Advances on Mesh and Dimension Reduction Methods

Submission Deadline: 01 February 2024 (closed) View: 186

Guest Editors

Prof. Leiting Dong, Beihang University, China
Prof. Zhuojia Fu, Hohai University, China
Dr. Elena Atroshchenko, University of New South Wales, Australia
Prof. Mingjing Li, Beihang University, China

Summary

Numerical simulation methods have been increasingly used as important and powerful tools for solving science and engineering problems during the past decades, thanks to the rapid development of advanced algorithms and computer technology. Nowadays, as the problems to be solved are becoming larger in scale and more complex in mathematical descriptions, conventional mesh-based finite element and finite volume methods have encountered significant difficulties. Alternatively, a large number of meshless and mesh/dimension reduction methods have been developed.

Besides avoiding or reducing the domain discretization using volume elements, these methods have exhibited advantages for various types of problems. For example, boundary element method is advantageous for the modeling of physics in infinitely-large domains and problems involving degenerate/moving boundaries, meshless methods are very useful for solving large deformation problems, and particle methods are powerful in solving extreme fluid dynamic problems. Due to their unique features, these methods have attracted great attention and been applied successfully in many fields of science and engineering, e.g. fluid dynamics, fracture mechanics, electromagnetic waves, etc.

You are invited to submit original research papers or review papers to this special issue with subjects covering the entire range from theory to application of mesh and dimension reduction methods. Topics of interest include but are not restricted to:

- Boundary element method

- Element-free Galerkin method

- Meshless local Petrov Galerkin method

- Smoothed particle hydrodynamics

- Material point method

- Boundary-type meshless methods

- Generalized finite difference method

- Collocation meshless method

- Peridynamics

- Fragile Points Method

- Isogeometric Method

- Combination of different methods

- Advanced implementation of mesh reduction methods

- Application of mesh reduction methods in realistic applications

Keywords

Boundary element method; Meshless method; Particle method; Isogeometric method; Complex science and engineering problems.

Published Papers

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Open Access

ARTICLE

Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials
Xu Xu, Xiaoteng Wang, Haitian Yang, Zhenjun Yang, Yiqian He
CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1831-1861, 2024, DOI:10.32604/cmes.2024.048199
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms (DOFs). A basic framework of the Multiscale Scaled Boundary Finite Element Method (MsSBFEM) was presented in our previous works, but those works only addressed two-dimensional problems. In order to solve more realistic problems, a three-dimensional MsSBFEM is further developed in this article. In the proposed method, the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales, the three-dimensional image-based analysis can be conveniently… More >

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A Novel Accurate Method for Multi-Term Time-Fractional Nonlinear Diffusion Equations in Arbitrary Domains
Tao Hu, Cheng Huang, Sergiy Reutskiy, Jun Lu, Ji Lin
CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1521-1548, 2024, DOI:10.32604/cmes.2023.030449
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract A novel accurate method is proposed to solve a broad variety of linear and nonlinear (1+1)-dimensional and (2+1)- dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity. For (1+1)-dimensional problems, analytical solutions that satisfy the boundary requirements are derived. Such solutions are numerically calculated using the trigonometric basis approximation for (2+1)-dimensional problems. With the aid of these analytical or numerical approximations, the original problems can be converted into the fractional ordinary differential equations, and solutions to the fractional ordinary differential equations are approximated by modified radial basis functions with time-dependent coefficients. An More >

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ARTICLE

Boundary Element Analysis for Mode III Crack Problems of Thin-Walled Structures from Micro- to Nano-Scales
Bingrui Ju, Wenzhen Qu, Yan Gu
CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2677-2690, 2023, DOI:10.32604/cmes.2023.025886
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract This paper develops a new numerical framework for mode III crack problems of thin-walled structures by integrating multiple advanced techniques in the boundary element literature. The details of special crack-tip elements for displacement and stress are derived. An exponential transformation technique is introduced to accurately calculate the nearly singular integral, which is the key task of the boundary element simulation of thin-walled structures. Three numerical experiments with different types of cracks are provided to verify the performance of the present numerical framework. Numerical results demonstrate that the present scheme is valid for mode III crack More >

