I am trying to solve nonlinear problems using the script below.
I am starting with one-dimensioal problem.
func = lambda x: x**2
a = BilinearForm(fes, symmetric=True)
a += SymbolicBFI(v * func(u))
a += - v * x * dx
c = Preconditioner(a, type="bddc")
res = gfu.vec.CreateVector()
du = gfu.vec.CreateVector()
for niter in range(10):
a.Apply(gfu.vec, res)
a.AssembleLinearization(gfu.vec)
solvers.CG(sol=du.data, rhs=res.data, mat=a.mat, pre=c.mat, printrates='', tol=1e-10, maxsteps=10000)
gfu.vec.data -= du
It seems working. I obtained the solusion as u = \sqrt{x}.
What are the functions that can be used in SymboliBFIs?
I want to use an interploated function from the measured data.
I tried with BSpline CoefficientFunction , but could not find a way to work with it.