The generalized finite difference method for the inverse Cauchy problem in two-dimensional isotropic linear elasticity

Li, Po-Wei; Fu, Zhuojia; Gu, Yan; Song, Lina

doi:10.1016/j.ijsolstr.2019.06.001

Cited by 46 publications

(12 citation statements)

References 41 publications

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“…Thanks to this spare system, this method is highly efficient and suitable for the numerical simulations of large-scale problems. Many physical applications have been addressed by the GFDM, such as the thin elastic plate bending analysis [49], the electroelastic analysis of 3D piezoelectric structures [50], the acoustic wave propagation [51], the inverse Cauchy problem in 2D elasticity [52], the heat conduction problems [53], and the stationary flow in a dam [54].…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

Wang

Kim

2022

Mathematics

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In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation is based on the Crank–Nicolson scheme. A boundary value problem in space with the Dirichlet or mixed boundary condition is then formed at each time node, which is simulated by introducing the GFDM. The proposed algorithm is truly meshless and easy to program. Four linear or nonlinear numerical examples, including ones with complicated geometry domains, are provided to verify the performance of the developed approach, and the results illustrate the good accuracy and convergency of the method.

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Section: Introductionmentioning

confidence: 99%

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

Wang

Kim

2022

Mathematics

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“…The local methods compute the solutions at particular points; in contrast, the global ones obtain the solutions overall the problem domain 6,7 . For example, the finite element and finite difference methods are local, 8‐13 while the spectral methods are global 14‐18 . The spectral methods gained importance due to their high convergence speed, accuracy, and applicability to either bounded or unbounded domains 16‐19 .…”

Section: Introductionmentioning

confidence: 99%

Accurate spectral algorithm for two‐dimensional variable‐order fractional percolation equations

Abdelkawy

Mahmoud

Abualnaja

et al. 2021

Math Methods in App Sciences

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A highly accurate spectral algorithm for (2 + 1) fractional percolation equations with variable order (VO‐FPEs) is considered. We propose a shifted Legendre–Gauss–Lobatto collocation (SL‐GL‐C) method in conjunction with shifted Chebyshev–Gauss–Radau collocation (SC‐GR‐C) method to solve the two‐dimensional VO‐FPEs. A complete theoretical formulation is presented, and numerical results are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle VO‐FPEs is revealed, even when dealing with non‐smooth time solutions.

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“…The local methods listed the approximate solution at specific points, while the global methods give the approximate solution in whole the mentioned interval. The numerical approximations for differential equations [1][2][3][4] are listed at specific points using finite difference methods. While the finite element methods subdivide the whole interval into subintervals and give the approximate solution in them.…”

Section: Introductionmentioning

confidence: 99%

A Spectral Collocation Technique for Riesz Fractional Chen-Lee-Liu Equation

Abdelkawy

Alyami

2021

Journal of Function Spaces

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This paper discusses the study of optical solitons that are modeled by Riesz fractional Chen-Lee-Liu model, one of the versions of the famous nonlinear Schrödinger equation. This model is solved by the assistance of consecutive spectral collocation technique with two independent approaches. The first is the approach of the spatial variable, while the other is the approach of the temporal variable. It is concluded that the method of the current paper is far more efficient and credible for the proposed problem. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.

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The generalized finite difference method for the inverse Cauchy problem in two-dimensional isotropic linear elasticity

Cited by 46 publications

References 41 publications

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions

Accurate spectral algorithm for two‐dimensional variable‐order fractional percolation equations

A Spectral Collocation Technique for Riesz Fractional Chen-Lee-Liu Equation

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