Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains

Authors:
Hendrik Speleers;Paul Dierckx;Stefan Vandewalle
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001 Leuven, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 9
Cited 0

Curve and surface fitting with splines

Curve and surface fitting with splines
A robust finite element method for nonhomogeneous Dirichlet problems in domains with curved boundaries

Mathematics of Computation
Constrained surface fitting using Powell-Sabin splines

An international conference on curves and surfaces on Wavelets, images, and surface fitting
On calculating normalized Powell-Sabin B-splines

Computer Aided Geometric Design
√3-subdivision

Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Piecewise Quadratic Approximations on Triangles

ACM Transactions on Mathematical Software (TOMS)
Weighted Extended B-Spline Approximation of Dirichlet Problems

SIAM Journal on Numerical Analysis
Local subdivision of Powell-Sabin splines

Computer Aided Geometric Design
Numerical solution of partial differential equations with Powell-Sabin splines

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

Powell-Sabin splines are piecewise quadratic polynomials with a global C^1-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.