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ARTICLE

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains
Chengxin Zhang, Chao Wang, Shouhai Chen, Fajie Wang
CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2407-2424, 2023, DOI:10.32604/cmes.2023.024884
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of More >

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A Modified Formulation of Singular Boundary Method for Exterior Acoustics
Yi Wu, Zhuojia Fu, Jian Min
CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 377-393, 2023, DOI:10.32604/cmes.2022.023205
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract This paper proposes a modified formulation of the singular boundary method (SBM) by introducing the combined Helmholtz integral equation formulation (CHIEF) and the self-regularization technique to exterior acoustics. In the SBM, the concept of the origin intensity factor (OIF) is introduced to avoid the singularities of the fundamental solutions. The SBM belongs to the meshless boundary collocation methods. The additional use of the CHIEF scheme and the self-regularization technique in the SBM guarantees the unique solution of the exterior acoustics accurately and efficiently. Consequently, by using the SBM coupled with the CHIEF scheme and the More >

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ARTICLE

Application of Smoothed Particle Hydrodynamics (SPH) for the Simulation of Flow-Like Landslides on 3D Terrains
Binghui Cui, Liaojun Zhang
CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.1, pp. 357-376, 2023, DOI:10.32604/cmes.2022.022309
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract Flow-type landslide is one type of landslide that generally exhibits characteristics of high flow velocities, long jump distances, and poor predictability. Simulation of its propagation process can provide solutions for risk assessment and mitigation design. The smoothed particle hydrodynamics (SPH) method has been successfully applied to the simulation of two-dimensional (2D) and three-dimensional (3D) flow-like landslides. However, the influence of boundary resistance on the whole process of landslide failure is rarely discussed. In this study, a boundary condition considering friction is proposed and integrated into the SPH method, and its accuracy is verified. Moreover, the… More >
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ARTICLE

The Localized Method of Fundamental Solution for Two Dimensional Signorini Problems
Zhuowan Fan, Yancheng Liu, Anyu Hong, Fugang Xu, Fuzhang Wang
CMES-Computer Modeling in Engineering & Sciences, Vol.132, No.1, pp. 341-355, 2022, DOI:10.32604/cmes.2022.019715
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract In this work, the localized method of fundamental solution (LMFS) is extended to Signorini problem. Unlike the traditional fundamental solution (MFS), the LMFS approximates the field quantity at each node by using the field quantities at the adjacent nodes. The idea of the LMFS is similar to the localized domain type method. The fictitious boundary nodes are proposed to impose the boundary condition and governing equations at each node to formulate a sparse matrix. The inequality boundary condition of Signorini problem is solved indirectly by introducing nonlinear complementarity problem function (NCP-function). Numerical examples are carried More >

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ARTICLE

Weakly Singular Symmetric Galerkin Boundary Element Method for Fracture Analysis of Three-Dimensional Structures Considering Rotational Inertia and Gravitational Forces
Shuangxin He, Chaoyang Wang, Xuan Zhou, Leiting Dong, Satya N. Atluri
CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1857-1882, 2022, DOI:10.32604/cmes.2022.019160
（This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)
Abstract The Symmetric Galerkin Boundary Element Method is advantageous for the linear elastic fracture and crackgrowth analysis of solid structures, because only boundary and crack-surface elements are needed. However, for engineering structures subjected to body forces such as rotational inertia and gravitational loads, additional domain integral terms in the Galerkin boundary integral equation will necessitate meshing of the interior of the domain. In this study, weakly-singular SGBEM for fracture analysis of three-dimensional structures considering rotational inertia and gravitational forces are developed. By using divergence theorem or alternatively the radial integration method, the domain integral terms caused More >

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Advances on Mesh and Dimension Reduction Methods

Guest Editors

Summary

Keywords

Published Papers

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807

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362

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1

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1390

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865

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1585

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942

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1

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1217

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969

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1

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1018

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814

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1

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1398

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930

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1

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1553

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999

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2338

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1227

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