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The domain composition method applied to Poisson's equation in two dimensions
Author(s) -
Charlesworth W. W.,
Cox J. J.,
Anderson D. C.
Publication year - 1994
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.1620371806
Subject(s) - finite element method , mixed finite element method , extended finite element method , polygon mesh , domain (mathematical analysis) , smoothed finite element method , poisson's equation , finite element limit analysis , mathematics , boundary knot method , hp fem , computer science , mathematical analysis , algorithm , geometry , mathematical optimization , structural engineering , engineering , boundary element method
Domain composition, a recently described method for formulating continuum field problems, removes certain restrictions on the construction of finite element models such that it is possible to solve a finite element problem without using a global compatible mesh. The domain composition method couples or otherwise constrains meshes in local regions to obtain a solution equivalent to that produced by conventional finite element methods. In particular, the domain composition method enables finite element models to be formulated with overlapping elements. Several advantages come from this, including an ability to automatically generate a finite element model from a solid geometric model, an ability to use a variety of element types in a single finite element model and an ability to exactly match element boundaries to the local geometry. This paper shows in detail a finite element formulation of Poisson's equation using domain composition and presents certain key algorithms that incorporate the domain composition method into well‐established finite element procedures.