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Algebraic multigrid for k ‐form Laplacians
Author(s) -
Bell Nathan,
Olson Luke N.
Publication year - 2008
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.577
Subject(s) - mathematics , multigrid method , algebraic number , context (archaeology) , generality , commutative property , algebra over a field , finite element method , pure mathematics , mathematical analysis , partial differential equation , psychology , paleontology , physics , psychotherapist , biology , thermodynamics
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.