  We present Fourier-space based methods to calculate the electronic structure
of wurtzite quantum dot systems with continuous alloy profiles. We incorporate
spatially varying elastic and dielectric constants in strain and piezoelectric
potential calculations. A method to incorporate smooth alloy profiles in all
aspects of the calculations is presented. We demonstrate our methodology for
the case of a 1D InGaN quantum dot array and show the importance of including
these spatially varying parameters in the modeling of devices. We demonstrate
that convergence of the lowest bound state energies is to good approximation
determined by the largest wave vector used in constructing the states. We also
present a novel approach of coupling strain into the
$\mathbf{k}\cdot\mathbf{p}$ Hamiltonian, greatly reducing the computational
cost of generating the Hamiltonian.
