We develope a parallel CUDA solver based on Waveform Relaxation (WR) methods for the numerical solution of large systems of Volterra Integral Equations (VIEs) on GPU platforms. The solver is based on discrete-time Picard and Jacobi WR Volterra Runge-Kutta methods. Such methods have been introduced in [1], where bounds on the stepsize h have been furnished which assure the convergence of the WR methods. Numerical experiments show the obtained speed-up on test problems of interest in applications, arising from the semi-discretization in space of Volterra-Fredholm integral equations (see [2] and references therein). [1] Crisci, M.R., Russo, E., Vecchio, A., Discrete-time waveform relax- ation Volterra-Runge-Kutta methods: Convergence analysis, Jour- nal of Computational and Applied Mathematics 86 (2), pp. 359-374 (1997). [2] Cardone, A., Messina, E., Russo, E., A fast iterative method for discretized Volterra-Fredholm integral equations, Journal of Computa- tional and Applied Mathematics, 189 (1-2), pp. 568-579, 2006.

Parallel methods for Volterra Integral Equations on GPUs

CONTE, Dajana
2014

Abstract

We develope a parallel CUDA solver based on Waveform Relaxation (WR) methods for the numerical solution of large systems of Volterra Integral Equations (VIEs) on GPU platforms. The solver is based on discrete-time Picard and Jacobi WR Volterra Runge-Kutta methods. Such methods have been introduced in [1], where bounds on the stepsize h have been furnished which assure the convergence of the WR methods. Numerical experiments show the obtained speed-up on test problems of interest in applications, arising from the semi-discretization in space of Volterra-Fredholm integral equations (see [2] and references therein). [1] Crisci, M.R., Russo, E., Vecchio, A., Discrete-time waveform relax- ation Volterra-Runge-Kutta methods: Convergence analysis, Jour- nal of Computational and Applied Mathematics 86 (2), pp. 359-374 (1997). [2] Cardone, A., Messina, E., Russo, E., A fast iterative method for discretized Volterra-Fredholm integral equations, Journal of Computa- tional and Applied Mathematics, 189 (1-2), pp. 568-579, 2006.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4521657
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