hypre: A Library of High Performance Preconditioners

By Robert D. Falgout, Ulrike Meier Yang. International Conference on Conceptual Structures, 2002

1,053 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/0354aff91dd843e01e396fbd635129bea73977b4

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Citations in the corpus

The Design and Implementation of hypre, a Library of Parallel High Performance Preconditioners (2006, methodology): “The hypre library [16, 21] has been designed with the primary goal of providing users with advanced scalable parallel preconditioners.”
A review of level-set methods and some recent applications (2018, methodology): “the Conjugate Gradient of the Petsc libraries [113, 114] preconditioned with the Hypre multigrid [115, 116].”
High order conservative finite difference scheme for variable density low Mach number turbulent flows (2007, methodology): “The pressure Poisson equation is then solved to enforce continuity using a combination of spectral methods, Krylov-based methods [25], and multi-grid methods [26], depending on the geometry of the problem.”
Choose a Transformer: Fourier or Galerkin (2021, background): “[24] Robert D Falgout and Ulrike Meier Yang.”
An adaptive, formally second order accurate version of the immersed boundary method (2007, methodology): “We note here, however, that the parallel implementation relies on the SAMRAI (Structured Adaptive Mesh Refinement Applications Infrastructure) object-oriented C++ framework which is developed at the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory [47–50], the PETSc ”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “, 2001) in DOLFIN together with the Bi-CGSTAB iterative solver (van der Vorst, 1992), and the BoomerAMG preconditioners from hypre (Falgout and Yang, 2002).”
On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems (2005, methodology): “For these problems, we make use of the structured multigrid solvers provided by the hypre project, a library of high performance preconditioners [39,40].”
An accurate conservative level set/ghost fluid method for simulating turbulent atomization (2008, methodology): “This variable-coefficient, elliptic equation is solved using a combination of Krylov-based methods [27] preconditioned using a multi-grid solver [28].”
An improved immersed boundary method with direct forcing for the simulation of particle laden flows (2012, methodology): “In contrast to [42], the present implementation makes use of the library hypre [5, 6] to solve (7e) and (7f).”
Effects of flexibility on the aerodynamic performance of flapping wings (2011, methodology): “The pressure correction equation is solved with either the GMRES linear solver with Jacobi preconditioner provided by PETSc (Balay et al. 1997, 2010, 2011) or the BoomerAMG linear solver provided by Falgout & Yang (2002).”
Parallel simulation of wormhole propagation with the Darcy-Brinkman-Forchheimer framework (2015, methodology): “The preconditioner DS [48] and the solver GMRES in Hypre are chosen to solve 𝑨𝒙 = 𝒃.”