  We present a parallel implicit-explicit time integration scheme for the
advection-diffusion-reaction systems arising from the equations governing
low-Mach number combustion with complex chemistry. Our strategy employs
parallelization across the method to accelerate the serial Multi-Implicit
Spectral Deferred Correction (MISDC) scheme used to couple the advection,
diffusion, and reaction processes. In our approach, referred to as Concurrent
Implicit Spectral Deferred Correction (CISDC), the diffusion solves and the
reaction solves are performed concurrently by different processors. Our
analysis shows that the proposed parallel scheme is stable for stiff problems
and that the sweeps converge to the fixed-point solution at a faster rate than
with serial MISDC. We present numerical examples to demonstrate that the new
algorithm is high-order accurate in time, and achieves a parallel speedup
compared to serial MISDC.

Numerical Analysis