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Abstract: We study the high-contrast biharmonic plate equation with HCT and Morleydiscretizations. We construct a preconditioner that is robust with respect tocontrast size and mesh size simultaneously based on the preconditioner proposedby Aksoylu et al. 2008, Comput. Vis. Sci. 11, pp. 319-331. By extending thedevised singular perturbation analysis from linear finite elementdiscretization to the above discretizations, we prove and numericallydemonstrate the robustness of the preconditioner. Therefore, we accomplish adesirable preconditioning design goal by using the same family ofpreconditioners to solve elliptic family of PDEs with varying discretizations.We also present a strategy on how to generalize the proposed preconditioner tocover high-contrast elliptic PDEs of order $2k, k>2$. Moreover, we prove afundamental qualitative property of solution of the high-contrast biharmonicplate equation. Namely, the solution over the highly-bending island becomes alinear polynomial asymptotically. The effectiveness of our preconditioner islargely due to the integration of this qualitative understanding of theunderlying PDE into its construction.



Author: Burak Aksoylu, Zuhal Yeter

Source: https://arxiv.org/



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