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Localized Jacobian ILU preconditioners for hydraulic fractures
Author(s) -
Peirce A. P.
Publication year - 2005
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1528
Subject(s) - preconditioner , jacobian matrix and determinant , incomplete lu factorization , mathematics , fracture (geology) , boundary (topology) , operator (biology) , algebraic number , class (philosophy) , linear system , mathematical analysis , eigenvalues and eigenvectors , matrix decomposition , computer science , physics , geology , chemistry , geotechnical engineering , repressor , quantum mechanics , artificial intelligence , transcription factor , gene , biochemistry
We discuss the properties of a class of sparse localized approximations to the Jacobian operator that arises in modelling the evolution of a hydraulically driven fracture in a multi‐layered elastic medium. The governing equations involve a highly non‐linear coupled system of integro‐partial differential equations along with the fracture front free boundary problem. We demonstrate that an incomplete LU factorization of these localized Jacobians yields an efficient preconditioner for the fully populated, stiff, non‐symmetric system of algebraic equations that need to be solved multiple times for every growth increment of the fracture. The performance characteristics of this class of preconditioners is explored via spectral analysis and numerical experiment. Copyright © 2005 John Wiley & Sons, Ltd.