Børre Bang

Computer simulation of wind speed, wind pressure and snow accumulation around buildings (SNOW-SIM)

Abstract This paper describes the present state of the project SNOW-SIM at Narvik Institute of Technology. The project is aimed at finding methods for simulations of wind and snowdrift around building construction. The purpose of this project is to develop an integrated planning environment suitable for determining wind loads and snow deposition in planning construction in the cold climate areas. Such problems are now mostly solved by using wind tunnel experiments, rough assumptions or by experience. Calculations in two and three dimensions are performed on commercial fluid dynamic software based on Navier-Stokes equations. This paper deals with wind loads on buildings, ventilation of the attic of a small house, and flow patterns around groups of buildings. The velocity is shown as a vector plot around the structures, and the wind pressure is given as characteristics pressure values on surfaces. Flow patterns around buildings are visualized by streamlines. Simulations of snow accumulations are done with a generalized drift-flux model which is described in the paper. Drifts around snow fences are simulated in two dimensions and compared with full-scale measurements. Three-dimensional snow deposition is calculated around a group of houses with snow deposition expressed as surfaces.

Application of homogenization theory related to Stokes flow in porous media

We consider applications, illustration and concrete numerical treatments of some homogenization results on Stokes flow in porous media. In particular, we compute the global permeability tensor corresponding to an unidirectional array of circular fibers for several volume-fractions. A 3-dimensional problem is also considered.

Computing n -variate orthogonal discrete wavelet transforms on graphics processing units

In [4,5] an algorithm was proposed for isometric mapping between smooth n-variate m-dimensional vector fields and fractal curves and surfaces, by using orthonormal wavelet bases This algorithm matched only the orthonormal bases of scaling functions (the “V-spaces” of multiresolution analyses) In the present communication we shall consider a new algorithm which matches the orthonormal bases of wavelets (the “W-spaces” of multiresolution analyses) Being of Cantor diagonal type, it was applicable for both bounded and unbounded domains, but the complexity of its implementation was rather high In [3] we proposed a simpler algorithm for the case of boundary-corrected wavelet basis on a bounded hyper-rectangle In combination with the algorithm for the “V-spaces” from [4,5], the new algorithm provides the opportunity to compute multidimensional orthogonal discrete wavelet transform (DWT) in two ways – via the “classical” way for computing multidimensional wavelet transforms, and by using a commutative diagram of mappings of the bases, resulting in an equivalent computation on graphics processing units (GPUs) The orthonormality of the wavelet bases ensures that the direct and inverse transformations of the bases are mutually adjoint (transposed in the case of real entries) orthogonal matrices, which eases the computations of matrix inverses in the algorithm 1D and 2D orthogonal wavelet transforms have been first implemented for parallel computing on GPUs using C++ and OpenGL shading language around the year 2000; our new algorithm allows to extend general-purpose computing on GPUs (GPGPU) also to higher-dimensional wavelet transforms If used in combination with the Cantor diagonal type algorithm of [4,5] (the “V-space” basis matching) this algorithm can in principle be applied for computing DWT of n-variate vector fields defined on the whole ℝn However, if boundary-corrected wavelets are considered for vector-fields defined on a bounded hyper-rectangle in ℝn, then the present algorithm for GPU-based computation of n-variate orthogonal DWT can be enhanced with the new simple “V-space”-basis matching algorithm of [3] It is this version that we consider in detail in the present study.

A Model of Enterprise Integration and Collaboration Tools and Communication Infrastructure for Inter- Enterprise Collaboration

This paper first discusses a model of enterprise integration that consists of a micro level, a midcro level, and a macro level integration. Secondly, the architecture for midcro inter-enterprise integration is composed consisting of three layers, a communication layer, a collaboration layer, and an application layer. To the collaboration layer, synchronous and asynchronous collaborations are discussed and a toolkit for those collaborations is studied and assembled. Then to the communication layer, a communication infrastructure for a research test-bed and a project for midcro inter-enterprise integration is described.

Evaluation of Smooth Spline Blending Surfaces Using GPU

Recent development in several aspects of research on blending type spline constructions has opened up new application areas. We propose a method for evaluation and rendering of smooth blending type spline constructions using the tessellation shader steps of modern graphics hardware. In this preliminary study we focus on concepts and terminology rather than implementation details. Our approach could lead to more efficient, dynamic and stable blending-type spline based applications in fields such as interactive modeling, computer games and more.

Smooth partition of unity with Hermite interpolation: applications to image processing

We explore the one-to one correspondence between parametric surfaces in 3D and two dimensional color images in the RGB color space. For the case of parametric surfaces defined on general parametric domains recently a new approximate geometric representation has been introduced1 which also works for manifolds in higher dimensions. This new representation has a form which is a generalization to the B´ezier representation of parametric curves and tensorproduct surfaces. The main purpose of the paper is to discuss how the so generated technique for modeling parametric surfaces can be used for respective modification (re-modeling) of images. We briefly consider also some of the possible applications of this technique.

Blending functions for hermite interpolation by beta-function b-splines on triangulations

In the present paper we compute for the first time Beta-function B-splines (BFBS) achieving Hermite interpolation up to third partial derivatives at the vertices of the triangulation. We consider examples of BFBS with uniform and variable order of the Hermite interpolation at the vertices of the triangulation, for possibly non-convex star-1 neighbourhoods of these vertices. We also discuss the conversion of the local functions from Taylor monomial bases to appropriately shifted and scaled Bernstein bases, thereby converting the Hermite interpolatory form of the linear combination of BFBS to a new, Bezier-type, form. This conversion is fully parallelized with respect to the vertices of the triangulation and, for Hermite interpolation of uniform order, the load of the computations for each vertex of the computation is readily balanced.

Regression analysis using a blending type spline construction

Regression analysis allows us to track the dynamics of change in measured data and to investigate their properties. A sufficiently good model allows us to predict the behavior of dependent variables with higher accuracy, and to propose a more precise data generation hypothesis.

Surface Constructions on Irregular Grids

“Big” surfaces defined on domains that can not be modeled on a single regular grid is typically made by joining several surfaces together with the aid of fillet surfaces or by intersecting the surfaces and joining them after trimming.

Blending type spline constructions: A brief overview

In this paper we are presenting a brief overview of research on blending splines from 2004-2015. We discuss some of the properties which can be interesting to investigate when blending splines are used both for finite element analysis and geometry. Blending splines are constructions where local geometry is blended together by a blending function to create global geometry. The different basis functions has different properties, which can be related to different application areas. Example application areas where blending splines are utilized is listed, together with a focus on the basis and future work towards utilizing parts of blending splines in an isogeometric analysis(IGA) context.