Mesh generation and refinement for FEM and BEM— A bibliography (1990–1993)

Mackerle, Jaroslav

doi:10.1016/0168-874x(93)90064-w

Cited by 14 publications

(7 citation statements)

References 182 publications

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“…Surveys of the literature in FEM include articles by Noor and Babus Ïka (1987), Oden and Demkovicz (1989), Haque (1992a, b), Babus Ïka andSuri (1994), and Ainsworth and Oden (1997). Mackerle (1993Mackerle ( , 1994 Zienkiewicz and Taylor (1989) includes a Chapter on``Error Estimation and Adaptivity'' (Chapter 14), which is supplemented by the papers by Zhu (1992a, b, 1994). Moreover, the book by Szabo Â and Babus Ïka (1991) is primarily dedicated to this subject.…”

Section: Motivation and Related Workmentioning

confidence: 98%

A methodology for adaptive finite element analysis: Towards an integrated computational environment

Paulino

Menezes

Neto

et al. 1999

Computational Mechanics

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This work introduces a methodology for selfadaptive 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 ®rst 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 ®nite element analysis, recovery procedures, error estimation/adaptivity and automatic mesh generation.Key words ®nite element analysis, error estimation, adaptivity, h-re®nement, sensitivity, superconvergent patch recovery (SPR), recovery by equilibrium in patches (REP), object oriented programming (OOP), interactive computer graphics. IntroductionThis work presents an integrated (object-oriented) computational environment for self-adaptive analyses of generic two-dimensional (2D) problems. This environment includes analysis procedures to insure a given level of accuracy according to certain criteria, and also the procedures to generate and modify the ®nite element discretization. This computational system, called FESTA (Finite Element System Technology in Adaptivity), involves ®ve main components (see shaded boxes in Figure 1):A graphical preprocessor, for de®ning the geometry of the problem, the initial ®nite element mesh (together with boundary conditions), and the main parameters used in a self-adaptive analysis. Here the geometrical model is dissociated from the ®nite element model. A ®nite element module for solving the current boundary value problem. The code has been developed so that it is highly modular, expandable, and user-friendly. Thus, it can be properly maintained and continued. Moreover, other users/developers should be able to modify the basic programming system to ®t their speci®c applications. An error estimation and sensitivity module. Discretization errors are estimated according to available recovery procedures, e.g. Zienkiewicz and Zhu (ZZ), superconvergent patch recovery (SPR) and recovery by equilibrium in patches (REP). Sensitivities of various orders (1st., 2nd. or higher) are calculated by means of...

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Section: Motivation and Related Workmentioning

confidence: 98%

A methodology for adaptive finite element analysis: Towards an integrated computational environment

Paulino

Menezes

Neto

et al. 1999

Computational Mechanics

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“…One of the most dicult problems in the pre-processing stage of numerical analyses is the discretization of the continuous physical problem by a grid. 1 This problem is known as mesh generation. The problem becomes more dicult as the domain of the problem becomes more complicated Ð for example, a non-simple tie domain with many cavities and subdomains.…”

Section: Introductionmentioning

confidence: 99%

Boundary spectral strip for geometries with arbitrary curvature

Michael

1998

Commun. Numer. Meth. Engng.

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SUMMARYThe non-element boundary spectral strip method is developed for solution of problems in curvature domains. The method, which uses a spectral Fourier approximation for expansion of the variables along the boundaries, shows an exponential convergence behaviour. A remarkable reduction in problem size and improved accuracy of results is achieved by the method as compared to the boundary element method. The method is illustrated by some physical problems from elastostatics. #

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“…Although signiÿcant progress has been made in three-dimensional (3-D) meshing algorithms (see, e.g. Reference [1]), the task of meshing a 3-D object with complicated geometry can be arduous, time consuming, computationally cumbersome and expensive. Such shortcomings are greatly ampliÿed when one considers problems with changing geometry such as crack propagation, ÿnite deformation, phase change or shape optimization.…”

Section: Introductionmentioning

confidence: 99%

A ‘pure’ boundary node method for potential theory

Gowrishankar

Mukherjee

2002

Commun. Numer. Meth. Engng.

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SUMMARYThe standard boundary node method (BNM) uses a (meshless) di use interpolation (in terms of neighbouring scattered boundary points) for the primary variables. The method is not 'truly meshless', however, since cells on the boundary of a body are used for integration. This paper presents a 'pure' version of the BNM in which integration cells are dispensed with. Instead (overlapping), regions of in uence (ROIs) of boundary nodes are used for integration. Initial results for 2-D potential theory, presented here, are encouraging.

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Mesh generation and refinement for FEM and BEM— A bibliography (1990–1993)

Cited by 14 publications

References 182 publications

A methodology for adaptive finite element analysis: Towards an integrated computational environment

A methodology for adaptive finite element analysis: Towards an integrated computational environment

Boundary spectral strip for geometries with arbitrary curvature

A ‘pure’ boundary node method for potential theory

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