Does anyone have an idea or thoughts on this issue?

```
from ngsolve import *
mesh = Mesh(unit_square.GenerateMesh(maxh=1))
for b in [False, True]:
fes = H1(mesh, order=0, complex=b)
u, v = fes.TnT()
gfu = GridFunction(fes)
res = gfu.vec.CreateVector()
a = BilinearForm(fes)
a += 1 * v * dx
a.Apply(gfu.vec, res)
print(sum(res))
```

It would be crucial for a Newton-Raphson scheme with a complex function space, see [1].

Best,

Valentin

Actually, there are not so many complex-valued problems which can be solved by Newtonâ€™s method - complex differentiable is a very strong condition.

Thus, the Apply for complex symbolic forms is not overloaded, and falls back to the base class. The base class calls CalcElementMatrix, and then matrix-vector multiplication (assuming to have a bilinear form in the precise definition). Since no trial-functions are found, it gives the 0-matrix.

Recommendation: Use a LinearForm for the residual, and setup an (approximate) linearization (with a BilinearForm) by hand.

Joachim