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Fast numerical solutions of patient‐specific blood flows in 3D arterial systems
Author(s) -
Mut Fernando,
Aubry Romain,
Löhner Rainald,
Cebral Juan R.
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1235
Subject(s) - solver , eigenvalues and eigenvectors , compressibility , conjugate gradient method , mathematics , rate of convergence , poisson distribution , convergence (economics) , poisson's equation , mathematical optimization , computer science , algorithm , geometry , mathematical analysis , mechanics , physics , computer network , statistics , quantum mechanics , economics , economic growth , channel (broadcasting)
The study of hemodynamics in arterial models constructed from patient‐specific medical images requires the solution of the incompressible flow equations in geometries characterized by complex branching tubular structures. The main challenge with this kind of geometries is that the convergence rate of the pressure Poisson solver is dominated by the graph depth of the computational grid. This paper presents a deflated preconditioned conjugate gradients (DPCG) algorithm for accelerating the pressure Poisson solver. A subspace deflation technique is used to approximate the lowest eigenvalues along the tubular domains. This methodology was tested with an idealized cylindrical model and three patient‐specific models of cerebral arteries and aneurysms constructed from medical images. For these cases, the number of iterations decreased by up to a factor of 16, while the total CPU time was reduced by up to 4 times when compared with the standard PCG solver. Copyright © 2009 John Wiley & Sons, Ltd.