Numerical Design of an Optimal Bypass for a Partially Blocked Artery

A parallel domain decomposition method is introduced for numerical design of an optimal bypass for a partially blocked artery. The optimal bypass is described as the solution of a shape optimization problem governed by the steady-state incompressible Navier-Stokes equations that are used to model the blood flow. The problem is discretized with a finite element method on unstructured moving meshes and then solved by a parallel one-shot Lagrange-Newton-Krylov-Schwarz algorithm. In order to accelerate the convergence of the inexact Newton method, we introduce a two-level inexact Newton method which solves a coarse grid problem to generate a good initial guess for the fine grid inexact Newton method. Numerical experiments show that our algorithms perform well on a supercomputer with hundreds of processors.