19,114 research outputs found
The Modified Direct Method: an Approach for Smoothing Planar and Surface Meshes
The Modified Direct Method (MDM) is an iterative mesh smoothing method for
smoothing planar and surface meshes, which is developed from the non-iterative
smoothing method originated by Balendran [1]. When smooth planar meshes, the
performance of the MDM is effectively identical to that of Laplacian smoothing,
for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian
smoothing for tri-quad meshes. When smooth surface meshes, for trian-gular,
quadrilateral and quad-dominant mixed meshes, the mean quality(MQ) of all mesh
elements always increases and the mean square error (MSE) decreases during
smoothing; For tri-dominant mixed mesh, the quality of triangles always
descends while that of quads ascends. Test examples show that the MDM is
convergent for both planar and surface triangular, quadrilateral and tri-quad
meshes.Comment: 18 page
Well-Centered Triangulation
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 that seeks to transform a
given triangulation in two or three dimensions into a well-centered one by
minimizing a cost function and moving the interior vertices while keeping the
mesh connectivity and boundary vertices fixed. The cost function is a direct
result of a new characterization of well-centeredness in arbitrary dimensions
that we present. Ours is the first optimization-based heuristic for
well-centeredness, and the first one that applies in both two and three
dimensions. We show the results of applying our algorithm to small and large
two-dimensional meshes, some with a complex boundary, and obtain a
well-centered tetrahedralization of the cube. We also show numerical evidence
that our algorithm preserves gradation and that it improves the maximum and
minimum angles of acute triangulations created by the best known previous
method.Comment: Content has been added to experimental results section. Significant
edits in introduction and in summary of current and previous results. Minor
edits elsewher
A multilevel approach for obtaining locally optimal finite element meshes
In this paper we consider the adaptive finite element solution of a general class of variational problems using a combination of node insertion, node movement and edge swapping. The adaptive strategy that is proposed is based upon the construction of a hierarchy of locally optimal meshes starting with a coarse grid for which the location and connectivity of the nodes is optimized.
This grid is then locally refined and the new mesh is optimized in the same manner. Results presented indicate that this approach is able to produce better meshes than those possible by more conventional adaptive strategies and in a relatively efficient manner
Parallel implementation of an optimal two level additive Schwarz preconditioner for the 3-D finite element solution of elliptic partial differential equations
This paper presents a description of the extension and parallel implementation of a new two level additive Schwarz (AS) preconditioner for the solution of 3-D elliptic partial differential equations (PDEs). This preconditioner, introduced in Bank et al. (SIAM J. Sci. Comput. 2002; 23: 1818), is based upon the use of a novel form of overlap between the subdomains which makes use of a hierarchy of meshes: with just a single layer of overlapping elements at each level of the hierarchy. The generalization considered here is based upon the restricted AS approach reported in (SIAM J. Sci. Comput. 1999; 21: 792) and the parallel implementation is an extension of work in two dimensions (Concurrency Comput. Practice Experience 2001; 13: 327)
Tetrahedral mesh improvement using moving mesh smoothing, lazy searching flips, and RBF surface reconstruction
Given a tetrahedral mesh and objective functionals measuring the mesh quality
which take into account the shape, size, and orientation of the mesh elements,
our aim is to improve the mesh quality as much as possible. In this paper, we
combine the moving mesh smoothing, based on the integration of an ordinary
differential equation coming from a given functional, with the lazy flip
technique, a reversible edge removal algorithm to modify the mesh connectivity.
Moreover, we utilize radial basis function (RBF) surface reconstruction to
improve tetrahedral meshes with curved boundary surfaces. Numerical tests show
that the combination of these techniques into a mesh improvement framework
achieves results which are comparable and even better than the previously
reported ones.Comment: Revised and improved versio
Locally optimal unstructured finite element meshes in 3 dimensions
This paper investigates the adaptive finite element solution of a general class of variational problems in three dimensions using a combination of node movement, edge swapping, face swapping and node insertion. The adaptive strategy proposed is a generalization of previous work in two dimensions and is based upon the construction of a hierarchy of locally optimal meshes.
Results presented, both for a single equation and a system of coupled equations, suggest that this approach is able to produce better meshes of tetrahedra than those obtained by more conventional adaptive strategies and in a relatively efficient manner
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