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An Adaptive Generalized Multiscale Finite Element Method Based Two-Grid Preconditioner for Large Scale High-Contrast Linear Elasticity Problems

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Abstract

In this paper, we propose an efficient and robust two-grid preconditioner for the linear elasticity equation with high contrasts. To tackle the challenges imposed by multiple scales and high-contrast, a coarse space (to form the coarse preconditioner) is constructed via a carefully designed spectral problem within the framework of the GMsFEM (Generalized Multiscale Finite Element Method). The dimension of coarse space can be adaptively controlled by a predefined eigenvalue tolerance. We also consider linear elasticity problems with stochastic coefficients and an efficient preconditioner with parameter-independent multiscale basis is proposed. The logarithm of Young’s modulus is decomposed using a truncated Karhunen–Lo\(\grave{e}\)ve expansion, and some sample parameters are used to generate the multiscale basis. Numerical results of both 2D and 3D examples demonstrate that our proposed preconditioner is robust with respect to the contrast of the material and highly efficient for large-scale elasticity problems.

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Funding

Yanfang Yang’s work is supported by the National Natural Science Foundation of China (Grant No. 11901129), Basic Research Project of Guangzhou, and Introduction of talent research start-up fund at Guangzhou University. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, People’s Republic of China

    Yanfang Yang

  2. Department of Mathematics, University of Wisconsin-Madison, Madison, WI, USA

    Shubin Fu

  3. Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, People’s Republic of China

    Eric T. Chung

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  1. Yanfang Yang
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  2. Shubin Fu
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  3. Eric T. Chung
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Correspondence to Shubin Fu.

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Yang, Y., Fu, S. & Chung, E.T. An Adaptive Generalized Multiscale Finite Element Method Based Two-Grid Preconditioner for Large Scale High-Contrast Linear Elasticity Problems. J Sci Comput 92, 21 (2022). https://doi.org/10.1007/s10915-022-01869-w

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  • DOI: https://doi.org/10.1007/s10915-022-01869-w

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