Automatic generation of triangular finite element meshes

Automatic generation of hexahedral finite element meshes

An algorithm for the generation of hexahedral element meshes is demonstrated. The algorithm starts by creating a structured grid in the interior of an object. Then the boundary region is meshed by means of an isomorphism technique that uses basically 2D-operations. Examples are given that demonstrate the quality of the algorithm.

Convergence Analysis for Eigenvalue Approximations on Triangular Finite Element Meshes

The paper is devoted to the eigenvalue problem for a second order strongly elliptic operator. The problem is considered on curved domains, which require interpolated boundary conditions in approximating finite element formulation. The necessary triangulations for solving the eigenvalue problem consists of isoparametric elements of degree n, where n is any integer greater than two. An approximat...

Generation of Tetrahedral Finite Element Meshes: Variational Delaunay Approach

The goal is to generate tetrahedral decomposition of a general solid body, whose surface is given as a collection of triangular facets. The principle idea is that a vertex set in general positions guarantees existence of a unique triangulation which satisses the Delaunay empty-sphere property. (Algorithms for robust, parallel construction of such triangulations are available.) However, all of t...

Automatic Conversion of Triangular Meshes into Quadrilateral Meshes with Directionality

This paper presents a triangular-to-quadrilateral mesh conversion method that can control the directionality of the output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts th...

A Linear Immersed Finite Element Space Defined by Actual Interface Curve on Triangular Meshes