Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures

Rahimian, Abtin; Lashuk, Ilya; Veerapaneni, Shravan; Chandramowlishwaran, Aparna; Malhotra, Dhairya; Moon, Logan; Sampath, Rahul S.; Shringarpure, Aashay; Vetter, Jeffrey S.; Vuduc, Richard; Zorin, Denis; Biros, George

doi:10.1109/sc.2010.42

Cited by 121 publications

(82 citation statements)

References 32 publications

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“…In this paper, we focus on the mathematical formulation and not on performance and parallelization. We report, preliminary results on a high-performance parallel implementation of this method in [51].…”

Section: Contributionsmentioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

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136

143

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Vesicles are locally-inextensible fluid membranes that can sustain bending. In this paper, we extend "A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows", Veerapaneni et al. Journal of Computational Physics, 228(19), 2009 to general non-axisymmetric vesicle flows in three dimensions.Although the main components of the algorithm are similar in spirit to the axisymmetric case (spectral approximation in space, semi-implicit time-stepping scheme), important new elements need to be introduced for a full 3D method. In particular, spatial quantities are discretized using spherical harmonics, and quadrature rules for singular surface integrals need to be adapted to this case; an algorithm for surface reparameterization is neeed to ensure sufficient of the timestepping scheme, and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs. To characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi-implicit time-stepping scheme, we perform a spectral analysis of the evolution operator on the unit sphere.By introducing these algorithmic components, we obtain a time-stepping scheme that, in our numerical experiments, is unconditionally stable. We present results to analyze the cost and convergence rates of the overall scheme. To illustrate the applicability of the new method, we consider a few vesicle-flow interaction problems: a single vesicle in relaxation, sedimentation, shear flows, and many-vesicle flows.

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Section: Contributionsmentioning

confidence: 99%

A fast algorithm for simulating vesicle flows in three dimensions

Veerapaneni

Rahimian

Biros

et al. 2011

Journal of Computational Physics

Self Cite

136

143

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“…A number of open-source libraries for fast multipole methods for distributed memory have been released 2 3 4 . Hierarchical N -body methods have been at the core of many Gordon Bell Prizes [19,20,22,24,29,[35][36][37]. Looking inward in strong scaling within a fixed memory rather than outward in weak scaling with expanding memory, they have also been effectively implemented on GPGPUs [4,6,10,15,23,26,27,30,40,41].…”

Section: Exascale Features Of the Fast Multipole Methodsmentioning

confidence: 99%

Communication Complexity of the Fast Multipole Method and its Algebraic Variants

Yokota

Turkiyyah

Keyes

2014

JSFI

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A combination of hierarchical tree-like data structures and data access patterns from fast multipole methods and hierarchical low-rank approximation of linear operators from H-matrix methods appears to form an algorithmic path forward for efficient implementation of many linear algebraic operations of scientific computing at the exascale. The combination provides asymptotically optimal computational and communication complexity and applicability to large classes of operators that commonly arise in scientific computing applications. A convergence of the mathematical theories of the fast multipole and H-matrix methods has been underway for over a decade. We recap this mathematical unification and describe implementation aspects of a hybrid of these two compelling hierarchical algorithms on hierarchical distributed-shared memory architectures, which are likely to be the first to reach the exascale. We present a new communication complexity estimate for fast multipole methods on such architectures. We also show how the data structures and access patterns of H-matrices for low-rank operators map onto those of fast multipole, leading to an algebraically generalized form of fast multipole that compromises none of its architecturally ideal properties.

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“…In [11], authors show results of simulations of approximately 50000 cells at 45% hematocrit, including aggregation of cells, use simple continuous model and take into account only the stretching and bending stiffness of the object. There have been even larger simulations done [12], but even though they deal with individual deformable cells, they model them as very simple ellipsoidal sacs and with no aggregation.…”

Section: Computational Complexitymentioning

confidence: 99%

Recent advances in mesh-based modeling of individual cells in biological fluids

Cimrák

Jančigová

Tóthová

2014

The 10th International Conference on Digital Technologies 2014

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The problem of modeling blood flow can be approached on different levels of accuracy. We investigate a model consisting of two major components: the fluid representing blood plasma and the elastic objects representing all types of cells in blood, e.g. red blood cells. The elastic objects are immersed in the fluid and they interact with each other.Our research is focused on spring-network models of elastic objects. We present the results concerning the scalability of meshes. We investigate the relation between mechanical properties of physical cells and the stiffness parameters of underlying meshes. Further, we present new metric that supplements energy-based approaches in cases when the energy is difficult to calculate.To demonstrate the abilities of our software implementation, we provide tests concerning the computational complexity. We show the significant speed-up caused by using templates when generating many cells with the same elastic properties. We also demonstrate the quadratic dependence of the computational time on increasing number of simulated cells.We suggest several directions for further model enhancements, such as better implementation of cell-cell collisions, inclusion of adhesion processes, monitoring the rupture of cells, and development of physically more relevant implementation of forces for some cell's elastic moduli.

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Petascale Direct Numerical Simulation of Blood Flow on 200K Cores and Heterogeneous Architectures

Cited by 121 publications

References 32 publications

A fast algorithm for simulating vesicle flows in three dimensions

A fast algorithm for simulating vesicle flows in three dimensions

Communication Complexity of the Fast Multipole Method and its Algebraic Variants

Recent advances in mesh-based modeling of individual cells in biological fluids

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