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On Object-Oriented Programming techniques for adaptive
finite element grids
E J Holm¹ & H P Langtangen
¹ Institute for Energy Technology,
P.O. Box 40, N-2007 Kjeller, Norway.
Email: { tt Erik.Holm@ife.no
Abstract
We describe a grid refinement technique for tensor product elements of
Lagrange-type in an arbitray number of space dimensions.
The grid is implemented as a C++ subclass of a grid class for standard
(unstructured) finite element grids. Using object-oriented programming,
the new adaptive grid can very easily be utilized by existing finite
element solvers.
The use of C++ also simplifies the handling of the cascade of grids
involved solving dynamic problems, using many levels of refinement.
The refinement algorithm leads to irregular nodes and associated
constraint equations. We present a simple and general way of handling
such constraint equations.
For the advection of a 2D concentration spot
we evaluate the performance of the dynamic adaptive
grid. A 3D Poisson equation problem with singularities is also discussed.
Moreover, we investigate the efficiency of various nodal numbering
strategies for the adaptive grids and their influence on incomplete
factorization preconditioners.
Last modified Fri Jun 21 19:19:13 GB-Eire 1996
(DBD)