Paper Info
Title
A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers
Abstract
This study presents a fair performance comparison of the continuous finite element method, the symmetric interior penalty discontinuous Galerkin method, and the hybridized discontinuous Galerkin (HDG) method. Modern implementations of high-order methods with state-of-the-art multigrid solvers for the Poisson equation are considered, including fast matrix-free implementations with sum factorization on quadrilateral and hexahedral elements. For the HDG method, a multigrid approach that combines a grid transfer from the trace space to the space of linear finite elements with algebraic multigrid on further levels is developed. It is found that high-order continuous finite elements give best time to solution for smooth solutions, closely followed by the matrix-free solvers for the other two discretizations. Their performance is up to an order of magnitude higher than that of the best matrix-based methods, even after including the superconvergence effects in the matrix-based HDG method. This difference is because of the vastly better performance of matrix-free Operator evaluation as compared to sparse matrix-vector products. A roofline performance model confirms the superiority of the matrix-free implementation.
Year
DOI
Venue
2018
10.1137/16M110455X
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
high-order finite elements,discontinuous Galerkin method,hybridizable discontinuous Galerkin,multigrid method,matrix-free method,high-performance computing
Discontinuous Galerkin method,Supercomputer,Mathematical analysis,Finite element method,Mathematics,Multigrid method
Journal
Volume
Issue
ISSN
40
5
1064-8275
Citations 
PageRank 
References 
2
0.38
13
Authors
2
Name
Order
Citations
PageRank
Martin Kronbichler132331.00
Wolfgang A. Wall26122.07