Additive Average Schwarz with Adaptive Coarse Space for Morley FE
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We propose an additive average Schwarz preconditioner with two adaptively enriched coarse space for the nonconforming Morley finite element method for fourth order biharmonic equation with highly varying and discontinuous coefficients. In this paper, we extend the work of [9, 10]: (additive average Schwarz with adaptive coarse spaces: scalable algorithms for multiscale problems). Our analysis shows that the condition number of the preconditioned problem is bounded independent of the jump of the coefficient, and it depends only on the ratio of the coarse to the fine mesh.
KeywordsAdditive average Schwarz Nonconforming finite element Domain decomposition methods Fourth order problems with highly varying coefficients
The authors are deeply thankful for Prof. Talal Rahman for his invaluable comments, discussions, and suggestions in this work.
- 2.Bjørstad, P.E., Dryja, M., Vainikko, E.: Additive Schwarz methods without subdomain overlap and with new coarse spaces. In: 1995 Domain Decomposition Methods in Sciences and Engineering, Beijing, pp. 141–157 (1997)Google Scholar
- 5.Ciarlet, P.G.: Basic error estimates for elliptic problems. In: Handbook of Numerical Analysis, vol. II, pp. 17–351. North-Holland, Amsterdam (1991)Google Scholar
- 9.Marcinkowski, L., Rahman, T.: Two new enriched multiscale coarse spaces for the additive average Schwarz method. In: Lee, C.-O., et al. (eds.) Domain Decomposition Methods in Science and Engineering XXIII. LNCSE, vol. 116, pp. 389–396. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-52389-7_40CrossRefGoogle Scholar