RETRACTED: A hybrid Finite element-Meshfree method based on partition of unity for transient wave propagation problems in homogeneous and inhomogeneous media

In this work, the edge-based smoothed finite element method (ES-FEM) is incorporated with the Bathe time integration scheme to solve the transient wave propagation problems. The edge-based gradient smoothing technique (GST) can properly soften the “overly soft” system matrices from the standard finite element approach; then, the spatial numerical dispersion error of the calculated solutions for wave problems can be significantly reduced. To effectively solve the transient wave propagation problems, the Bathe time integration scheme is employed to perform the involved time integration. Due to the appropriate “numerical dissipation effects” from the Bathe time integration method, the spurious oscillations in the relatively large wave numbers (high frequencies) can be effectively suppressed; then, the temporal numerical dispersion error in the calculated solutions can also be notably controlled. A number of supporting numerical examples are considered to examine the capabilities of the present approach. The numerical results show that ES-FEM works very well with the Bathe time integration technique, and much more numerical solutions can be reached for solving transient wave propagation problems compared to the standard FEM.

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“…Following the basic finite element discretizations [47,48], we can obtain the corresponding matrix form of (1):…”

Section: Formulation Of the Edge-based Smoothed Fem For Wave Problemsmentioning

confidence: 99%

“…For the time-independent form of the wave equation, the following matrix equation can be obtained without considering the boundary condition [47,48]:…”

Section: Dispersion Error From Spatial Discretizationmentioning

confidence: 99%

Transient Wave Propagation Dynamics with Edge-Based Smoothed Finite Element Method and Bathe Time Integration Technique

Chai

Zhang

2020

Mathematical Problems in Engineering

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“…On the other hand, researchers and scientists also find ways to improve the existing meshbased methods in meshfree directions. The hybrid finite element-meshfree method ( [15], [16]), the meshfree finite volume method (FVM) ( [17]) and the meshfree finite difference method ( [18]). There is also an innovative approach being suggested to solve the mesh nodes and the meshfree points which are arbitrarily mixed in the computational domain using FVM ( [19], [20]).…”

Section: Introductionmentioning

confidence: 99%

An Improved Finite Cloud Method With Uniformly Distributed Clouds and Enhanced Boundary Conditions

Oh¹,

Hang²

2023

Int. J. Anal. Appl.

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Finite cloud method (FCM) employs the fixed kernel reproducing technique to construct the interpolation function and point collocation approach is adopted for the discretization. In this study, an improved FCM is proposed such that a node of interest is approximated with its nearest cloud. This feature enables a set of uniformly distributed clouds of various densities such that all the information in the problem domain is captured and stored in the clouds. Additionally, the instability of FCM near the boundaries is treated by having the boundary nodes also satisfy the governing differential equation. Besides, a splitting mechanism is suggested for the node refinement to improve the accuracy of solution. Parameters are introduced to control the density of clouds and the singularity of the moment matrices associated with the clouds. Thus, a more controllable numerical simulation is developed. Numerical examples are presented and the results have shown that the improved FCM produces a stable and better accuracy of solution.

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“…Sandia National Laboratories estimates that over 80% of the total analysis time is allocated to preprocessing [9]. To alleviate the preprocessing burden, researchers have proposed several alternative approaches, such as the boundary element method (BEM) [10], the isogeometric analysis (IGA) [11], the meshfree method [12][13][14], and deep neural networks (DNNs).…”

Section: Introductionmentioning

confidence: 99%

A PSBFEM Approach for Solving Seepage Problems Based on the Pixel Quadtree Mesh

Yan,

Yang,

Zhang

et al. 2023

Geofluids

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This paper presents a PSBFEM approach that integrates the quadtree mesh generation technique based on digital images for solving seepage problems. The quantitative representation of the distribution of geometrical information and material parameters is achieved by utilizing the color intensity of each pixel, which can then be applied to seepage analysis. The presented method addresses the issue of hanging nodes by treating them as nodes of a polygonal element. We validate the proposed technique by solving three benchmark seepage problems. Results show that the image-based domain can be automatically discretized using a quadtree decomposition of the images. Furthermore, the computational efficiency and precision of the PSBFEM surpass that of the standard FEM. Therefore, the proposed technique allows for the convenient automatic discretization of the domain using pixel meshes to solve seepage problems in engineering applications.

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RETRACTED: A hybrid Finite element-Meshfree method based on partition of unity for transient wave propagation problems in homogeneous and inhomogeneous media

Cited by 10 publications

References 34 publications

Transient Wave Propagation Dynamics with Edge-Based Smoothed Finite Element Method and Bathe Time Integration Technique

Transient Wave Propagation Dynamics with Edge-Based Smoothed Finite Element Method and Bathe Time Integration Technique

An Improved Finite Cloud Method With Uniformly Distributed Clouds and Enhanced Boundary Conditions

A PSBFEM Approach for Solving Seepage Problems Based on the Pixel Quadtree Mesh

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