Two-Level Methods for Blood Flow Simulation

We consider two-level Newton-Krylov-Schwarz algorithms for blood flow in arteries, which is a computationally difficult and practically important application area [6, 8]. In particular, the similar densities of blood and artery wall make the coupling between fluid and structure strong in both directions, so that partitioned or iterative procedures have difficulties due to the added-mass effect [ 4]. Instead of a partitioned procedure, we adopt a monolithic computational approach, coupling fluid to structure in one large system that is solved all at once. This tight coupling allows for robustness to parameters and makes our method immune to the added-mass effect. The resulting system is difficult to solve, but we show here that it can be solved efficiently with effective preconditioning strategies specifically designed for parallel computing.