Numerical Simulation of Three-dimensional Blood Flows Using Domain Decomposition Method on Parallel Computer

A good numerical blood flow simulation tool based on patient-specific anatomy and physiological conditions can be clinically helpful for physicians or researchers to study vascular diseases, to enhance diagnoses, as well as to plan surgery procedures. Such a tool is computationally very expensive, and often requires the use of large scale supercomputers with many core processors. In this paper, we focus on developing parallel domain decomposition algorithms for solving nonlinear systems arising from the discretization of three-dimensional blood flow model equations with a stabilized finite element method for the spatial variables and an implicit backward Euler finite difference method for the temporal variable. More precisely speaking, at each time step, the resulting nonlinear system is solved by the Newton-Krylov-Schwarz algorithm. We implement the parallel fluid solver using PETSc and integrate it with other state-of-the-art software packages into a parallel blood flow simulation system, which includes Cubit, ParMETIS and Para View for mesh generation, mesh partitioning, and visualization, respectively. We validate our parallel code and investigate the parallel performance of our algorithms for both a straight artery model and an end-to-side graft model.