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Finite element solution of three‐dimensional incompressible fluid flow problems by a preconditioned conjugate residual method
Author(s) -
Robichaud Michel P.,
Tanguy Philippe A.
Publication year - 1987
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.1620240211
Subject(s) - incomplete lu factorization , conjugate residual method , mathematics , finite element method , residual , conjugate gradient method , incomplete cholesky factorization , factorization , newton's method , conjugate , generalized minimal residual method , linear system , matrix (chemical analysis) , mathematical analysis , mathematical optimization , algorithm , matrix decomposition , computer science , eigenvalues and eigenvectors , physics , materials science , engineering , structural engineering , gradient descent , quantum mechanics , machine learning , nonlinear system , composite material , artificial neural network
A new algorithm for the solution of the three‐dimensional Navier–Stokes equation using the mixed formulation and an incomplete factorization technique is presented. The linear system obtained at each modified Newton–Raphson iteration is solved by the preconditioned conjugate residual method (PCR) using an out‐of‐core incomplete LU factorization as preconditioning. This factorization is performed on a matrix stored by a new static storage method called the packed skyline method. The performance of the proposed algorithm is assessed for the wall‐driven cubic cavity problem using the Q 1 +− P 1 enriched element.