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Accelerated gradient flows for large bending deformations of nonlinear plates

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arxiv 2402.12152 v2 pith:CHAZRJ6A submitted 2024-02-19 math.NA cs.NA

Guozhi Dong , Hailong Guo , Shuo Yang This is my paper · ORCID
classification math.NAcs.NA
keywords flowsgradientplatesacceleratedalgorithmsbendingnonlinearaccuracy
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In this paper, we propose novel algorithms integrated projection-free techniques with accelerated gradient flows to minimize bending energies for nonlinear plates with non-convex metric constraints. We discuss the stability and constraint consistency in a semi-discrete setting for both bilayer and prestrained plates. The proposed algorithms exhibit substantial improvements in efficiency and accuracy compared to the current state-of-the-art methods based on gradient flows.

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  1. Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs

    math.AP 2024-12 conditional novelty 7.0 of 10

    The accelerated Allen-Cahn equation formally converges to the hyperbolic interface law ∂_t v = (1-v^2)(h-αv), and a large-step FISTA discretization empirically accelerates Ginzburg-Landau minimization.

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