In the following we demonstrate some features of the library, developed within the NFN Geometry + Simulation.

Domain parameterization

The parameterization of surfaces described by their boundary curves is a common process in computer-aided design. For IGA, the ability to obtain exact, non-singular parameterizations of not only surfaces but also volumes and bulks is a prerequisite.

The Geometry + Simulation logo represented as a multi-patch trivariate cubic spline domain.

The multipatch model consists of 31 volumetric tensor-product B-spline patches.

For a live WebGL demo click here

Left: Parameter lines of a regular parameterization of Austria with THB-splines

Right: THB-mesh of a domain representing the (rotated) state of Indiana.

Adaptively refined THB-splines allow a high resolution in areas with many details, as well as a coarse representation of straight parts of the boundary

Falini et. al., tech. report

mesh of indiana

Four examples showing parameterization of Multi-Patch domains for Isogeometric Analysis using Patch Adjacency Graphs.

Buchegger et. al., tech. report

Parameterization Result of the Jet example Parameterization Result of the Hammer example Parameterization Result of the Muffin example Parameterization Result of the Car example



The THB-spline surface and control grid obtained by fitting of point data measured from a turbine blade.

adaptive fitting

The surface obtained by fitting point data using the standard B-spline technology often suffers from oscillations (left).

This problem can be solved using THB-splines (right) Kiss et al.

detail of the fillet fitted with B-splinesdetail of the fillet fitted with THB-splines

The animations shows different interpolation of a function representing a steep cliff along a parametrized curve using HLR and prescribed refinement.

As time progress the number of refinement levels is increased, from 0 to 11. The oscillations are caused by the choice of the interpolation points: a fixed number per mesh element.

Bressan et. al., tech. report

Solving PDEs


Isogeometric Analysis on a 2D turbline blade.

From M.Sc. thesis "Isogeometric Analysis for Compressible Flows with Application in Turbomachinery" Jaeschke, A.M., TU Delft

turbine blade

A G-shaped volume domain. We solve a diffusion problem with adaptively refined THB-splines.

The color corresponds to the value of the solution of the problem. Four levels of adaptive refinement are used here.

The refinement is driven by a residual error estimator and is concentrated to the regions of activity of the solution.

The parametric element mesh with elements are colored according to the hierarchical level of refinement. Giannelli et al. tech. report

Mesh grading for isogeometric analysis Langer et al.

Isogeometric solution with an interior point singularity

Interior singularity on cubical domain

3D Heart-shaped domain with a singularity on curved boundaries,

heart-shaped domain with boundary singularity

Solution of a heat equation on jigsaw puzzle with zero source function and fixed boundary conditions Falini et al., tech. report.

We solve the Poisson Equation on a triangle domain with three patches in the new basis of multipatch B-splines with enhanced smoothness (MPBES).

The first picture shows the domain and the exact solution, the second picture compares the derivative of the numerical solutions that are achieved using C0 multipatch (on the left) and the new MPBES (on the right). Buchegger et al.

Triangle Example - Patchlayout and Solution Triangle Example - First Derivative

Poisson Equation solving on a tunnel-shaped domain with ten patches with MPBES using adaptive refinement.

The first picture shows the domain and the exact solution, the second picture shows the mesh after seven adaptive refinement steps. Buchegger et al.

Tunnel Example - Patchlayout and Solution Tunnel Example - Final Mesh

Vector field visualization using line integral convolution. First two images show a scalar field in addition, the last two fields show results of a linear elasticity equation. Accessible in class gsRender for 3D NURBS and 3D B-Splines.


Lohfink, Garth – TU Kaiserslautern –

Surface visualization. Pictures on the right show different modi: All outer surfaces, UV-surface, UW-surface, VW-surface. Accessible in class gsRender for 3D NURBS and 3D B-Splines.

Surface rendering gsRender

Lohfink, Garth – TU Kaiserslautern –

Glyph based visualization of scalar fields (color, shape) and vector fields (rotation). Accessible in class gsRender for 3D NURBS and 3D B-Splines.

Glyphs in gsRender

Lohfink, Garth – TU Kaiserslautern –

Volume visualization using opacity. Top left image shows the result of a simple heat equation on a cube, remaining images show the possibility to isolate areas of a chosen range of scalar values by changing the transfer function. Accessible in class gsRender for 3D NURBS and 3D B-Splines.

Volumerendering in gsRender

Lohfink, Garth – TU Kaiserslautern –

We solve the Stokes Equation on a Flow-Passage domain utilizing isogeometric Taylor Hood elements of hierarchical MPBES.

The first picture shows the pressure field of the numeric solution, the second picture shows the magnitude of the velocity, the third picture visualizes the streamlines and the last picture shows the mesh after six levels of adaptive refinement. (Florian Buchegger, Dissertation)

Calculated Pressure Field Calculated Magnitude of Velocity Field Streamlines of the computed solution Final Mesh after Adaptive Refinement

Last modified 16 months ago Last modified on 2016-07-20T09:24:47+01:00

Attachments (52)