Powell-Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and Neumann conditions, and we show that a particular choice of the PS-triangles at the boundary can greatly simplify the corresponding constraints. Finally, we consider an application where the techniques developed in this paper are used: the numerical solution of a partial differential equation by the Galerkin and collocation method.
Speleers, H., Dierckx, P., Vandewalle, S. (2007). Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 206(1), 55-72 [10.1016/j.cam.2006.05.023].
Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains
Speleers H.;
2007-09-01
Abstract
Powell-Sabin splines are piecewise quadratic polynomials with a global C1-continuity, defined on conforming triangulations. Imposing boundary conditions on such a spline leads to a set of constraints on the spline coefficients. First, we discuss boundary conditions defined on a polygonal domain, before we treat boundary conditions on a general curved domain boundary. We consider Dirichlet and Neumann conditions, and we show that a particular choice of the PS-triangles at the boundary can greatly simplify the corresponding constraints. Finally, we consider an application where the techniques developed in this paper are used: the numerical solution of a partial differential equation by the Galerkin and collocation method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.