We study several versions of the problem of generating triangular meshes for finite element methods. We show how to triangulate a planar point set or polygonally bounded domain with triangles of bounded aspect ratio; how to triangulate a planar point set with triangles having no obtuse angles; how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio; and how ...

This chapter describes the general principles of unstructured mesh generation in two and three dimensions, together with the use of finite elements in modelling space plasmas. Particular attention is given to the requirement of generating meshes that are aligned along magnetic field lines, in order to properly capture the strong anisotropy of magnetised plasmas. Example results are given in 2D ...

The ever-growing demand for higher accuracy in scientific simulations based on the discretization of equations given on physical domains is typically coupled with an increase in the number of mesh elements. Conventional mesh generation tools struggle to keep up with the increased workload, as they do not scale with the availability of, for example, multi-core CPUs. We present a parallel mesh ge...

The goal of this paper is to help evaluate the tetrahedral mesh generation, adaptation and optimization algorithms. To achieve this goal, benchmarks are proposed consisting of simple and complete geometries. In order to evaluate the quality of the meshes, the concept of tetrahedron shape measure is clarified and used. Finally, as an example, these benchmarks are used to evaluate meshes optimize...

Local transformation, or topological reconnection, is one of effective procedures of mesh improvement method, especially for three-dimensional tetrahedral mesh. Although the existing local transformations such as 2-3/3-2 flip are effective in removing poorly-shaped tetrahedra, it is still possible to improve the quality of mesh further by expanding the space of transformation region. The author...

A flexible mesh-generation framework for image representation based on Delaunay triangulations is proposed. By fixing the various degrees of freedom available within this framework, two mesh-generation methods, known as ID1 and ID2, are derived. These two methods are shown to perform extremely well, producing meshes of significantly higher quality than state-of-the-art schemes at relatively low...

In this poster we focus and present our preliminary results pertinent to the integration of multiple parallel Delaunay mesh generation methods into a coherent hierarchical framework. The goal of this project is to study our telescopic approach and to develop Delaunay-based methods to explore concurrency at all hardware layers using abstractions at (a) medium-grain level for many cores within a ...

Parallel mesh generation is a relatively new research area between the boundaries of two scientific computing disciplines: computational geometry and parallel computing. In this chapter we present a survey of parallel unstructured mesh generation methods. Parallel mesh generation methods decompose the original mesh generation problem into smaller subproblems which are meshed in parallel. We org...

Creating in parallel guaranteed quality large unstructured meshes is a challenging problem. Parallel mesh generation procedures decompose the original mesh generation problem into smaller subproblems that can be solved in parallel. The subproblems can be treated as either completely or partially coupled, or they can be treated as completely decoupled. In this paper we present a parallel guarant...

1 preprint numerics no. 1/2012 norwegian university of science and technology trondheim, norway This paper discusses numerical solution of boundary value problems using spectral methods combined with nonlinear and adaptive mappings between the reference domain and the physical domain. A brief review of existing methods for adaptive mesh generation is given, and a method for finding close to opt...