Chebyshev tau meshless method based on the integration–differentiation for Biharmonic-type equations on irregular domain

Shao, Wenting; Wu, Xun; Chen, Suqin

doi:10.1016/j.enganabound.2012.06.005

Cited by 15 publications

(7 citation statements)

References 23 publications

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“…Some extensions It is known that spectral methods have a big limitation, the geometry of the domain must be simple enough to allow the use of an appropriate orthogonal basis in which to expand the full set of possible solutions to the problem. In the previous work [19], we have taken advantage of the Domain Embedding Methods [20][21][22][23][24] to solve the problems defined on irregular domains. The idea of these methods is to approximate the solution to the original problem by the solution of an auxiliary problem in a fictitious regular domain in which the irregular geometry is embedded.…”

Section: The Ctmmid-ddm In Two-dimensional Casementioning

confidence: 99%

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An effective Chebyshev tau meshless domain decomposition method based on the integration–differentiation for solving fourth order equations

Shao

2015

Applied Mathematical Modelling

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Section: The Ctmmid-ddm In Two-dimensional Casementioning

confidence: 99%

“…The starting point is the Chebyshev expansion of the mixed partial derivative u xxyy , then the lower derivatives or higher derivatives in both directions through an integration-differentiation process [19].…”

Section: The Differential Matricesmentioning

confidence: 99%

An effective Chebyshev tau meshless domain decomposition method based on the integration–differentiation for solving fourth order equations

Shao

2015

Applied Mathematical Modelling

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“…Hence, a comparison between the SEM and the isoparametric SEM is presented in figure 6 and table 1. For comparison of the two methods, the accuracy of a numerical solution produced by approximate schemes is measured via the L 2 norm error [19]:…”

Section: Rectangular Area Pierced By a Circular Holementioning

confidence: 99%

“…In numerical methods, the meshing of the irregular domains remains one of the most cumbersome and important steps in the entire solution process. To deal with problems with irregular domains, some methods have been proposed to overcome this problem, such as meshless local strong form method [9], the Chebyshev tau meshless method based on the integration-differentiation (CMMID) [19], direct expansion method of boundary condition (DEMBC) [24], boundary element method (BEM) [10], the finite element method (FEM) based on the triangular elements [23], the level-set function [21], the fractional step projection scheme [4], the Coons method, the Laplace method and boundary-blending method [3], isoparametric method [13], etc.…”

Section: Introductionmentioning

confidence: 99%

Spectral element method for wave propagation on irregular domains

2018

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A spectral element approximation of acoustic propagation problems combined with a new mapping method on irregular domains is proposed. Following this method, the Gauss-Lobatto-Chebyshev nodes in the standard space are applied to the spectral element method (SEM). The nodes in the physical space are mapped according to the length scale of the beeline segment or the curve segment. Using the Bubnov-Galerkin method, some acoustic problems with two kinds of irregular domains are simulated in detail. First, the basic problem with analytical solution is analysed numerically. Numerical results show that the SEM integrated with the lengthscale method has the same precision as the isoparametric SEM. Also, it can save nearly half of the time cost. Additionally, the acoustic propagations with inlet flow are simulated numerically. All the results indicate that the SEM integrated with the length-scale method has the ability to simulate the acoustic problems with irregular domains. It is shown that the mapping method maintains the curve edges and provides a useful alternative for isoparametric element, which represents a curved edge with a straight edge.

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“…Shao et al. 7 used the Chebyshev tau meshless method based on integration–differentiation (CTMMID) for numerically solving bi-harmonic-type equations in irregular domains with complex boundary conditions. Then, Shao and Wu 8 use the Chebyshev tau meshless method (CTMM), which was based on the highest derivative, that solved the fourth-order equations in irregularly shaped domains with complex boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of the plate with the regular and irregular domain by using the Barycentric Lagrange interpolation

Yeh

2018

Journal of Low Frequency Noise, Vibration and Active Control

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This paper uses the Barycentric Lagrange interpolation method to explore the free vibration of a plate with the regular and irregular domain using the Chebyshev function, allowing us to consider multiple dimensions. From our results, it can be shown that the Barycentric Lagrange interpolation method can solve three-dimensional problems. In the analysis, we can see that the Barycentric Lagrange interpolation method can solve the dynamic motion of the plate with regular domain, and the error of the simulation can be reduced to 0.15%. The effect of the geometric node number on the simulated error of the natural frequency of the plate is very profound. The Barycentric Lagrange interpolation method and the extrapolation difference method can solve the natural frequency of the plate with irregular domain. The error of the simulation on the natural frequency can be reduced to 1.084%. This allows us to understand the vibration of the plate with the regular and irregular domain under various boundary conditions quickly.

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Chebyshev tau meshless method based on the integration–differentiation for Biharmonic-type equations on irregular domain

Cited by 15 publications

References 23 publications

An effective Chebyshev tau meshless domain decomposition method based on the integration–differentiation for solving fourth order equations

An effective Chebyshev tau meshless domain decomposition method based on the integration–differentiation for solving fourth order equations

Spectral element method for wave propagation on irregular domains

Vibration analysis of the plate with the regular and irregular domain by using the Barycentric Lagrange interpolation

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