We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for r ≥ 0, discontinuous polynomials of r for the displacement, H(div)-conforming polynomials of order r+1 for the stress, and H(curl)-conforming polynomials of order r + 1 for the vector representation of the multiplier. We prove that this tripl...

In this paper we present a fast and robust approach for simulating elasto-plastic materials and fracture in real time. Our method extends the warped stiffness finite element approach for linear elasticity and combines it with a strain-state-based plasticity model. The internal principal stress components provided by the finite element computation are used to determine fracture locations and ori...

In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR framework that works independently of the used element type, such as for example lines, triangles, tetrahedra, quadrilaterals, hexahedra, and prisms. Along with a detailed mathematical discussion, this requires the imple...

Indium is a typical chalcophile element of the Earth’s crust, with a very low average content that seldom forms specific minerals, occurring mainly as dispersed in polymetallic sulphides. Indium recovery is based primarily on zinc extraction from sphalerite, the prototype of so-called tetrahedral sulphides, wherein metal ions fill half of the available tetrahedral sites within the cubic closest...

The problem of generating realistic computer models of objects represented by 3D segmented images is important in many biomedical applications. Labelled 3D images impose particular challenges for meshing algorithms because multi-material junctions form features such as surface pacthes, edges and corners which need to be preserved into the output mesh. In this paper, we propose a feature preserv...

SeisSol is a simulation software for seismic wave propagation and earthquake scenarios. It solves the fully elastic wave equations in heterogeneous media. Incorporating dynamic rupture simulation it performs complex multiphysics earthquake simulations. To account for complicated geometries SeisSol uses a fully unstructured tetrahedral mesh. Recent publications [1], [2] have shown that SeisSol i...

SUMMARY We present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, we formulate two optimization objective funct...

The zero level set of a piecewise-affine function with respect to a consistent tetrahedral subdivision of a domain in R3 is a piecewise-planar hyper-surface. We prove that if a family of consistent tetrahedral subdivions satisfies the minimum angle condition, then after a simple postprocessing this zero level set becomes a consistent surface triangulation which satisfies the maximum angle condi...