A cubic spline approach for solving the arterial graft design problem

A new algorithm is proposed by the cubic spline to describe the shape of the domain in an arterial graft design problem, which is mathematically modeled with a flow-based shape optimization. The optimization method based on the coefficients of the spline is then studied, where a mixed finite element formulation is used for the flow problem and the moving mesh technique is adopted to track the optimized shape. The numerical results are illustrated to show the convergence of the proposed scheme.