High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners

@article{Franco2020HighorderMI,
  title={High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners},
  author={Michael Franco and Sylvain Camier and Julian Andrej and Will Pazner},
  journal={ArXiv},
  year={2020},
  volume={abs/1910.03032}
}
View PDF on arXiv
11 Citations
Background Citations
3
Methods Citations
3

11 Citations

Accelerating High-Order Mesh Optimization Using Finite Element Partial Assembly on GPUs
TLDR
A new GPU-oriented mesh optimization method based on high-order finite elements that uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together.
Conservative and accurate solution transfer between high-order and low-order refined finite element spaces
TLDR
Under natural restrictions on the low-order refined space, it is proved that both the high-to-low-order and low- to-high-order linear mappings are conservative, constant preserving and high-order accurate.
Matrix-free Monolithic Multigrid Methods for Stokes and Generalized Stokes Problems
TLDR
This work considers the widely used continuous Qk-Qk−1 quadrilateral or hexahedral Taylor-Hood elements for the finite element discretization of the Stokes and generalized Stokes systems in two and three spatial dimensions and proposes and analyzes matrix-free monolithic geometric multigrid solvers based on appropriately scaled Chebyshev-Jacobi smoothers.
Matrix-free approaches for GPU acceleration of a high-order finite element hydrodynamics application using MFEM, Umpire, and RAJA
TLDR
Focusing on MARBL’s ALE hydrodynamics package, this work demonstrates scalability on different platforms and highlights that many of the innovations have been contributed back to open-source software libraries, such as MFEM (finite element algorithms) and RAJA (kernel abstractions).
Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting
  • Will Pazner
  • Computer Science
    Computer Methods in Applied Mechanics and Engineering
  • 2021
MFEM: a modular finite element methods library
Invariant domain preserving high-order spectral discontinuous approximations of hyperbolic systems
TLDR
A limiting procedure to preserve invariant domains with time explicit discrete high-order spectral discontinuous approximate solutions to hyperbolic systems of conservation laws and derives a condition on the time step to guaranty that the cell-averaged approximate solution is a convex combination of states in the invariant domain.
A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow
High-Performance Implementation of Discontinuous Galerkin Methods with Application in Fluid Flow
A Matrix-free GMRES Algorithm on GPU Clusters for Implicit Large Eddy Simulation
...
...

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