(t,0) ~ 0.0, u(t,1) ~ 0.0,
       v(t,0) ~ 0.0, v(t,1) ~ 0.0]

domains = [t ∈ IntervalDomain(0.0,1.0),
           x ∈ IntervalDomain(0.0,1.0),
           y ∈ IntervalDomain(0.0,1.0)]

pdesys = PDESystem(eqs,bcs,domains,[t,x,y],[u(t,x),v(t,y)])
discretization = MOLFiniteDifference([x=>0.1,y=>0.1],t;grid_align=edge_align)
prob = discretize(pdesys,discretization)

error:

ERROR: ArgumentError: invalid index: nothing of type Nothing
Stacktrace:

[1] to_index(i::Nothing)

@ Base ./indices.jl:300

[2] to_index(A::Vector{Matrix{Num}}, i::Nothing)

@ Base ./indices.jl:277

[3] to_indices

@ ./indices.jl:333 [inlined]

[4] to_indices

@ ./indices.jl:325 [inlined]

[5] getindex(A::Vector{Matrix{Num}}, I::Nothing)

@ Base ./abstractarray.jl:1170

[6] symbolic_discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{Vector{Pair{Num, Float64}}, Num})

@ DiffEqOperators ~/Documents/SciML/DiffEqOperators.jl/src/MOLFiniteDifference/MOL_discretization.jl:149

[7] discretize(pdesys::PDESystem, discretization::MOLFiniteDifference{Vector{Pair{Num, Float64}}, Num})

@ DiffEqOperators ~/Documents/SciML/DiffEqOperators.jl/src/MOLFiniteDifference/MOL_discretization.jl:305

[8] top-level scope

@ ~/Documents/SciML/DiffEqOperators.jl/test/MOL/MOLtest.jl:358

[valentinsulzer]

Code assumes x and y are in a ProductDomain even though they aren't here. Perhaps we should not assume that when two IntervalDomain are given, and ask for explicit ProductDomain in 2D?

[valentinsulzer]

I am making some progress with this by discretizing each equation independently based on the independent variables in the equation (different grid, etc for each equation). Hopefully that will also then address #387