Iterative and parallel performance of high-order compact systems

Representative transport PDE problems in one, two, and three dimensions are approximated by a class of high-order compact (HOC) difference schemes and their iterative and parallel performance are studied. The eigenvalues and condition numbers of the HOC schemes are analyzed and the performance of standard Krylov-space methods is compared for HOC, central differencing, and standard first-order upwinding schemes. Finally, CPU times, MFLOP rates, and speedup curves are presented for fixed-problem-size cases and scaled-problem-size cases.