  We present a numerical approach to efficiently calculate spin-wave
dispersions and spatial mode profiles in magnetic waveguides of arbitrarily
shaped cross section with any non-collinear equilibrium magnetization which is
translationally invariant along the waveguide. Our method is based on the
propagating-wave dynamic-matrix approach by Henry et al. and extends it to
arbitrary cross sections using a finite-element method. We solve the linearized
equation of motion of the magnetization only in a single waveguide cross
section which drastically reduces computational effort compared to common
three-dimensional micromagnetic simulations. In order to numerically obtain the
dipolar potential of individual spin-wave modes, we present a plane-wave
version of the hybrid finite-element/boundary-element method by Frekdin and
Koehler which, for the first time, we extend to a modified version of the
Poisson equation. Our method is applied to several important examples of
magnonic waveguides including systems with surface curvature, such as magnetic
nanotubes, where the curvature leads to an asymmetric spin-wave dispersion. In
all cases, the validity of our approach is confirmed by other methods. Our
method is of particular interest for the study of curvature-induced or
magnetochiral effects on spin-wave transport but also serves as an efficient
tool to investigate standard magnonic problems.
