Breakdown evaluation of Krylov subspace methods in parallel two-phase flow simulation

抄録

Two-phase flow simulations on distributed-memory systems can expose solver breakdowns caused by inner-product reductions, even when the same Krylov solver is stable in serial runs. This study evaluates breakdown occurrence in parallel two-phase flow analyses and quantifies the trade-off between robustness and runtime. We compare standard BiCGSTAB, BiCGSTAB with reduced summation-order dependence, BiCGSTAB with quasi quadruple inner products, BiCGSAFE, and IDR(s). In the two-phase tests, standard BiCGSTAB broke down in parallel, whereas double-double BiCGSTAB, the order-stabilized BiCGSTAB and IDR(s) avoided breakdown.