thanks a lot
for your responading
I hope you are able to solve it in time, best of luck!
Julia has finite element libraries too, see Gridap.jl. I don’t know how well it supports complex valued problems.
the integral that appears from the model comes from the PDE solution form by the finite element method, where it is necessary to use a weighted residuals method, which basically equates the PDE residual to the value of a test function \phi, and integral For the \Omega solution domain, which is known as the strong form of the equation, then you can apply Green’s theorem of vector calculus to reduce the order of derivatives of the strong form, thus deriving the weak form of the problem, which is widely used to finite element solution.
In this case, to solve a PDE using the elements method, it is very important to be clear about the space where this problem will be solved, so I believe you could start by defining this point and also the governing equations of the problem in question to define the weak form of the problem .
with that in hand you can use Gridap.jl to create a finite element model from a mesh that defines your domain of your solution and solve the weak form of the problem directly.
res(E,ϕ) = ∫((r/μ)*∇(E)*∇(ϕ)+(1/(μ*r))*E*ϕ+(r/μ)*(∇(E)*∇(ϕ)))*dΩ
however, you must define some other objects to have the complete solution, read in the tutorials in the package (they are quite complete).
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but how did you pass from the first form to this form