Journal
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
Volume 88, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.euromechsol.2021.104248
Keywords
Dual reciprocity method; Dual interpolation boundary face method; Augmented thin plate spline; Moving least squares interpolation; Poisson equation; Complex geometry
Categories
Funding
- NSF of China [11771454]
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This paper introduces a new implementation of the dual reciprocity method in combination with the dual interpolation boundary face method for solving the Poisson equation. The method utilizes relationships between source nodes and virtual nodes for interpolation and boundary integration, showing superior performance for Poisson equations with various geometries.
This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpolation is used to interpolate the physical variables, while boundary integrals are evaluated on the source nodes only. Moreover, moving least squares (MLS) interpolation is used and provides additional constraints equations to establish the relationship between source and virtual nodes. Additionally, augmented thin plate spline (ATPS) is used to better interpolate the non-homogeneous term. Finally, it is claimed that the proposed method is much superior to the DRM for Poisson type equation with different geometries, especially for complex geometry. Numerical examples are evaluated and compared with the DRM to ensure the superiority of the proposed method.
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