Parallel methods for weakly singular Volterra integral equations on GPUs

The purpose of this paper is to employ graphics processing units for the numerical solution of large systems of weakly singular Volterra Integral Equations (VIEs), by means of Waveform Relaxation (WR) methods. A CUDA solver based on different kinds of WR iterations is developed. Numerical results on large systems of VIEs arising from the semi-discretization in space of fractional diffusion-wave equations are presented, showing the obtained speed-up.