An implicit and explicit integration algorithm were ported to CUDA graphical processing units (GPUs) and used to concurrently solve sets of independent ordinary differential equations (ODEs) arising from finite-rate chemical kinetics. The GPU-enabled 4th-order accurate adaptive Runge-Kutta-Fehlberg (RKF45) ODE solver achieved a maximum speedup of 20.2x over the baseline implicit 5th-order accurate DVODE CPU run-time for larger numbers of ODEs with comparable solution accuracy. The GPU implementation of the DVODE solver achieved a maximum speed-up of 7.7x over the baseline CPU run-time. The performance impact of mapping one thread to each ODE was compared to mapping an entire CUDA thread-block per ODE (i.e., multiple threads per ODE). The one-thread-per-ODE approach achieved greater overall speed-up compared to the one-block-per-ODE approach but only when the number of ODEs was large: 1,000 ODEs were needed just to break even with the scalar CPU version and over 50,000 ODEs to reach maximum parallel efficiency. The performance difference is most pronounced with the RKF45 algorithm. The peak performance with the one-thread-per-ODE method was nearly 2x faster than the one-block-per-ODE approach. The one-block-per-problem implementation of RKF45 and DVODE both achieved lower peak speed-ups but outperformed the scalar CPU performance with as few as 100 ODEs. The new GPU-enabled ODE solvers demonstrate a method to significantly reduce the computational cost of detailed finite-rate combustion simulations with turn-around cost savings exceeding an order of magnitude.
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