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Efficient ordinary differential equation solvers for chemical kinetics musttake into account the available thread and instruction-level parallelism of theunderlying hardware, especially on many-core coprocessors, as well as thenumerical efficiency. A stiff Rosenbrock and nonstiff Runge-Kutta solver areimplemented using the single instruction, multiple thread (SIMT) and singleinstruction, multiple data (SIMD) paradigms with OpenCL. The performances ofthese parallel implementations were measured with three chemical kinetic modelsacross several multicore and many-core platforms. Two runtime benchmarks wereconducted to clearly determine any performance advantage offered by eithermethod: evaluating the right-hand-side source terms in parallel, andintegrating a series of constant-pressure homogeneous reactors using theRosenbrock and Runge-Kutta solvers. The right-hand-side evaluations with SIMDparallelism on the host multicore Xeon CPU and many-core Xeon Phi co-processorperformed approximately three times faster than the baseline multithreadedcode. The SIMT model on the host and Phi was 13-35% slower than the baselinewhile the SIMT model on the GPU provided approximately the same performance asthe SIMD model on the Phi. The runtimes for both ODE solvers decreased 2.5-2.7xwith the SIMD implementations on the host CPU and 4.7-4.9x with the Xeon Phicoprocessor compared to the baseline parallel code. The SIMT implementations onthe GPU ran 1.4-1.6 times faster than the baseline multithreaded CPU code;however, this was significantly slower than the SIMD versions on the host CPUor the Xeon Phi. The performance difference between the three platforms wasattributed to thread divergence caused by the adaptive step-sizes within theODE integrators. Analysis showed that the wider vector width of the GPU incursa higher level of divergence than the narrower Sandy Bridge or Xeon Phi.

Accelerating finite-rate chemical kinetics with coprocessors: comparing vectorization methods on GPUs, MICs, and CPUs