Wrong Helmholtz problem formulation #774
Description
Describe the bug
The HelmholtzProblem formulation has several issues.
First, the analytical solution does not satisfy the imposed boundary conditions for arbitrary values of alpha. The boundary values vanish only when alpha is an integer; for non-integer values the Dirichlet condition on the boundary is violated.
Second, the roles of alpha and k are not clearly separated when moving from the problem definition to the equation. The forcing term mixes these parameters in a way that obscures their respective meaning.
Finally, the formulation does not support different frequency parameters along the two spatial dimensions. The implementation should allow independent parameters (e.g., alpha_x and alpha_y) rather than a single shared alpha.