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The Localized Method of Fundamental Solution for Two Dimensional Signorini Problems

Zhuowan Fan1, Yancheng Liu1, Anyu Hong1,*, Fugang Xu1,*, Fuzhang Wang2
1 School of Civil Engineering and Architecture, Nanchang University, Nanchang, 330031, China
2 Nanchang Institute of Technology, Nanchang, 330044, China
* Corresponding Authors: Anyu Hong. Email: ; Fugang Xu. Email:
(This article belongs to this Special Issue: Advances on Mesh and Dimension Reduction Methods)

Computer Modeling in Engineering & Sciences 2022, 132(1), 341-355.

Received 10 October 2021; Accepted 14 December 2021; Issue published 02 June 2022


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 out to validate the reliability and effectiveness of the LMFS in solving Signorini problems.


Signorini problem; localized method of fundamental solution; collocation method; nonlinear boundary conditions

Cite This Article

Fan, Z., Liu, Y., Hong, A., Xu, F., Wang, F. (2022). The Localized Method of Fundamental Solution for Two Dimensional Signorini Problems. CMES-Computer Modeling in Engineering & Sciences, 132(1), 341–355.

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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