Algebraic multigrid for k-form Laplacians

Nathan Bell, Luke N. Olson

Research output: Contribution to journalArticle

Abstract

In this paper we describe an aggregation-based algebraic multigrid method for the solution of discrete k-form Laplacians. Our work generalizes Reitzinger and Schöberl's algorithm to higher-dimensional discrete forms. We provide conditions on the tentative prolongators under which the commutativity of the coarse and fine de Rham complexes is maintained. Further, a practical algorithm that satisfies these conditions is outlined, and smoothed prolongation operators and the associated finite element spaces are highlighted. Numerical evidence of the efficiency and generality of the proposed method is presented in the context of discrete Hodge decompositions.

Original languageEnglish (US)
Pages (from-to)165-185
Number of pages21
JournalNumerical Linear Algebra with Applications
Volume15
Issue number2-3 SPEC. ISS.
DOIs
StatePublished - Mar 1 2008

Keywords

  • Algebraic multigrid
  • Discrete forms
  • Hodge decomposition
  • Mimetic methods
  • Whitney forms

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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