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A meshless method with conforming and nonconforming sub‐domains
Author(s) -
Guo YongMing,
Yagawa Genki
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5431
Subject(s) - regularized meshless method , meshfree methods , singular boundary method , collocation (remote sensing) , domain (mathematical analysis) , mathematics , simple (philosophy) , collocation method , helmholtz equation , boundary value problem , poisson's equation , helmholtz free energy , boundary (topology) , convergence (economics) , numerical analysis , domain decomposition methods , computational mechanics , mathematical analysis , computer science , boundary element method , finite element method , differential equation , physics , ordinary differential equation , philosophy , epistemology , quantum mechanics , machine learning , economic growth , economics , thermodynamics
Summary An accurate and easy integration technique is desired for the meshless methods of weak form. As is well known, a sub‐domain method is often used in computational mechanics. The conforming sub‐domains, where the sub‐domains are not separated nor overlapped each other, are often used, while the nonconforming sub‐domains could be employed if needed. In the latter cases, the integrations of the sub‐domains may be performed easily by choosing a simple configuration. And then, the meshless method with nonconforming sub‐domains is considered one of the reasonable choices for computational mechanics without the troublesome integration. In this paper, we propose a new sub‐domain meshless method. It is noted that, because the method can employ both the conforming and the nonconforming sub‐domains, the integration for the weak form is necessarily accurate and easy by selecting the nonconforming sub‐domains with simple configuration. The boundary value problems including the Poisson's equation and the Helmholtz's equation are analyzed by using the proposed method. The numerical solutions are compared with the exact solutions and the solutions of the collocation method, showing that the relative errors by using the proposed method are smaller than those by using the collocation method and that the proposed method possesses a good convergence. Copyright © 2016 John Wiley & Sons, Ltd.