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20
Wellcentered triangulation
, 2010
"... Meshes composed of wellcentered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primaldual mesh pairs. We prove that wellcentered meshes also have optimality properties and relationships to Delaunay and minm ..."
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Cited by 26 (7 self)
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Meshes composed of wellcentered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primaldual mesh pairs. We prove that wellcentered 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 wellcentered 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 wellcenteredness in arbitrary dimensions that we present. Ours is the first optimizationbased heuristic for wellcenteredness and the first one that applies in both two and three dimensions. We show the results of applying our algorithm to small and large twodimensional meshes, some with a complex boundary, and obtain a wellcentered 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.
Metrics and models for reordering transformations
 inProceedings of the 2nd ACM SIGPLAN Workshop on Memory System Performance (MSP04
, 2004
"... Irregular applications frequently exhibit poor performance on contemporary computer architectures, in large part because of their inefficient use of the memory hierarchy. Runtime data and iterationreordering transformations have been shown to improve the locality and therefore the performance of i ..."
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Cited by 22 (4 self)
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Irregular applications frequently exhibit poor performance on contemporary computer architectures, in large part because of their inefficient use of the memory hierarchy. Runtime data and iterationreordering transformations have been shown to improve the locality and therefore the performance of irregular benchmarks. This paper describes models for determining which combination of runtime data and iterationreordering heuristics will result in the best performance for a given dataset. We propose that the data and iterationreordering transformations be viewed as approximating minimal linear arrangements on two separate hypergraphs: a spatial locality hypergraph and a temporal locality hypergraph. Our results measure the efficacy of locality metrics based on these hypergraphs in guiding the selection of dataand iterationreordering heuristics. We also introduce new iteration and datareordering heuristics based on the hypergraph models that result in better performance than do previous heuristics.
A Comparison of Two Optimization Methods for Mesh Quality Improvement
"... We compare inexact Newton and coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the meanratio metric. The e#ects of problem size, element size heterogeneity, and various vertex dis ..."
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Cited by 7 (2 self)
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We compare inexact Newton and coordinate descent optimization methods for improving the quality of a mesh by repositioning the vertices, where the overall quality is measured by the harmonic mean of the meanratio metric. The e#ects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.
A Comparison of Inexact Newton and Coordinate Descent Mesh Optimization Techniques
"... We compare inexact Newton and coordinate descent methods for optimizing the quality of a mesh by repositioning the vertices, where quality is measured by the harmonic mean of the meanratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on th ..."
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Cited by 6 (0 self)
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We compare inexact Newton and coordinate descent methods for optimizing the quality of a mesh by repositioning the vertices, where quality is measured by the harmonic mean of the meanratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.
Simple and effective variational optimization of surface and volume triangulations
 In Proc. 17th Int. Meshing Roundtable
, 2008
"... Summary. Optimizing surface and volume triangulations is critical for advanced numerical simulations. We present a simple and effective variational approach for optimizing triangulated surface and volume meshes. Our method minimizes the differences between the actual elements and ideal reference el ..."
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Cited by 6 (1 self)
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Summary. Optimizing surface and volume triangulations is critical for advanced numerical simulations. We present a simple and effective variational approach for optimizing triangulated surface and volume meshes. Our method minimizes the differences between the actual elements and ideal reference elements by minimizing two energy functions based on conformal and isometric mappings. We derive simple, closedform formulas for the values, gradients, and Hessians of these energy functions, which reveal important connections of our method with some wellknown concepts and methods in mesh generation and surface parameterization. We then introduce a simple and efficient iterative algorithm for minimizing the energy functions, including a novel asynchronous stepsize control scheme. We demonstrate the effectiveness of our method experimentally and compare it against Laplacian smoothing and other mesh optimization techniques. Key words: mesh optimization; isometric mapping; conformal mapping; inverse mean ratio; variational methods 1
An AllHex Meshing Strategy for Bifurcation Geometries in Vascular Flow Simulation
 In 14th International Meshing Roundtable
, 2005
"... Summary. We develop an automated allhex meshing strategy for bifurcation geometries arising in subjectspecific computational hemodynamics modeling. The key components of our approach are the use of a natural coordinate system, derived from solutions to Laplace’s equation, that follows the tubular ..."
