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Use of the over‐relaxation technique in the simulation of large groundwater basins by the finite element method
Author(s) -
Gambolati Giuseppe
Publication year - 1975
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.1620090116
Subject(s) - relaxation (psychology) , instability , finite element method , dimension (graph theory) , transient (computer programming) , dynamic relaxation , relaxation technique , matrix (chemical analysis) , stability (learning theory) , groundwater , computer science , mechanics , mathematics , geology , physics , geotechnical engineering , geometry , engineering , structural engineering , chemistry , pathology , chromatography , alternative medicine , operating system , psychology , social psychology , machine learning , medicine , pure mathematics
The over‐relaxation technique has been used in conjunction with the finite element method in a regional time‐dependent simulation of the subsidence of Venice. One year of computer experiments have shown that in basins with a ratio h/R ⩽ 10 −2 between the vertical and the horizontal dimension, the over‐relaxation technique can lead to unsatisfactory results. In single precision and for relatively large time steps, the solution of the final linear system can be inaccurate if the optimum over‐relaxation factor ω is not correctly assessed. In transient analyses, instability can also occur. The latter may be avoided by properly reducing the time step or by switching to double precision. Steady state simulations can also require double precision to provide accurate results even when the best ω is used. Instability and inaccuracy disappear in basins for which h/R ⩾ 10 −1 . In addition the processor time diminishes significantly as in this case the number of iterations necessary to obtain a good solution is considerably smaller than the order of the matrix.