Spurious oscillations in computing microstructures

David S. Kinderlehrer; Roy A. Nicolaides; Han Wang

doi:10.1117/12.148418

22 July 1993 Spurious oscillations in computing microstructures

David S. Kinderlehrer, Roy A. Nicolaides, Han Wang

Proceedings Volume 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures; (1993) https://doi.org/10.1117/12.148418
Event: 1993 North American Conference on Smart Structures and Materials, 1993, Albuquerque, NM, United States

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 E_h. 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.

Citation Download Citation

David S. Kinderlehrer, Roy A. Nicolaides, and Han Wang "Spurious oscillations in computing microstructures", Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); https://doi.org/10.1117/12.148418

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