Highorder matrixfree incompressible flow solvers with GPU acceleration and loworder refined preconditioners
Abstract
We present a matrixfree flow solver for highorder finite element discretizations of the incompressible NavierStokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems resulting from the finite element discretization can be prohibitively expensive, both in terms of computational complexity and memory. For this reason, it is necessary to develop matrixfree operators and preconditioners, which can be used to efficiently solve these linear systems without access to the matrix entries themselves. The matrixfree operator evaluations utilize GPUaccelerated sumfactorization techniques to minimize memory movement and maximize throughput. The preconditioners developed in this work are based on a loworder refined methodology with parallel subspace corrections. The saddlepoint Stokes system is solved using blockpreconditioning techniques, which are robust in mesh size, polynomial degree, time step, and viscosity. For the incompressible NavierStokes equations, we make use of projection (fractional step) methods, which require Helmholtz and Poisson solves at each time step. The performance of our flow solvers is assessed on several benchmark problems in two and three spatial dimensions.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.03032
 Bibcode:
 2019arXiv191003032F
 Keywords:

 Mathematics  Numerical Analysis
 EPrint:
 20 pages, 11 figures