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.
Accelerated gradient flows for large bending deformations of nonlinear plates
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abstract
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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2024 1verdicts
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Momentum-based minimization of the Ginzburg-Landau functional on Euclidean spaces and graphs
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.