A new preconditioning technique for implicitly coupled multidomain simulations with applications to hemodynamics

Authors:
Mahdi Esmaily-Moghadam;Yuri Bazilevs;Alison L. Marsden
Affiliations:
Department of Mechanical and Aerospace Engineering, University of California, San Diego, USA;Department of Structural Engineering, University of California, San Diego, USA;Department of Mechanical and Aerospace Engineering, University of California, San Diego, USA
Venue:
Computational Mechanics
Year:
2013

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Abstract

In cardiovascular blood flow simulations a large portion of computational resources is dedicated to solve the linear system of equations. Boundary conditions in these applications are critical for obtaining accurate and physiologically realistic solutions, and pose numerical challenges due to the coupling between flow and pressure. Using an implicit time integration setting can lead to an ill-conditioned tangent matrix that causes deterioration in performance of traditional iterative linear equation solvers (LS). In this paper we present a novel and efficient preconditioner (PC) for this class of problems that exploits the strong coupling between the flow and pressure. We implement this PC in a LS algorithm designed for solving systems of equations governing incompressible flows. Excellent efficiency and stability properties of the proposed method are illustrated on a set of clinically relevant hemodynamics simulations.