This study makes the first attempt to extend the singular boundary method (SBM) to inhomogeneous problems in conjunction with the dual reciprocity method (DRM). The SBM is a new boundary-type meshless method and utilizes the fundamental solution to calculate the homogeneous solution of the governing equation of interest, where the inverse interpolation technique is designed to evaluate the origin intensity factor while overcoming the singularity of the fundamental solution at the origin. In this study, the DRM is employed to evaluate the particular solution of Poisson equation with multiquadratic functions. The efficiency and accuracy of the proposed SBM-DRM scheme are tested to the three benchmark inhomogeneous Poisson problems. We also demonstrate the stability of the SBM-DRM scheme in dealing with noisy boundary data.
Wei, Xing; Chen, Wen; and Fu, Zhuo-Jia
"SOLVING INHOMOGENEOUS PROBLEMS BY SINGULAR BOUNDARY METHOD,"
Journal of Marine Science and Technology: Vol. 21:
1, Article 2.
Available at: https://jmstt.ntou.edu.tw/journal/vol21/iss1/2