In this paper, we set out to implement a code for processing the edges of a plane domain with a complex geometric shape. The algorithm that enabled us to write this code is based on the classical properties of analytic geometry. The coordinates of the vertices of the polygon-like domain must first be given. The code developed automatically generates indices for interior and edge points. Any point located at a distance defined by user from the edge of a domain is considered an edge point. To this condition, we add a second condition that requires the edge point to be inside the circle with a diameter of two consecutive vertices of the polygon. An illustration is included to clarify the readers of this paper.
References
[1]
Brézis, H. (2005) Analyse fonctionnelle: Théorie et application. Dunod.
[2]
Mercier, B. (1989) An Introduction to the Numerical Analysis of Spectral Methods (Lecture Notes in Physics). Springer, 318 p.
[3]
Bengt, F. (1998) A Practical Guide to Pseudospectral Methods. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press.
[4]
Seworé, G. (2014) Développement des codes numériques adaptés aux schémas pseudo-spectraux pour les équations aux dérivées partielles paraboliques non linéaires. Thése de Doctorat, Université Cheikh Anta Diop de Dakar.
[5]
Hilaire Nkounkou, A., Traore, S., Gabyi, M., Abani, A. and Mampassi, B. (2011) Spectral Differentiation on Unstructured Meshes Using Jacobi Gauss-Lobatto Points. Far East Journal of Applied Mathematics, 59, 105-1221.
[6]
Amann, H. (1986) Parabolic Evolution Equations with Nonlinear Boundary Conditions. Proceedings of a Symposium in Pure Mathematics of the American mathematical Society, 45, 17-27.
[7]
Amann, H. (1986) Quasilinear Evolution Equations and Parabolic Systems. Transactions of the American Mathematical Society, 293, 191-227. https://doi.org/10.1090/S0002-9947-1986-0814920-4