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How to Achieve Kronecker Delta Condition in Moving Least Squares Approximation along the Essential Boundary

Jin Yeon Cho1

Associate Professor, Department of Aerospace Engineering, INHA University, 253 Yonghyun-Dong, Nam-Gu, Incheon, 402-751, Korea. E-mail:

Computers, Materials & Continua 2007, 5(2), 99-116.


A novel way is proposed to fulfill Kronecker delta condition in moving least squares (MLS) approximation along the essential boundary. In the proposed scheme, the original MLS weight is modified to boundary interpolatable (BI) weight based on the observation that the support of weight function is exactly the same as the support of MLS nodal shape function. The BI weight is zero along the boundary edges except the edges containing the nodal point associated with the concerned weight. In order to construct the BI weight from the original weight, concept of edge distance function is introduced, and the BI weight construction procedure is presented in detail. Furthermore, it is explained theoretically why the MLS nodal shape functions obtained by BI weights satisfy Kronecker delta condition along the boundary edges. To identify the validity and usefulness of the proposed BI MLS approximation scheme through numerical tests, the scheme is applied to the model problems with rectangular domain and complex shaped domain. Through the tests, theoretical prediction is identified numerically, and it is confirmed that one can handle the essential and natural boundary conditions through the proposed BI MLS scheme in exactly the same manner used in traditional finite element methods.


Cite This Article

J. Y. Cho, "How to achieve kronecker delta condition in moving least squares approximation along the essential boundary," Computers, Materials & Continua, vol. 5, no.2, pp. 99–116, 2007.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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