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

  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},
Accelerating High-Order Mesh Optimization Using Finite Element Partial Assembly on GPUs
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
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
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
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
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.


Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods
This paper designs preconditioners for the matrix-free solution of high-order continuous and discontinuous Galerkin discretizations of elliptic problems based on FEM-SEM equivalence and additive Schwarz methods and presents results on a variety of examples.
Domain Decomposition Method and Fast Diagonalization Solver for Spectral Element Simulations
The P N — P N-2 spectral element method of Maday and Patera is employed for the discretization of the Navier-Stokes equations, employing a suitable domain decomposition along with the influence-matrix technique of Schumann and Benner.
Interior penalty tensor-product preconditioners for high-order discontinuous Galerkin discretizations
An interior penalty tensor-product preconditioner for the implicit time integration of discontinuous Galerkin discretizations of partial differential equations with second-order spatial derivatives is introduced.
Multigrid for Matrix-Free High-Order Finite Element Computations on Graphics Processors
A GPU parallelization of a matrix-free geometric multigrid iterative solver targeting moderate and high polynomial degrees, with support for general curved and adaptively refined hexahedral meshes with hanging nodes is developed.
A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier-Stokes Equations
This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier?Stokes equations. We extend a discontinuous finite element
A matrix‐free high‐order discontinuous Galerkin compressible Navier‐Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows
A high‐performance DG solver for the compressible Navier‐Stokes equations based on a highly efficient matrix‐free implementation that targets modern cache‐based multicore architectures with Flop/Byte ratios significantly larger than 1.1 is presented.