Premium
AN ADAPTIVE UNSTRUCTURED TRI‐TREE ITERATIVE SOLVER FOR MIXED FINITE ELEMENT FORMULATION OF THE STOKES EQUATIONS
Author(s) -
WILLE S. Ø.
Publication year - 1996
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/(sici)1097-0363(19960515)22:9<899::aid-fld385>3.0.co;2-l
Subject(s) - preconditioner , solver , finite element method , iterative method , multigrid method , grid , mathematics , computer science , mathematical optimization , computational science , partial differential equation , geometry , mathematical analysis , physics , thermodynamics
An iterative adaptive equation solver for solving the implicit Stokes equations simultaneously with tri‐tree grid generation is developed. The tri‐tree grid generator builds a hierarchical grid structure which is mapped to a finite element grid at each hierarchical level. For each hierarchical finite element grid the Stokes equations are solved. The approximate solution at each level is projected onto the next finer grid and used as a start vector for the iterative equation solver at the finer level. When the finest grid is reached, the equation solver is iterated until a tolerated solution is reached. In order to reduce the overall work, the element matrices are integrated analytically beforehand. The efficiency and behaviour of the present adaptive method are compared with those of the previously developed iterative equation solver which is preconditioned by incomplete LU factorization with coupled node fill‐in. The efficiency of the incomplete coupled node fill‐in preconditioner is shown to be largely dependent on the global node numbering. The preconditioner is therefore tested for the natural node ordering of the tri‐tree grid generator and for different ways of sorting the nodes.