Finite Element Methods with B-Splines

Finite Element Approximation with Hierarchical B-Splines

Finite Element Methods with Hierarchical WEB-splines

Piecewise polynomial approximations are fundamental to geometric modeling, computer graphics, and finite element methods. The classical finite element method uses low order piecewise polynomials defined on polygonal domains. The domains are discretized into simple polygons called the mesh. These polygons might be triangles, quadrilaterals, etc., for two-dimensional domains, and tetrahedra, hexa...

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...

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