Document Type

Pre-Print

Publication Date

5-2018

Subjects

Finite element method, Inequalities (Mathematics)

Abstract

We generalize the construction and analysis of auxiliary space preconditioners to the n-dimensional finite element subcomplex of the de Rham complex. These preconditioners are based on a generalization of a decomposition of Sobolev space functions into a regular part and a potential. A discrete version is easily established using the tools of finite element exterior calculus. We then discuss the four-dimensional de Rham complex in detail. By identifying forms in four dimensions (4D) with simple proxies, form operations are written out in terms of familiar algebraic operations on matrices, vectors, and scalars. This provides the basis for our implementation of the preconditioners in 4D. Extensive numerical experiments illustrate their performance, practical scalability, and parameter robustness, all in accordance with the theory.

Description

This is the pre-print version of the article.

Persistent Identifier

http://archives.pdx.edu/ds/psu/25348

Included in

Mathematics Commons

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