Computational Mechanics, Vol. 23, No.5-6, pp.361-388.
G.H. Paulino,
Department of Civil & Environmental Engineering and Graduate Group in Applied
Mathematics (GGAM), University of California, Davis, CA 95616-5294, USA.
I.F. M. Menezes
TeCGraf (Computer Graphics Technology Group), PUC-Rio, Rio de Janeiro, R.J., 22453-900,
Brazil.
J. B. Cavalcante Neto & L.F. Martha,
Department of Civil Engineering, PUC-Rio, Rio de Janeiro, R.J., 22453-900, Brazil.
Abstract
This work introduces a methodology for self-adaptive numerical procedures, which relies on
the various components of an integrated, object-oriented, computational environment
involving pre-analysis, and post-processing modules. A basic platform for numerical
experiments and further development is provided, which allows implementation of new
elements/error estimators and sensitivity analysis. A general implementation of the
Superconvergent Patch Recovery (SPR) and the recently proposed Recovery by Equilibrium in
Patches (REP) is presented. Both SPR and REP are compared and used for error estimation
and for guiding the adaptive remeshing process. Moreover, the SPR is extended for
calculating sensitivity quantities of first and higher orders. The mesh (re-)generation
process is accomplished by means of modern methods combining quadtree and Delaunay
triangulation techniques. Surface mesh generation in arbitrary domains is performed
automatically (i.e. with no user intervention) during the self-adaptive analysis using
either quadrilateral or triangular elements. These ideas are implemented in the Finite
Element System Technology in Adaptivity (FESTA) software. The effectiveness and
versatility of FESTA are demonstrated by representative numerical examples illustrating
the interconnections among finite element analysis, recovery procedures, error
estimation/adaptivity and automatic mesh generation.
Key words: finite element analysis, error estimation, adaptivity, h-refinement, sensitivity, superconvergent patch recovery (SPR), recovery by equilibrium in patches (REP), object oriented programming (OOP), interactive computer graphics, mesh generation, Delaunay triangulation, advancing front method.
Representative Results
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Self-adaptive capabilities of FESTA | |
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FESTA: overview and analysis | |
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Finite element meshes from the self-adaptive analysis |