Solving Inhomogeneous Problems by Singular Boundary Method

Xing Wei ； Wen Chen ； Zhuo-Jia Fu

《Journal of Marine Science and Technology》 21卷1期 (2013/02) Pp. 8-14

https://doi.org/10.6119/JMST-011-0704-1

並列摘要

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.

並列關鍵字

singular boundary method ； inhomogeneous equation,noisy boundary ； meshless method.

參考文獻

Brebbia, C. A., Telles, J., and Wrobel, L., Boundary Element Techniques Theory and Applications in Engineering, Springer-Verlag, Berlin (1984).

Chen, J. T., Chang, M. H., Chen, K. H., and Chen, I. L., “Boundary collocation method for acoustic eigenanalysis of three dimensional cavities using radial basis function,” Computational Mechanics, Vol. 29, Nos. 4-5, pp. 392-408 (2002).

Chen, J. T., Chang, M. H., Chen, K. H., and Lin, S. R., “The boundary collocation method with meshless concept for acoustic eigenanalysis of two-dimensional cavities using radial basis function,” Journal of Sound and Vibration, Vol. 257, No. 4, pp. 667-711 (2002).

Chen, J. T., Shieh, H. G., Tsai, J. J., and Lee, J. W., “A study on the method of fundamental solutions using the image concept,” Applied Mathematical Modelling, Vol. 34, pp. 4253-4266 (2010).

Chen, W., Fu, Z. J., and Jin, B. T., “A truly boundary-only meshfree method for inhomogeneous problems based on recursive composite multiple reciprocity technique,” Engineering Analysis with Boundary Elements, Vol. 34, pp. 196-205 (2010).