We consider 1D scattering problems related to quantum transport in diodes. We discuss the efficient numerical integration of ODEs like epsilon^2u"+a(x)u=0 for 0<epsilon<<1 on coarse grids, but still yielding accurate solutions; including oscillatory (for given a(x)>0) and evanescent regimes (for a(x)<0), partly including turning points. In the oscillatory case we use a marching method that is based on an analytic WKB-preprocessing of the equation. Then we shall discuss two approaches to couple the oscillatory regime to smooth regimes across turning points and close to them: In the former (evanescent) case we use a FEM with WKB-ansatz functions; in the latter case an automated switching to a Runge-Kutta method with adaptive step size controller.
Co-authors: Claudia Negulescu; Kirian Döpfner, Jannis Körner; Christian Klein, Bernhard Ujvari