Journal of Computational Methods in Engineering

Journal of Computational Methods in Engineering

An enrichment Technique for the Finite Point Method by Equilibrated Singular Basis Functions for Weak Singularities

Document Type : Original Article

Authors
Nima noormohammadi 1
Mehran Abolghasemi 2
1 Department of Civil Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
2 Department of Civil Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran.
10.47176/jcme.45.1.1081
Abstract
This paper presents a novel approach to improve the accuracy and stability of the finite point method (FPM) in the vicinity of points with weak singularities by incorporating equilibrated singular basis functions (EqSBFs). Singular points play a crucial role in the intensification of the flux field in applied physics. Conventional numerical methods fail to correctly capture the solution function in singular areas due to the usage of smooth basis functions. FPM is a meshfree method based on strong point-wise application of the governing partial differential equation (PDE) along with the boundary conditions, which in its classical form suffers from inconsistency of its polynomial type basis functions with the singular region, leading to accuracy reduction, slow convergence, and local instabilities. To address this issue, EqSBFs are incorporated alongside the conventional smooth basis functions. EqSBFs are derived by the weighted residual imposition of the homogeneous PDE, with the capability of automatically identifying the singularity order of the problem, thus avoiding the solution of a parallel identical problem to extract the required singular terms. EqSBFs may be simply merged with the smooth basis functions of the FPM through the weighted least squares (WLS) approximation. The proposed formulation significantly improves the numerical representation of the singular solution, while maintaining the desirable advantages of the FPM.
Keywords
Harmonic
Weak singularity
Equilibrated Singular Basis Functions
Finite Point Method
Enrichment
Subjects
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