GPU accelerated solution of time fractional diffusion systems

Fractional diffusion systems model a number of important applications, as for example water diffusion magnetic resonance imaging, since the biological tissues are heterogeneous and the signal exhibits a heavy tail which is characteristic of anomalous diffusion [3]. In this talk, we consider a time-fractional diffusion system discretized by a mixed method, consisting of a spectral method along time and a finite difference scheme along space [1]. As the spatial mesh becomes finer, the computational cost becomes very large and prevents getting high accuracy. In this context, our contribution is a suitable parallel implementation on GPUs (Graphics Processing Units) of this model. This massively multi-processors architecture has been recently used in several scientific applications to improve performance of software [4] and to get accurate and accelerated solutions in similar fractional diffusion problems [2]. Experiments show the gain of performance in execution time and accuracy terms of the parallel implementation. References [1] Burrage, K. and Cardone, A. and D’Ambrosio, R. and Paternoster, B. 2017 Numerical solution of time fractional diffusion systems, Appl. Numer. Math. 116, 82–94. [2] De Luca, P., Galletti, A., Ghehsareh, H.R., Marcellino, L., & Raei, M. A gpucuda framework for solving a two-dimensional inverse anomalous diffusion problem.In: Foster, I., Joubert, G.R., Kučera, L., Nagel, W.E., Peters, F. (eds) Parallel Computing: Technology Trends, Advances in Parallel Computing. Vol 36. pp 311 -320. IOS Press, 2020. [3] Höfling, F. and Franosch, T. 2013 Anomalous transport in the crowded world of biological cells, Rep. Prog. Phys. 76, 046602. [4] Kurzak, J., Gates, M., Charara, A., YarKhan, A., Yamazaki, I., & Dongarra, J. (2019, August). Linear systems solvers for distributed-memory machines with gpu accelerators. In European Conference on Parallel Processing (pp. 495-506). Springer, Cham.