Greedy Dissection Method for Shared Parallelism in Incomplete Factorization Within INMOST Platform

Terekhov, Kirill M.

doi:10.1007/978-3-030-92864-3_7

Cited by 5 publications

(1 citation statement)

References 26 publications

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“…At every Newton iteration, the linear system for the update is solved iteratively with the multilevel preconditioner 103,104 . The iterative convergence tolerances are

τ_{italicabs} = 10^{- 12}

τ_{italicrel} = 10^{- 18}

, dropping tolerances in the second‐order incomplete factorization are

τ_{1} = 10^{- 3}

and

τ_{2} = 10^{- 5}

, pivoting by condition estimation is

κ = 2.5

.…”

Section: Problem Solutionmentioning

confidence: 99%

Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

Terekhov

Butakov

Danilov

et al. 2023

Numer Methods Biomed Eng

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In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier–Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite‐volume methods for the Navier–Stokes equations, advection–diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier–Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf‐sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.

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“…At every Newton iteration, the linear system for the update is solved iteratively with the multilevel preconditioner 103,104 . The iterative convergence tolerances are