Programming finite element methods with weighted 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...

Programming Multigrid Methods with B-Splines

Multigrid algorithms are the method of choice for solving large Ritz-Galerkin systems for elliptic boundary value problems. Using b-spline bases provides geometric flexibility as well as many computational advantages and permits particularly efficient and elegant implementations. This is described for a fairly general discretization which covers all principal features of b-spline elements.

Weighted Quadrature Rules for Finite Element Methods

We discuss the numerical integration of polynomials times exponential weighting functions arising from multiscale finite element computations. The new rules are more accurate than standard quadratures and are better suited to existing codes than formulas computed by symbolic integration. We test our approach in a multiscale finite element method for the 2D reaction-diffusion equation. Standard ...

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...