As-rigid-as-possible (ARAP) surface modelling is widely used for interactive deformation of triangle meshes. We show that ARAP can be interpreted as minimizing a discretization an elastic energy based on non-conforming elements defined over dual orthogonal cells the mesh. Using intrinsic Voronoi rather than extrinsic mesh guarantees non-negative each cell. represent Delaunay edges extrinsically...

In this paper we propose a simple technique for tetrahedral mesh improvement without inserting Steiner vertices, concentrating mainly on boundary conforming meshes. The algorithm makes local changes to the mesh to remove tetrahedra which are poor according to some quality criterion. While the algorithm is completely general with regard to quality criterion, we target improvement of the dihedral...

The thesis presents a novel numerical method based on the high order Discontinuous Galerkin (DG) method for three dimensional electrostatic and electro-quasistatic field problems where materials are of very complex shape and may move over time. A well-known example is water droplets oscillating on the surface of high voltage power transmission line insulators. The electric field at the surface ...

We have developed a new programming framework, called Sieve, to support parallel numerical PDE1 algorithms operating over distributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic algorithms operating on distributed containers conforming to the Sieve interface. Sieve makes instances of the incidence relation, or arrows, the conceptual first-cl...

Abstract We propose a quality-based optimization strategy to reduce the total number of degrees freedom associated with discrete problem defined over polygonal tessellation Virtual Element Method. The presented Quality Agglomeration algorithm relies only on geometrical properties mesh, agglomerating groups neighboring elements. test this approach in context fractured porous media, which generat...

Adaptive mesh refinement (AMR) has been shown to allow solving partial differential equations to significantly higher accuracy at reduced numerical cost. This paper presents a state-of-the-art AMR algorithm applied to the multigroup neutron diffusion equation for reactor applications. In order to follow the physics closely, energy group-dependent meshes are employed. We present a novel algorith...

This work introduces “generalized meshes”, a type of meshes suited for the discretization partial differential equations in non-regular geometries. Generalized extend regular simplicial by allowing overlapping elements and more flexible adjacency relations. They can have several distinct “generalized” vertices (or edges, faces) that occupy same geometric position. These generalized facets are n...

When performing computational fluid dynamics (CFD) simulations of complex flows, the a priori knowledge of the flow physics and the location of the dominant flow features are usually unknown. For this reason, the development of adaptive remeshing techniques is crucial for large-scale computational problems. Some work has been made recently to provide Nek5000 with adaptive mesh refinement (AMR) ...

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that pr...