Optimizing Voronoi Diagrams for Polygonal Finite Element Computations
نویسندگان
چکیده
We present a 2D mesh improvement technique that optimizes Voronoi diagrams for their use in polygonal finite element computations. Starting from a centroidal Voronoi tessellation of the simulation domain we optimize the mesh by minimizing a carefully designed energy functional that effectively removes the major reason for numerical instabilities—short edges in the Voronoi diagram. We evaluate our method on a 2D Poisson problem and demonstrate that our simple but effective optimization achieves a significant improvement of the stiffness matrix condition number.
منابع مشابه
Efficient Computation of Discrete Voronoi Diagram and Homotopy-Preserving Simplified Medial Axis of a 3D Polyhedron
AVNEESH SUD: Efficient Computation of Discrete Voronoi Diagram and Homotopy-Preserving Simplified Medial Axis of a 3D Polyhedron. (Under the direction of Dinesh Manocha.) The Voronoi diagram is a fundamental geometric data structure and has been well studied in computational geometry and related areas. A Voronoi diagram defined using the Euclidean distance metric is also closely related to the ...
متن کاملGeneralized Voronoi Diagrams on Polyhedral Terrains
We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) ...
متن کاملReduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements
We present a method to reduce mesh bias in dynamic fracture simulations using the finite element method with adaptive insertion of extrinsic cohesive zone elements along element boundaries. The geometry of the domain discretization is important in this setting because cracks are only allowed to propagate along element facets and can potentially bias the crack paths. To reduce mesh bias, we cons...
متن کاملError estimates for generalized barycentric interpolation
We prove the optimal convergence estimate for first order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress approach explicitly constructs rational functions, the Sibson approach uses Voronoi diagrams on the vertices of the polygon to define the functions, and the Ha...
متن کاملApplicability of Elastic Analysis for Predicting the Settlement Distribution Around Tunneling in Soft Ground (TECHNICAL NOTE)
In this article a brief review of the literature on the subject is cited. The method of analysis by a finite element program is discussed in which the effect of different influential parameters are examined. The results of these computations are then compared to the corresponding empirical data and two other existing formulae for two dimensional cases. The comparisons show quite reliable and ac...
متن کامل