A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

Numer Methods Biomed Eng

Kheyfets

Finol

et al. 2019

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Computational fluid dynamics (CFD) is increasingly used to study blood flows in patient‐specific arteries for understanding certain cardiovascular diseases. The techniques work quite well for relatively simple problems but need improvements when the problems become harder when (a) the geometry becomes complex (eg, a few branches to a full pulmonary artery), (b) the model becomes more complex (eg, fluid‐only to coupled fluid‐structure interaction), (c) both the fluid and wall models become highly nonlinear, and (d) the computer on which we run the simulation is a supercomputer with tens of thousands of processor cores. To push the limit of CFD in all four fronts, in this paper, we develop and study a highly parallel algorithm for solving a monolithically coupled fluid‐structure system for the modeling of the interaction of the blood flow and the arterial wall. As a case study, we consider a patient‐specific, full size pulmonary artery obtained from computed tomography (CT) images, with an artificially added layer of wall with a fixed thickness. The fluid is modeled with a system of incompressible Navier‐Stokes equations, and the wall is modeled by a geometrically nonlinear elasticity equation. As far as we know, this is the first time the unsteady blood flow in a full pulmonary artery is simulated without assuming a rigid wall. The proposed numerical algorithm and software scale well beyond 10 000 processor cores on a supercomputer for solving the fluid‐structure interaction problem discretized with a stabilized finite element method in space and an implicit scheme in time involving hundreds of millions of unknowns.

“…Equation 6 is reduced to (7) if we replace the wall displacement unknowns d h Γ w ,s by the fluid displacement unknowns d h Γ w ,m as follows:…”

Section: Seamless Coupling Discretizationmentioning

confidence: 99%

mentioning

confidence: 99%

Simulation of unsteady blood flows in a patient‐specific compliant pulmonary artery with a highly parallel monolithically coupled fluid‐structure interaction algorithm

Numer Methods Biomed Eng

Kheyfets

Finol

et al. 2019

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“…Once we figure out the initial state, the main cost of the simulation is to solve over and over again using the solution of the previous time step as the initial solution. In the next section, we describe a scalable and robust NKS method, which has been successfully studied for a transonic full potential equation in Cai et al, elasticity problems, and fluid‐structure interactions . The standard setup of NKS used in previous studies does not work well for the case of pulmonary artery because of the complexity of the geometry.…”

Section: Problem Definitionmentioning

confidence: 99%

“…We show numerically that the proposed version of the parallel algorithm is scalable to thousands of processor cores for large‐scale problems with hundreds of millions of unknowns. We also mention that the NKS method has been successfully applied to several classes of problems including the Bidomain reaction‐diffusion system in Munteanu et al, some elasticity problems in Kong and Cai, and fluid‐structure interaction problems in other works …”

Section: Introductionmentioning

confidence: 99%

An efficient parallel simulation of unsteady blood flows in patient‐specific pulmonary artery

Numer Methods Biomed Eng

Kheyfets

Finol

et al. 2018

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Simulation of blood flows in the pulmonary artery provides some insight into certain diseases by examining the relationship between some continuum metrics, eg, the wall shear stress acting on the vascular endothelium, which responds to flow-induced mechanical forces by releasing vasodilators/constrictors. V. Kheyfets, in his previous work, studies numerically a patient-specific pulmonary circulation to show that decreasing wall shear stress is correlated with increasing pulmonary vascular impedance. In this paper, we develop a scalable parallel algorithm based on domain decomposition methods to investigate an unsteady model with patient-specific pulsatile waveforms as the inlet boundary condition. The unsteady model offers tremendously more information about the dynamic behavior of the flow field, but computationally speaking, the simulation is a lot more expensive since a problem which is similar to the steady-state problem has to be solved many times, and therefore, the traditional sequential approach is not suitable anymore. We show computationally that simulations using the proposed parallel approach with up to 10 000 processor cores can be obtained with much reduced compute time. This makes the technology potentially usable for the routine study of the dynamic behavior of blood flows in the pulmonary artery, in particular, the changes of the blood flows and the wall shear stress in the spatial and temporal dimensions.

“…The fully coupled Schwarz serves as the preconditioner of the linear solvers for both the eigenvalue and the transient problems. We also note that the fully coupled Schwarz preconditioner has been successfully applied to elasticity and fluid–structure interaction problems. Here, we extend and adapt the algorithm to the transient multigroup neutron diffusion equations.…”

Section: Introductionmentioning

confidence: 99%

A fully coupled two‐level Schwarz preconditioner based on smoothed aggregation for the transient multigroup neutron diffusion equations

Numerical Linear Algebra App

Wang

Peterson

et al. 2018

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Summary The multigroup neutron diffusion equations (an approximation of the neutron transport equation) are widely used for studying the motion of neutrons and their interactions with stationary background materials. Solving the multigroup neutron diffusion equations is challenging because the unknowns are tightly coupled through scattering and fission events, and solutions with high spatial resolution of full reactor cores in multiphysics environments are frequently required. In this paper, we focus on the development of a scalable, parallel preconditioner for solving the system of equations arising from the finite‐element discretization of the multigroup neutron diffusion equations in space and an implicit finite‐difference scheme in time. The parallel preconditioner (here referred to as the “fully coupled Schwarz preconditioner”) is constructed by monolithically applying the overlapping domain decomposition method together with a smoothed aggregation‐based coarse space to the coupled system. Our approach is different from the traditional block Gauss–Seidel sweep method that applies the preconditioner from the fast group to the thermal group sequentially, and we demonstrate that it provides significant improvements in terms of both the number of iterations required and the total compute time for a system of equations with millions of unknowns on a large supercomputer.