Non-uniform grid spacing? about diffeqoperators.jl HOT 6 CLOSED

Hi,
Yes it does support non-uniform spacing and we might support in the future. Problems come when we try to create a transpose operator. The whole function (stencils) changes and we don't know how to implement it without a matrix.

from diffeqoperators.jl.

It's fine to have no transpose in that case. non-uniform with the BC handling is super useful by itself, and many iterative solvers don't need the transpose.

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Upon further thought, we can get the transposed stencils very easily actually (except for :periodic maybe)
We can generate the 'essential' full matrix linear operator ie. one which is much smaller is size (O((derivative_order+approximation_order)^2)) and since it contains the essential information about all the coefficients, we can take it's transpose and get the transposed stencils. eg.

julia> A = LinearOperator{Float64}(2,4,1.0,100,:D0,:D0);
julia> full(A,5)
5×5 Array{Float64,2}:
 -2.5         1.33333    -0.0833333   0.0         0.0      
  1.33333    -2.5         1.33333    -0.0833333   0.0      
 -0.0833333   1.33333    -2.5         1.33333    -0.0833333
  0.0        -0.0833333   1.33333    -2.5         1.33333  
  0.0         0.0        -0.0833333   1.33333    -2.5      

full(A,5)', in this case the same matrix, will have the transposed stencils which we can store for fast calculation of transposes.
Using A' will just meaning changing a flag variable in the LinearOperator to start using the transposed stencils created at initialization.

from diffeqoperators.jl.

Don't worry about this until way way later. Non-uniform spacing with an iterative method that requires a transpose is a very niche topic.

from diffeqoperators.jl.

For the moment, anyone who needs the transpose can just use the full matrix operator, so the functionality is still there, just not optimal. With that caveat, supporting non-uniform spacing is actually very straightforward.

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work going on here #49

from diffeqoperators.jl.