Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Auxiliary Space Preconditioning of Finite Element Equations Using a Nonconforming Interior Penalty Reformulation and Static Condensation

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/19M1286815· OSTI ID:1633520
 [1];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Portland State Univ., OR (United States)
+ Show Author Affiliations

We modify the well-known interior penalty finite element discretization method so that it allows for element-by-element assembly. This is possible due to the introduction of additional unknowns associated with the interfaces between neighboring elements. The resulting bilinear form, and a Schur complement (reduced) version of it, are utilized in a number of auxiliary space preconditioners for the original conforming finite element discretization problem. Furthermore, these preconditioners are analyzed on the fine scale, and their performance is illustrated on model second order scalar elliptic problems discretized with high order elements.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA); NSF
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1633520
Report Number(s):
LLNL-JRNL--788660; 986694
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 42; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

References (11)

Sparse matrix element topology with application to AMG(e) and preconditioning journal January 2002
On some versions of the element agglomeration AMGe method journal September 2008
An improved convergence analysis of smoothed aggregation algebraic multigrid: AN IMPROVED ANALYSIS OF SA AMG journal March 2011
The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids journal September 1996
Almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non-matching grids journal December 2003
An Elliptic Collocation-Finite Element Method with Interior Penalties journal February 1978
An Interior Penalty Finite Element Method with Discontinuous Elements journal August 1982
Multigrid Smoothers for Ultraparallel Computing journal January 2011
Spectral AMGe ($\rho$AMGe) journal January 2003
Two-grid Method for Linear Elasticity on Unstructured Meshes journal January 1999
Polynomial of Best Uniform Approximation to and Smoothing in Two-level Methods journal January 2012

Similar Records

A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems
Journal Article · Wed Oct 07 00:00:00 EDT 2020 · SIAM Journal on Scientific Computing · OSTI ID:1671181
Preconditioning of elliptic saddle point systems by substructuring and a penalty approach.
Conference · Fri Dec 31 23:00:00 EST 2004 · OSTI ID:947799
Approximate Schur complement preconditioning of the lowest order nodal discretizations
Conference · Mon Dec 30 23:00:00 EST 1996 · OSTI ID:433355

Related Subjects

97 MATHEMATICS AND COMPUTING
algebraic multigrid
auxiliary space
finite element method
interior penalty
preconditioning
static condensation