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...

The Powell singular function was introduced 1962 by M.J.D. Powell as an unconstrained optimization problem. The function is also used as nonlinear least squares problem and system of nonlinear equations. The function is a classic test function included in collections of test problems in optimization as well as an example problem in text books. In the global optimization literature the function ...

Cavallini, D. & Stirpe, F. (1957). Ital. J. Biochem. 6, 1. Dodgson, K. S., Powell, G. M., Rose, F. A. & Tudball, N. (1961). Biochem. J. 79, 209. Dodgson, K. S., Powell, G. M. & Tudball, N. (1960). Biochem. biophy8. Be8. Commun. 2, 130. Dodgson, K. S. & Tudball, N. (1960). Biochem. J. 74, 154. Doy, C. H. (1960). Nature, Lond., 529, 4724. Knox, W. E. & Pitt, B. M. (1957). J. biol. Chem. 225, 675....

About the year 1625 the Olive, a ship returning to Britain from Pernambuco and driven by bad weather, arrived at Barbados. The island was found to be uninhabited, although the presence of fruits and hogs suggested earlier visits by other ships. The ground "they found by tryalls in several parts, to be so overgrown with Wood; as there could be found no Champions or Savannahs for men to dwell in"...

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...

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.

Recently we developed multiscale spaces of C piecewise quadratic polynomials relative to arbitrary polygonal domains Ω ⊂ R. These multiscale bases are weakly stable with respect to the L2 norm. In this paper we show that these bases form strongly stable Riesz bases for the Sobolev spaces Hs(Ω) with s ∈ (2, 5 2 ).