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

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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.

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Acknowledgments

Funding for this work was provided by a Leducq Foundation Network of Excellent Grant, a Burroughs Wellcome Fund Career Award at the Scientific Interface, NIH grant RHL102596A, and the NSF CAREER Awards OCI 1150184 and 1055091.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA, USA

    Mahdi Esmaily-Moghadam & Alison L. Marsden

  2. Department of Structural Engineering, University of California, San Diego, CA, USA

    Yuri Bazilevs

Authors
  1. Mahdi Esmaily-Moghadam
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  2. Yuri Bazilevs
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  3. Alison L. Marsden
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Corresponding author

Correspondence to Yuri Bazilevs.

Additional information

Alison L. Marsden is a part of the Modeling Of Congenital Hearts Alliance (MOCHA). MOCHA Investigators are: Edward Bove MD and Adam Dorfman MD (University of Michigan, USA); Andrew Taylor MD, Alessandro Giardini MD, Sachin Khambadkone MD, Marc de Leval MD, Silvia Schievano PhD, and T-Y Hsia MD (Institute of Child Health, UK); G. Hamilton Baker MD and Anthony Hlavacek (Medical University of South Carolina, USA); Francesco Migliavacca PhD, Giancarlo Pennati PhD, and Gabriele Dubini PhD (Politecnico di Milano, Italy); Richard Figliola PhD and John McGregor PhD (Clemson University, USA); Alison Marsden PhD (University of California, San Diego, USA); Irene Vignon-Clementel (National Institute of Research in Informatics and Automation, France).

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Esmaily-Moghadam, M., Bazilevs, Y. & Marsden, A.L. A new preconditioning technique for implicitly coupled multidomain simulations with applications to hemodynamics. Comput Mech 52, 1141–1152 (2013). https://doi.org/10.1007/s00466-013-0868-1

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