Damrong Guoy

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We propose sink-insertion as a new technique to improve the mesh quali ty of Delaunay triangulations. We compare it with the conventional circumcenter-insertion technique under three scheduling regimes: incremental, in blocks, and in parallel. Justification for sink-insertion is given in terms of mesh quality, numerical robustness, running time, and ease of(More)
We present an algorithm to construct meshes suitable for spacetime discontinuous Galerkin finite-element methods. Our method generalizes and improves the ‘Tent Pitcher’ algorithm of Üngör and Sheffer. Given an arbitrary simplicially meshed domain X of any dimension and a time interval [0, T], our algorithm builds a simplicial mesh of the spacetime domain X(More)
We present results on a two-step improvement of mesh quality in three-dimensional Delaunay triangulations. The first step refines the triangulation by inserting sinks and eliminates tetrahedra with large circumradius over shortest edge length ratio. The second step assigns weights to the vertices to eliminate slivers. Our experimental findings provide(More)
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. We present an iterative algorithm(More)
We present an iterative algorithm to transform a given planar triangle mesh into a well-centered one by moving the interior vertices while keeping the connectivity fixed. A well-centered planar triangulation is one in which all angles are acute. Our approach is based on minimizing a certain energy that we propose. Well-centered meshes have the advantage of(More)
We describe our parallel 3-D surface and volume mesh modification strategy for large-scale simulation of physical systems with dynamically changing domain boundaries. Key components include an accurate, robust, and efficient surface propagation scheme, frequent mesh smoothing without topology changes, infrequent remeshing at regular intervals or when(More)
We propose a new algorithm for constructing finite-element meshes suitable for spacetime discontinuous Galerkin solutions of linear hyperbolic PDEs. Given a triangular mesh of some planar domain &#937; and a target time value <i>T</i>, our method constructs a tetrahedral mesh of the spacetime domain &#937; X [0,<i>T</i>] in constant running time per(More)
We present an automatic algorithm to construct blocking scheme for multiblock structured meshes in 2D multiphase flow problems. Our solution is based on the concepts of medial axis and Delaunay triangulation. We show that the quality of the blocking scheme strongly depends on the quality of Delaunay triangulation. Therefore, well-known techniques and issues(More)
A completely well-centered tetrahedral mesh is a triangulation of a three dimensional domain in which every tetrahedron and every triangle contains its circumcenter in its interior. Such meshes have applications in scientific computing and other fields. We show how to triangulate simple domains using completely well-centered tetrahedra. The domains we(More)