Efficient low-order refined preconditioners for high-order matrix-free continuous and discontinuous Galerkin methods

by   Will Pazner, et al.

In this paper, we design 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. The high-order operators are applied without forming the system matrix, making use of sum factorization for efficient evaluation. The system is preconditioned using a spectrally equivalent low-order finite element operator discretization on a refined mesh. The low-order refined mesh is anisotropic and not shape regular in p, requiring specialized solvers to treat the anisotropy. We make use of a structured, geometric multigrid V-cycle with ordered ILU(0) smoothing. The preconditioner is parallelized through an overlapping additive Schwarz method that is robust in h and p. The method is extended to interior penalty and BR2 discontinuous Galerkin discretizations, for which it is also robust in the size of the penalty parameter. Numerical results are presented on a variety of examples, verifying the uniformity of the preconditioner.



There are no comments yet.


page 12

page 17


A Family of Independent Variable Eddington Factor Methods with Efficient Linear Solvers

We present a family of discretizations for the Variable Eddington Factor...

Fast Tensor Product Schwarz Smoothers for High-Order Discontinuous Galerkin Methods

In this article, we discuss the efficient implementation of powerful dom...

Hybrid multigrid methods for high-order discontinuous Galerkin discretizations

The present work develops hybrid multigrid methods for high-order discon...

A Hermite-like basis for faster matrix-free evaluation of interior penalty discontinuous Galerkin operators

This work proposes a basis for improved throughput of matrix-free evalua...

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

We present a matrix-free flow solver for high-order finite element discr...

Linearizing the hybridizable discontinuous Galerkin method: A linearly scaling operator

This paper proposes a matrix-free residual evaluation technique for the ...

Uniform subspace correction preconditioners for discontinuous Galerkin methods with hp-refinement

In this paper, we develop subspace correction preconditioners for discon...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.