Algebraic multigrid for k-form Laplacians

Authors

  • Nathan Bell,

    Corresponding author
    1. Siebel Center for Computer Science, University of Illinois at Urbana-Champaign, 201 North Goodwin Avenue, Urbana, IL 61801, U.S.A.
    • Siebel Center for Computer Science, University of Illinois at Urbana-Champaign, 201 North Goodwin Avenue, Urbana, IL 61801, U.S.A.
    Search for more papers by this author
  • Luke N. Olson

    1. Siebel Center for Computer Science, University of Illinois at Urbana-Champaign, 201 North Goodwin Avenue, Urbana, IL 61801, U.S.A.
    Search for more papers by this author

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. Copyright © 2008 John Wiley & Sons, Ltd.

Ancillary