In the investigation, the complex geometric domain is a concave geometrical pattern. Due to the symmetric character, the left side of the geometric pattern,?i.e.?the L-shaped region is calculated in the study. The governing equation is expressed with?Laplace?equations. And the analysis is solved by eigenfunction expansion and point-match method. Besides, visual?C++?helps obtain the results of numerical calculation. The local values and the mean values of the function are also discussed in this study.
References
[1]
Alliney, S. (1982) A Numerical Study of Two Dimensional Potential Flows by Boundary and Finite Elements. Applied Mathematical Modelling, 6, 291-298. https://doi.org/10.1016/S0307-904X(82)80037-1
[2]
Rangogni, R. (1986) Numerical Solution of the Generalized Laplace Equation by Coupling the Boundary Element Method and the Perturbation Method. Applied Mathematical Modelling, 10, 266-270. https://doi.org/10.1016/0307-904X(86)90057-0
[3]
Kirkup, S.M. and Henwood, D.J. (1994) An Empirical Error Analysis of the Boundary Element Method Applied to Laplace’s Equation. Applied Mathematical Modelling, 18, 32-38. https://doi.org/10.1016/0307-904X(94)90180-5
[4]
Bailey, R.T., Hsieh, C.K. and Li, H. (1995) Grid Generation in Two Dimensions Using the Complex Variable Boundary Element Method. Applied Mathematical Modelling, 19, 322-332. https://doi.org/10.1016/0307-904X(95)00008-8
[5]
Wang C.Y. ,et al. (1994)Diffusion across a Corrugated Saw-Tooth Plate Mechanics Research Communications 116, 233-237.
[6]
Chen, J.T. and Chen, K.H. (1998) Analytical Study and Numerical Experiments for Laplace Equation with Overspecified Boundary Conditions. Applied Mathematical Modelling, 22, 703-725. https://doi.org/10.1016/S0307-904X(98)10054-9
[7]
Gavete, L., Gavete, M.L. and Benito, J.J. (2003) Improvements of Generalized Finite Difference Method and Comparison with Other Meshless Method. Applied Mathematical Modelling, 27, 831-847. https://doi.org/10.1016/S0307-904X(03)00091-X
[8]
Nyambuya, G.G. (2015) Four Poisson-Laplace Theory of Gravitation (I). Journal of Modern Physics, 6, Article ID: 58605, 11 p.
[9]
Hu H.P. ,et al. (2015)The Two-Dimensional Analysis of Laminar Flow Between the Moving Plates with Arrayed Rods Journal of the Chinese Society of Mechanical Engineers 4, 317-322.
