A meshless approach to solving partial differential equations using the finite cloud method for the purposes of computer aided design

Burke, Daniel J.

doi:10.22215/etd/2013-08586

Cited by 2 publications

(1 citation statement)

References 36 publications

(66 reference statements)

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“…FCM is a meshfree method that employs fixed RKPM for the construction of interpolation functions and then adopts the point collocation approach to discretize the governing differential equation. FCM has been applied in various fields, like computer-aided design ( [23], [24], [25]) and the simulation of the behavior of hydrogel ( [26]). Several papers related to some improvements to FCM are found in the literature ( [27], [28], [29], [30]).…”

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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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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A Hybrid Multiscale Finite Cloud Method and Finite Volume Method in Solving High Gradient Problem

Hoe

2022

Int. J. Comput. Methods

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Meshfree methods are always the alternatives to be considered besides the finite element method in dealing with complex engineering problems. Among these complex problems, there are problems where discontinuities or high gradients may only emerge at a small region of a domain and the remaining parts of the domain are smooth and continuous. In this case, adding nodes to the critical region is essential for the better accuracy of solutions. It would be effective if a meshfree method is applied to the critical region and a mesh-based method is employed to solve the remaining part of the domain since node refinement is easier for a meshfree method whereas a mesh-based method is simple to develop and capable of producing accurate solutions for smooth regions. In this study, the finite cloud method (FCM) is coupled with the finite volume method (FVM) such that node refinement only takes place at the region where the FCM is applied. A handshaking approach is proposed to enforce the continuity near the interface where both methods are applied. Numerical examples and computation methods are presented in this paper and the numerical results are examined.

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A meshless approach to solving partial differential equations using the finite cloud method for the purposes of computer aided design

Cited by 2 publications

References 36 publications

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

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

A Hybrid Multiscale Finite Cloud Method and Finite Volume Method in Solving High Gradient Problem

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