Commenced in January 2007
Paper Count: 31742
A Finite Point Method Based on Directional Derivatives for Diffusion Equation
Abstract:This paper presents a finite point method based on directional derivatives for diffusion equation on 2D scattered points. To discretize the diffusion operator at a given point, a six-point stencil is derived by employing explicit numerical formulae of directional derivatives, namely, for the point under consideration, only five neighbor points are involved, the number of which is the smallest for discretizing diffusion operator with first-order accuracy. A method for selecting neighbor point set is proposed, which satisfies the solvability condition of numerical derivatives. Some numerical examples are performed to show the good performance of the proposed method.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334291Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1153
 L. J. Shen, G. X. Lv and Z. J. Shen, "A Finite Point Method Based on Directional Differences", SIAM J. Numer. Anal., vol. 47(3), pp. 2224- 2242, 2009.
 G. X. Lv, L. J. Shen and Z. J. Shen, "Study on Finite Point Method", Chinese J. comput. phys., vol. 25(5), pp. 505-524, 2008.
 E. O╦£nate, S. Idelsohn, O. C. Zienkiewicz, and R. L. Taylor, "A finite point method in computing mechanics application to convective transport and fluid flow", Internat. J. Numer. Methods Engrg., vol. 39, pp. 3839-3866, 1996.
 B. Boroomand, A. A. Tabatabaei, and E. O╦£nate, "Simple modifications for stabilization of the finite point method", Intern. J. Numer. Methods Engrg., vol. 63, pp. 351-379, 2005.
 Z. J. Shen, L. J. Shen, G. X. Lv,W. Chen, and G. W. Yuan, "A Lagrangian finite point method for two-dimensional fluid dynamic problems", Chinese J. comput. phys., vol. 22(5), pp. 377-385, 2005.
 D. Sridar and N. Balakrishnan, "An upwind finite difference scheme for meshless solvers", J. Comput. Phys., vol. 189, pp. 1-29, 2003.
 P. S. Jensen, "Finite difference techniques for variable grids", Comp. Structures, vol. 2, pp. 17-29, 1972.
 K. C. Chung, "A generalized finite difference method for heat transfer problems of irregular geometries", Numer. Heat Transfer, Part A: Applications, vol. 4, pp. 345-357, 1981.
 G. B. Wright and B. Fornberg, "Scattered node compact finite differencetype formulas generated from radial basis functions", J. Comput. Phys., vol. 212, pp. 99-123, 2006.
 J. M. Wu, Z. H. Dai, Z. M. Gao and G. W. Yuan, "The linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes", J. Comput. Phys., vol. 229, pp. 3382-3401, 2010.