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We propose and study a nonlinear elimination preconditioned inexact Newton method for the numerical simulation of diseased human arteries with a heterogeneous hyperelastic model. We assume the artery is made of layers of distinct tissues and also contains plaque. Traditional Newton methods often work well for smooth and homogeneous arteries but suffer from slow or no convergence due to the heterogeneousness of diseased soft tissues when the material is quasiincompressible. The proposed nonlinear elimination method adaptively finds a small number of equations causing the nonlinear stagnation and then eliminates them from the global nonlinear system. By using the theory ofmore »

Computational fluid dynamics (CFD) is increasingly used to study blood flows in patientspecific 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, fluidonly to coupled fluidstructure 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 inmore »

Simulation of blood flows in the pulmonary artery provides some insight into certain diseases by examining the relationship between some continuum metrics, e.g., the wall shear stress acting on the vascular endothelium, which responds to flowinduced mechanical forces by releasing vasodilators/constrictors. V. Kheyfets, in his previous work, studies numerically a patientspecific 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 patientspecific pulsatile waveforms as the inlet boundary condition.

Nonlinear fluid–structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patientspecific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically.