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Abstract data structures for a finite element package.: Design principles of ALBERT
Author(s) -
Schmidt A.,
Siebert K. G.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19990791313
Subject(s) - finite element method , polygon mesh , toolbox , dimension (graph theory) , computer science , degrees of freedom (physics and chemistry) , data structure , adaptive mesh refinement , element (criminal law) , theoretical computer science , computational science , algorithm , mathematics , programming language , structural engineering , engineering , pure mathematics , computer graphics (images) , physics , quantum mechanics , law , political science
Abstract Albert is an Adaptive multi‐Level finite element toolbox using Bisectioning refinement and Error control by Residual Techniques. Its design is based on appropriate data structures holding geometrical, finite element, and algebraic information. Using such data structures, abstract adaptive methods for stationary and tame dependent problems, assembly tools for discrete systems, and dimension dependent tasks like mesh modifications can be provided in a library. This allows dimension‐independent development and programming of a general class of applications. In ALBERT, hierarchical 2d and 3d meshes are stored in binary trees. Several sets of finite elements can be used on the same mesh, either using predefined ones, or by adding new sets for special applications. Depending on the currently used finite element spaces, all degrees of freedom are automatically managed during mesh modifications.