Adding NonLinearDiffusion operator to derivate_operator.jl returning discretized function #327
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The test issue should be fixed SciML/SciMLBase.jl#15. This needs tests. |
examples/Fast_Diffusion.jl
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| bc = DirichletBC(exp(-t),(1.0 + exp(2*t))^(-0.5)) | ||
| l = bc*u | ||
| k = l.^(-2) # Diffusion Coefficient | ||
| NonLinearDiffusion(n,m,approx_ord,k,l,h,nknots) |
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Can it be represented as an operator?
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| end | ||
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| discretization += (CenteredDifference(first_differential_order + second_differential_order,approx_order,dx,nknots)*q).*p[2:(nknots + 1)]; | ||
| return discretization |
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There only seems to be an out of place operation? It would be good to have a mul! definition and then an allocating version that uses the non-allocating one. Refer to https://www.youtube.com/watch?v=M2i7sSRcSIw or https://mitmath.github.io/18337/lecture2/optimizing on non-allocating operators.
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https://diffeq.sciml.ai/stable/features/diffeq_operator/ defines our operator format which is an extension of the simple examples posted above. I think this is all mathematically correct but needs a little bit of work to match the standard operator API. |
| @@ -26,6 +26,29 @@ struct DerivativeOperator{T<:Real,N,Wind,T2,S1,S2<:SArray,T3,F} <: AbstractDeriv | |||
| coeff_func :: F | |||
| end | |||
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| struct NonLinearDiffusion! end | |||
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if it's a function then it shouldn't be capitalized like a struct, or need the struct at all.
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Just the caps issue and the lack of an out of place dispatch to fix. |
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Great thanks! |
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Could you follow up with adding this to the documentation? |
Modifications should be done in derivate_operators.md or a new file needs to be created? |
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I think a nonlinear derivative operators page would be good |
This addition tries addressing #276.
It will return the required discretization as output given k (the diffusion coefficent) and u (the desired function) along with inner and outer differential orders.