A new finite element of C1 cubic splines

A New Kind of Trivariate C1 Splines

We propose a construction of trivariate C 1 spline functions over a special tetrahedron partition and compare our construction with other known constructions of C 1 spline functions which are summarized in this paper. We improve the Alfeld construction of C 1 quintic spline spaces. For those polygonal domains in R 3 which admit the special tetrahedron partition, our construction provides a more...

Local lagrange interpolation with cubic C1 splines on tetrahedral partitions

We describe an algorithm for constructing a Lagrange interpolation pair based onC1 cubic splines defined on tetrahedral partitions. In particular, given a set of points V ∈ R3, we construct a set P containing V and a spline space S3( ) based on a tetrahedral partition whose set of vertices include V such that interpolation at the points of P is well-defined and unique. Earlier results are exten...

Splines and Finite Element Spaces

Splines are piecewise polynomial functions that have certain “regularity” properties. These can be defined on all finite intervals, and intervals of the form (−∞, a], [b,∞) or (−∞,∞). We have already encountered linear splines, which are simply continuous, piecewise-linear functions. More general splines are defined similarly to the linear ones. They are labeled by three things: (1) a knot sequ...

Finite Element Thin Plate Splines

A Higher Order B-Splines 1-D Finite Element Analysis of Lossy Dispersive Inhomogeneous Planar Layers

In this paper we propose an accurate and fast numerical method to obtain scattering fields from lossy dispersive inhomogeneous planar layers for both TE and TM polarizations. A new method is introduced to analyze lossy Inhomogeneous Planar Layers. In this method by applying spline based Galerkin’s method of moment to scalar wave equation and imposing boundary conditions we obtain reflection and...