A High Accurate Simulation of Thin Plate Problems By Using the Method of Approximate Particular Solutions With High Order Polynomial Basis

Jingang Xiong, Nanchang University
Pengfei Jiang, Nanchang University
Hui Zheng, Nanchang University
Ching-Shyang Chen, University of Southern Mississippi


In this paper, a closed-form particular solution of polyharmonic splines has been obtained for high order partial differential operators. Instead of using complex derivation, the new particular solution is derived simply by adding or subtracting several available particular solutions. The proposed particular solution is further coupled with polynomial basis for numerically solving thin plate problems. The relationship between number of nodes and order of polynomials are fully studied. Numerical examples with irregular domains are presented to demonstrate the effectiveness of the proposed algorithm.