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Additive Schwarz‐type preconditioners for fourth‐order elliptic problems using Hermite cubic splines
Author(s) -
Liu SongTao
Publication year - 2006
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20089
Subject(s) - mathematics , hermite polynomials , preconditioner , linear subspace , schwarz alternating method , type (biology) , additive schwarz method , elliptic partial differential equation , hermite spline , partial derivative , order (exchange) , cubic hermite spline , pure mathematics , partial differential equation , mathematical analysis , domain decomposition methods , smoothing spline , finite element method , linear system , spline interpolation , polynomial , bilinear interpolation , ecology , biology , thermodynamics , statistics , physics , finance , nearest neighbor interpolation , economics , linear interpolation
Abstract In this note, we construct the additive Schwarz‐type preconditioner for fourth‐order elliptic problems with nested subspaces from Hermite cubic splines. We prove that after the preconditioning, the system is well conditioned. The numerical evidence strongly supports our theoretical result. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006