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A combination of the LTDRM and the ATPS in solving diffusion problems

Journal Article


Abstract


  • In the literature, augmented thin plate splines (ATPS) were thought to provide better numerical accuracy (cf. Golberg and Chen, Boundary Elements Communications, 1994, 5, 57–61) if they were adopted as the interpolation functions for the dual reciprocity boundary element method (DRBEM). Some strong numerical evidence is provided to show that Golberg and Chen's theoretical work is supported. For time-dependent linear diffusion problems, ATPS was adopted in the LTDRM (Laplace Transform Dual Reciprocity Method) algorithm proposed by Zhu et al. (Engineering Analysis with Boundary Elements, 1994, 13, 1–10) and the results compared with those presented in Zhu et al. (Engineering Analysis with Boundary Elements, 1994, 13, 1–10) and Lu (2nd Biennial Australian Engineering Mathematics, 1996). Through this comparison, it is demonstrated that the ATPS are indeed superior to their LINEAR and TPS (thin plate splines) counterparts.

Publication Date


  • 1998

Citation


  • Zhu, S., Liu, H. & Lu, X. (1998). A combination of the LTDRM and the ATPS in solving diffusion problems. Engineering Analysis with Boundary Elements, 21 (3), 285-289.

Number Of Pages


  • 4

Start Page


  • 285

End Page


  • 289

Volume


  • 21

Issue


  • 3

Place Of Publication


  • United Kingdom

Abstract


  • In the literature, augmented thin plate splines (ATPS) were thought to provide better numerical accuracy (cf. Golberg and Chen, Boundary Elements Communications, 1994, 5, 57–61) if they were adopted as the interpolation functions for the dual reciprocity boundary element method (DRBEM). Some strong numerical evidence is provided to show that Golberg and Chen's theoretical work is supported. For time-dependent linear diffusion problems, ATPS was adopted in the LTDRM (Laplace Transform Dual Reciprocity Method) algorithm proposed by Zhu et al. (Engineering Analysis with Boundary Elements, 1994, 13, 1–10) and the results compared with those presented in Zhu et al. (Engineering Analysis with Boundary Elements, 1994, 13, 1–10) and Lu (2nd Biennial Australian Engineering Mathematics, 1996). Through this comparison, it is demonstrated that the ATPS are indeed superior to their LINEAR and TPS (thin plate splines) counterparts.

Publication Date


  • 1998

Citation


  • Zhu, S., Liu, H. & Lu, X. (1998). A combination of the LTDRM and the ATPS in solving diffusion problems. Engineering Analysis with Boundary Elements, 21 (3), 285-289.

Number Of Pages


  • 4

Start Page


  • 285

End Page


  • 289

Volume


  • 21

Issue


  • 3

Place Of Publication


  • United Kingdom