NIK – Numerical analyzis and HPC

Author and abstract
Hans Jakob Rivertz and Ali Alsam:
Fast color edge preserving smoothing
An edge preserving smoothing algorithm is presented. To prevent smoothing over edges, the algorithm requires that diffusion in a direction should not result in an increase in neighbouring gradients. Intuitively, we think that smoothing reduces gradients. This is, however, not true in the vicinity of strong edges where smoothing over the edge results in surface deformation. The possibility of reducing the calculation cost is explored by reducing the frequency of calculating the edge strength.
Tatiana Kravetc:
Finite element method application of ERBS Triangles
In this paper we solve an eigenvalue problem on a circular membrane with fixed outer boundary by using a finite element method, where an element is represented as an expo-rational blending triangle. ERBS triangles combine properties of B-spline _nite elements and standard polynomial triangular elements. The overlapping of local triangles allows us to provide a exible handling of the surface while preserving the smoothness of the initial domain, also over the nodes and edges. Blending splines accurately approximate the outer boundary, while keeping a coarse discretization of the domain. We consider a mesh construction for such type of elements, evaluating of basis functions and their directional derivatives, local-to-global mapping, assembling of element matrices.
Hans Olofsen:
Blending functions based on trigonometric and polynomial approximations of the Fabius function
Most simple blending functions are polynomials, while more advanced blending functions are, for example, rational or expo-rational fractions. The Fabius function has the required properties of a blending function, but is a nowhere analytic function and cannot be calculated exactly everywhere on the required domain. We present a new set of trigonometric and polynomial blending functions with the shape and other properties similar to the Fabius function. They consist of combinations of trigonometric polynomials and piecewise polynomials. The main advanced of these are that they are easy to implement, have low processing costs and have simple derivatives. This makes them very suitable for the calculation of splines. Due to the selfdifferential property of the Fabius function, scaled versions of these functions can even be used to approximate their own derivatives.
Arne Maus:
RadixInsert, a much faster stable algorithm for sorting floating-point numbers