Multigrid methods with Powell-Sabin splines
نویسندگان
چکیده
منابع مشابه
Multigrid methods with Powell-Sabin splines
We present a multigrid algorithm for the solution of the linear systems that arise from a finite element discretization of second order elliptic partial differential equations with Powell-Sabin splines. We show that the method yields a uniform convergence independent of the mesh size.
متن کاملIsogeometric analysis with Powell-Sabin splines
This paper presents the use of Powell-Sabin splines in the context of isogeometric analysis for the numerical solution of advectiondiffusion-reaction equations. Powell-Sabin splines are piecewise quadratic C functions defined on a given triangulation with a particular macro-structure. We discuss the Galerkin discretization based on a normalized Powell-Sabin B-spline basis. We focus on the accur...
متن کاملLocal subdivision of Powell-Sabin splines
We present an algorithm for local subdivision of Powell-Sabin spline surfaces. The construction of such a spline is based on a particular PS-refinement of a given triangulation. We build the new triangulation on top of this PS-refinement by applying a √ 3-subdivision scheme on a local part of the domain. To avoid degeneration we introduce a simple heuristic for refinement propagation, driven by...
متن کاملQuasi-hierarchical Powell-Sabin B-splines
Hierarchical Powell-Sabin splines are C-continuous piecewise quadratic polynomials defined on a hierarchical triangulation. The mesh is obtained by partitioning an initial conforming triangulation locally with a triadic split, so that it is no longer conforming. We propose a normalized quasi-hierarchical basis for this spline space. The B-spline basis functions have a local support, they form a...
متن کاملNumerical solution of partial differential equations with Powell-Sabin splines
Powell-Sabin splines are piecewise quadratic polynomials with global C-continuity. They are defined on conformal triangulations of two-dimensional domains, and admit a compact representation in a normalized B-spline basis. Recently, these splines have been used successfully in the area of computer-aided geometric design for the modelling and fitting of surfaces. In this paper, we discuss the ap...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: IMA Journal of Numerical Analysis
سال: 2008
ISSN: 0272-4979,1464-3642
DOI: 10.1093/imanum/drm031