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ENGINEERING COMPUTATIONAL TECHNOLOGY
Edited by: B.H.V. Topping, Z. Bittnar
Projection Techniques embedded in the PCGM for handling Hanging Nodes and Boundary Restrictions
Faculty of Mathematics, Technical University of Chemnitz, Germany
A. Meyer, "Projection Techniques embedded in the PCGM for handling Hanging Nodes and Boundary Restrictions", in B.H.V. Topping, Z. Bittnar, (Editors), "Engineering Computational Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 7, pp 147-165, 2002. doi:10.4203/csets.8.7
Keywords: finite elements, adaptive work, preconditioned conjugate gradient.
We look for efficient implementations of adaptive finite element simulations for problems in mechanics and physics. Here, efficient means both with respect to memory requirements and with respect to time.
The first wish "low memory" requires data structures which allow quick execution of the main tasks
In our experiments we have defined three data structures:
For completing a finite element calculation on these data structures, we have to incorporate special projection procedures for handling "hanging nodes", (a necessary tool for most simple refinement ideas) and for all kinds of restrictions from boundary conditions.
We give a special variant of the well-known Preconditioned Conjugate Gradient Method running in a subspace of , which is defined from a special projection . Then we describe the structure of the projector for solving these problems for linear and qudratic elements:
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