Matrix analysis
Stiff ode slovers: a review of current and coming attractions
Journal of Computational Physics
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
ACM Transactions on Mathematical Software (TOMS)
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
The development of Runge-Kutta methods for partial differential equations
Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
Explicit Runge-Kutta methods for parabolic partial differential equations
Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
A semi-implicit numerical scheme for reacting flow: II. stiff, operator-split formulation
Journal of Computational Physics
An analysis of operator splitting techniques in the stiff case
Journal of Computational Physics
Parallel programming in OpenMP
Parallel programming in OpenMP
Fourth Order Chebyshev Methods with Recurrence Relation
SIAM Journal on Scientific Computing
OpenMP: An Industry-Standard API for Shared-Memory Programming
IEEE Computational Science & Engineering
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
Journal of Computational Physics
RKC time-stepping for advection-diffusion-reaction problems
Journal of Computational Physics
Modeling Low Mach Number Reacting Flow with Detailed Chemistry and Transport
Journal of Scientific Computing
Second-order splitting schemes for a class of reactive systems
Journal of Computational Physics
Programming Massively Parallel Processors: A Hands-on Approach
Programming Massively Parallel Processors: A Hands-on Approach
Accelerating S3D: a GPGPU case study
Euro-Par'09 Proceedings of the 2009 international conference on Parallel processing
CUDA by Example: An Introduction to General-Purpose GPU Programming
CUDA by Example: An Introduction to General-Purpose GPU Programming
Directive-based Programming for GPUs: A Comparative Study
HPCC '12 Proceedings of the 2012 IEEE 14th International Conference on High Performance Computing and Communication & 2012 IEEE 9th International Conference on Embedded Software and Systems
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The chemical kinetics ODEs arising from operator-split reactive-flow simulations were solved on GPUs using explicit integration algorithms. Nonstiff chemical kinetics of a hydrogen oxidation mechanism (9 species and 38 irreversible reactions) were computed using the explicit fifth-order Runge-Kutta-Cash-Karp method, and the GPU-accelerated version performed faster than single- and six-core CPU versions by factors of 126 and 25, respectively, for 524,288 ODEs. Moderately stiff kinetics, represented with mechanisms for hydrogen/carbon-monoxide (13 species and 54 irreversible reactions) and methane (53 species and 634 irreversible reactions) oxidation, were computed using the stabilized explicit second-order Runge-Kutta-Chebyshev (RKC) algorithm. The GPU-based RKC implementation demonstrated an increase in performance of nearly 59 and 10 times, for problem sizes consisting of 262,144 ODEs and larger, than the single- and six-core CPU-based RKC algorithms using the hydrogen/carbon-monoxide mechanism. With the methane mechanism, RKC-GPU performed more than 65 and 11 times faster, for problem sizes consisting of 131,072 ODEs and larger, than the single- and six-core RKC-CPU versions, and up to 57 times faster than the six-core CPU-based implicit VODE algorithm on 65,536 ODEs. In the presence of more severe stiffness, such as ethylene oxidation (111 species and 1566 irreversible reactions), RKC-GPU performed more than 17 times faster than RKC-CPU on six cores for 32,768 ODEs and larger, and at best 4.5 times faster than VODE on six CPU cores for 65,536 ODEs. With a larger time step size, RKC-GPU performed at best 2.5 times slower than six-core VODE for 8192 ODEs and larger. Therefore, the need for developing new strategies for integrating stiff chemistry on GPUs was discussed.