We present a new kind of high-order reconstruction operator of polynomial type, which is
used in combination with a high-order finite volume scheme for solving nonconservative hyperbolic
systems. The implementation of the scheme is carried out on Graphics Processing Units (GPUs), thus
achieving a substantial improvement of the speedup with respect to normal CPUs. As an application,
the two-dimensional shallow water equations with geometrical source term due to the bottom slope is
considered.
