We construct an overlapping additive Schwarz preconditioner for the biharmonic Dirichlet problems discretized by isogeometric analysis based on generalized B-splines (GB-splines) and analyze its optimal convergence rate bound that is cubic in ratio between subdomains overlap sizes. Our validated through a set of numerical experiments illustrate good behavior proposed with respect to model param...

A constructive approach is adopted to build B-spline like basis for cubic spline curves with a more general continuity than beta-continuity. This method provides not only a large variety of very interesting shape controls like biased, point, and interval tensions but, as a special case, also recovers a number of spline methods like nu-spline of Nielson[9], beta-splines[1], gamma-splines of Boeh...

Based on variational properties, we generalize the approximation properties of the univariate natural cubic spline to splines in arbitrary dimensions. In one dimension, the solution of the variational problem { given a = x1 < · · · < xN = b and values f(x1), . . . , f(xN ) in R, find a function s with s(xi)=f(xi), i=1, . . . ,N , that minimizes ‖s‖L2([a,b]) is given by the natural univariate cu...

This paper deals with solving the global illumination problem using compactly supported overlapping bases. Overlapping bases have not been used for their computational complexities. This paper is a step towards solving illumination ee-ciently using overlapping bases. Cubic B-splines are used as an example to show the eecient solution of global illumination. B-splines have properties that give a...

We extend the recently introduced divergence-conforming immersed boundary (DCIB) method [1] to fluid-structure interaction (FSI) problems involving closed co-dimension one solids. focus on capsules and vesicles, whose discretization is particularly challenging due higher-order derivatives that appear in their formulations. In two-dimensional settings, we employ cubic B-splines with periodic kno...

Root lattices are efficient sampling lattices for reconstructing isotropic signals in arbitrary dimensions, due to their highly symmetric structure. One root lattice, the Cartesian grid, is almost exclusively used since it matches the coordinate grid; but it is less efficient than other root lattices. Box-splines, on the other hand, generalize tensor-product B-splines by allowing non-Cartesian ...

The problem of interpolation of discrete set of data on the interval [a, b] representing the function f is investigated. A family of C splines with one free generating function is introduced in order to solve this problem. Cubic C splines belong to this family. The required conditions which must satisfy the generating function in order to obtain explicit interpolants are presented and examples ...