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Cited by 5 (1 self)
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Summary. We develop an automated allhex meshing strategy for bifurcation geometries arising in subjectspecific computational hemodynamics modeling. The key components of our approach are the use of a natural coordinate system, derived from solutions to Laplace’s equation, that follows the tubular vessels (arteries, veins, or grafts) and the use of a tripartitionedbased mesh topology that leads to balanced highquality meshes in each of the branches. The method is designed for situations where the required number of hexahedral elements is relatively small ( ∼ 1000– 4000), as is the case when spectral elements are employed in simulations at transitional Reynolds numbers or when finite elements are employed in viscous dominated regimes. 1
A LogBarrier Method for Mesh Quality Improvement
"... Summary. The presence of a few poorquality mesh elements can negatively affect the stability and efficiency of a finite element solver and the accuracy of the associated partial differential equation solution. We propose a mesh quality improvement method that improves the quality of the worst eleme ..."
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Cited by 2 (1 self)
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Summary. The presence of a few poorquality mesh elements can negatively affect the stability and efficiency of a finite element solver and the accuracy of the associated partial differential equation solution. We propose a mesh quality improvement method that improves the quality of the worst elements. Mesh quality improvement of the worst elements can be formulated as a nonsmooth unconstrained optimization problem, which can be reformulated as a smooth constrained optimization problem. Our technique solves the latter problem using a logbarrier interior point method and uses the gradient of the objective function to efficiently converge to a stationary point. The technique can be used with convex or nonconvex quality metrics. The method uses a logarithmic barrier function and performs global mesh quality improvement. Our method usually yields better quality meshes than existing methods for improvement of the worst quality elements, such as the active set, pattern search, and multidirectional search mesh quality improvement methods.
The FeasNewt Benchmark
"... Abstract — We describe the FeasNewt meshquality optimization benchmark. The performance of the code is dominated by three phases—gradient evaluation, Hessian evaluation and assembly, and sparse matrixvector products—that have very different mixtures of floatingpoint operations and memory access pa ..."
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Cited by 2 (0 self)
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Abstract — We describe the FeasNewt meshquality optimization benchmark. The performance of the code is dominated by three phases—gradient evaluation, Hessian evaluation and assembly, and sparse matrixvector products—that have very different mixtures of floatingpoint operations and memory access patterns. The code includes an optional runtime data and iterationreordering phase, making it suitable for research on irregular memory access patterns. Meshquality optimization (or “mesh smoothing”) is an important ingredient in the solution of nonlinear partial differential equations (PDEs) as well as an excellent surrogate for finiteelement or finitevolume PDE solvers. I.
Flexible representation of computational meshes
, 2005
"... A new representation of computational meshes is proposed in terms of a covering relation defined by discrete topological objects we call sieves. Fields over a mesh are handled locally by using the notion of refinement, dual to covering, and are later reassembled. In this approach fields are modeled ..."
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Cited by 2 (1 self)
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A new representation of computational meshes is proposed in terms of a covering relation defined by discrete topological objects we call sieves. Fields over a mesh are handled locally by using the notion of refinement, dual to covering, and are later reassembled. In this approach fields are modeled by sections of a fiber bundle over a sieve. This approach cleanly separates the topology of the mesh from its geometry and other valuestorage mechanisms. With these abstractions, finite element calculations are expressed using algorithms that are independent of mesh dimension, global topology, element shapes, and the finite element itself. Extensions and other applications are discussed.
Toolkit for registration and evaluation for 3d laser scanner acquisition
 Plzen: University of West Behemia
"... acquisition ..."
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