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Proceedings Paper

Spurious oscillations in computing microstructures
Author(s): David S. Kinderlehrer; Roy A. Nicolaides; Han Wang
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Paper Abstract

The purpose of this paper is to discuss some numerical difficulties in a two-dimensional mathematical model for displacive phase transformations. The usual approach to discretizing this model uses finite elements. Some previous work has computed certain microstructures by using a uniform square mesh discretization together with a form of derivative averaging. The overall scheme is equivalent to using bilinear elements with a one point quadrature approximation to discretize the energy functional E below. The resulting functional will be denoted by Eh. Although the square mesh respects a key symmetry property of the energy functional, when using this technique we have found a computational 'skewing' problem. This problem has a deleterious effect on the numerical solutions since it generates a grid scale spurious oscillation. In this paper, we will study this skewing phenomenon and attempt to show its effect on the computed microstructure.

Paper Details

Date Published: 22 July 1993
PDF: 9 pages
Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); doi: 10.1117/12.148418
Show Author Affiliations
David S. Kinderlehrer, Carnegie Mellon Univ. (United States)
Roy A. Nicolaides, Carnegie Mellon Univ. (United States)
Han Wang, Carnegie Mellon Univ. (United States)


Published in SPIE Proceedings Vol. 1919:
Smart Structures and Materials 1993: Mathematics in Smart Structures
H. Thomas Banks, Editor(s)

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