3,058 research outputs found
On discrete simplex splines and subdivision
Discrete analogoues of multivariate simplex splines are introduced. Their study yields a subdivision scheme for simplex splines
Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces
We introduce a coupled finite and boundary element formulation for acoustic
scattering analysis over thin shell structures. A triangular Loop subdivision
surface discretisation is used for both geometry and analysis fields. The
Kirchhoff-Love shell equation is discretised with the finite element method and
the Helmholtz equation for the acoustic field with the boundary element method.
The use of the boundary element formulation allows the elegant handling of
infinite domains and precludes the need for volumetric meshing. In the present
work the subdivision control meshes for the shell displacements and the
acoustic pressures have the same resolution. The corresponding smooth
subdivision basis functions have the continuity property required for the
Kirchhoff-Love formulation and are highly efficient for the acoustic field
computations. We validate the proposed isogeometric formulation through a
closed-form solution of acoustic scattering over a thin shell sphere.
Furthermore, we demonstrate the ability of the proposed approach to handle
complex geometries with arbitrary topology that provides an integrated
isogeometric design and analysis workflow for coupled structural-acoustic
analysis of shells
Smoothness of Nonlinear and Non-Separable Subdivision Schemes
We study in this paper nonlinear subdivision schemes in a multivariate
setting allowing arbitrary dilation matrix. We investigate the convergence of
such iterative process to some limit function. Our analysis is based on some
conditions on the contractivity of the associated scheme for the differences.
In particular, we show the regularity of the limit function, in and
Sobolev spaces
A Hermite interpolatory subdivision scheme for -quintics on the Powell-Sabin 12-split
In order to construct a -quadratic spline over an arbitrary
triangulation, one can split each triangle into 12 subtriangles, resulting in a
finer triangulation known as the Powell-Sabin 12-split. It has been shown
previously that the corresponding spline surface can be plotted quickly by
means of a Hermite subdivision scheme. In this paper we introduce a nodal
macro-element on the 12-split for the space of quintic splines that are locally
and globally . For quickly evaluating any such spline, a Hermite
subdivision scheme is derived, implemented, and tested in the computer algebra
system Sage. Using the available first derivatives for Phong shading, visually
appealing plots can be generated after just a couple of refinements.Comment: 17 pages, 7 figure
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