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An ILU preconditioner with coupled node fill‐in for iterative solution of the mixed finite element formulation of the 2D and 3D Navier‐Stokes equations
Author(s) -
Dahl O.,
Wille S. Ø
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650150503
Subject(s) - preconditioner , finite element method , jacobian matrix and determinant , mathematics , iterative method , navier–stokes equations , matrix (chemical analysis) , sparse matrix , mathematical analysis , mathematical optimization , physics , mechanics , materials science , quantum mechanics , gaussian , compressibility , composite material , thermodynamics
In the present paper, preconditioning of iterative equation solvers for the Navier‐Stokes equations is investigated. The Navier‐Stokes equations are solved for the mixed finite element formulation. The linear equation solvers used are the orthomin and the Bi‐CGSTAB algorithms. The storage structure of the equation matrix is given special attention in order to avoid swapping and thereby increase the speed of the preconditioner. The preconditioners considered are Jacobian, SSOR and incomplete LU preconditioning of the matrix associated with the velocities. A new incomplete LU preconditioning with fill‐in for the pressure matrix at locations in the matrix where the corner nodes are coupled is designed. For all preconditioners, inner iterations are investigated for possible improvement of the preconditioning. Numerical experiments are executed both in two and three dimensions.