  We demonstrate the first implementation of recently-developed fast explicit
kinetic integration algorithms on modern graphics processing unit (GPU)
accelerators. Taking as a generic test case a Type Ia supernova explosion with
an extremely stiff thermonuclear network having 150 isotopic species and 1604
reactions coupled to hydrodynamics using operator splitting, we demonstrate the
capability to solve of order 100 realistic kinetic networks in parallel in the
same time that standard implicit methods can solve a single such network on a
CPU. This orders-of-magnitude decrease in compute time for solving systems of
realistic kinetic networks implies that important coupled, multiphysics
problems in various scientific and technical fields that were intractible, or
could be simulated only with highly schematic kinetic networks, are now
computationally feasible.
