Numerical analysis for a nonlinear model of elastic strings with moving ends

Coupled parabolic-hyperbolic system often appears in the studies of thermoelasticity, magnetoelasticity, biological problems and radiation hydrodynamics with high temperature. In this paper, we investigate a problem of thermal diffusion in elastic body with moving boundary. Three numerical methods, two uncoupled and one coupled, all with quadratic convergence order in time and space, are presented and compared in relation to the execution time. Tables and figures of the approximate solution are shown to verify the efficiency and feasibility of the proposed method. In addition, we show that the numerical results are consistent with the theoretical results. The approximate numerical solutions are calculated using the finite element method in spatial variable and finite difference method in time. To compare different numerical schemes, we show the convergence rates through numerical simulations with calculated error and the execution time. KEYWORDScoupled and uncoupled method, finite elements method, moving boundary, numerical simulation, thermal diffusion INTRODUCTIONThe thermal diffusion in elastic body is governed by a coupled system of hyperbolic-parabolic equations. In [1], the theory was developed using the coupled thermoelastic model. Uniqueness and reciprocity theorems for the generalized problem of thermal diffusion in elastic body in isotropic media, was proved in [2], under restrictive assumptions on the elastic coefficients. In these works, one

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“…Let also the moving boundary defined by the function (other nonlinear boundary types can be found, for example in [17,18]):…”

Section: Examplementioning

confidence: 99%

Numerical methods for a problem of thermal diffusion in elastic body with moving boundary

Madureira

Rincon

Teixeira

2021

Numerical Methods Partial

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“…A neural network model [46][47][48] is designed to obtain smoothness parameter using image quality parameters.…”

Section: The Calculation Of Smoothness Parametermentioning

confidence: 99%

An Adaptive Smoothness Parameter Strategy for Variational Optical Flow Model

Alsharif

Shu

Zhu

et al. 2021

Scientific Programming

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The smoothness parameter is used to balance the weight of the data term and the smoothness term in variational optical flow model, which plays very significant role for the optical flow estimation, but existing methods fail to obtain the optimal smoothness parameters (OSP). In order to solve this problem, an adaptive smoothness parameter strategy is proposed. First, an amalgamated simple linear iterative cluster (SLIC) and local membership function (LMF) algorithm is used to segment the entire image into several superpixel regions. Then, image quality parameters (IQP) are calculated, respectively, for each superpixel region. Finally, a neural network model is applied to compute the smoothness parameter by these image quality parameters of each superpixel region. Experiments were done in three public datasets (Middlebury, MPI_Sintel, and KITTI) and our self-constructed outdoor dataset with the proposed method and other existing classical methods; the results show that our OSP method achieves higher accuracy than other smoothness parameter selection methods in all these four datasets. Combined with the dual fractional order variational optical flow model (DFOVOFM), the proposed model shows better performance than other models in scenes with illumination inhomogeneity and abnormity. The OSP method fills the blank of the research of adaptive smoothness parameter, pushing the development of the variational optical flow models.

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