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Improving solve time of aggregation‐based adaptive AMG
Author(s) -
D'Ambra Pasqua,
Vassilevski Panayot S.
Publication year - 2019
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.2269
Subject(s) - mathematics , multigrid method , scalar (mathematics) , discretization , convergence (economics) , algorithm , vector valued function , reduction (mathematics) , partial differential equation , mathematical optimization , mathematical analysis , geometry , economics , economic growth
Summary This paper proposes improving the solve time of a bootstrap algebraic multigrid (AMG) designed previously by the authors. This is achieved by incorporating the information, a set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both memory and solve time. These savings with respect to the original bootstrap AMG are illustrated on some difficult (for standard AMG) linear systems arising from discretization of scalar and vector function elliptic partial differential equations in both 2D and 3D.