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Tetrahedral Mesh Improvement Via Optimization of the Element Condition Number
, 2002
"... this paper for smoothing and untangling are local techniques; a globally optimal solution is not guaranteed although empirical evidence suggests Copyright c fl 2000 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2000; 0:00 Prepared using nmeauth.cls ..."
Abstract

Cited by 28 (4 self)
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this paper for smoothing and untangling are local techniques; a globally optimal solution is not guaranteed although empirical evidence suggests Copyright c fl 2000 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Engng 2000; 0:00 Prepared using nmeauth.cls
Simultaneous untangling and smoothing of tetrahedral meshes
 Comput. Meth. in
, 2003
"... The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. The objective function is derived from some quality measure of the local ..."
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Cited by 20 (2 self)
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The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. The objective function is derived from some quality measure of the local submesh, that is, the set of tetrahedra connected to the adjustable or free node. Although these objective functions are suitable to improve the quality of a mesh in which there are noninverted elements, they are not when the mesh is tangled. This is due to the fact that usual objective functions are not defined on all R 3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures. Otherwise, when the mesh is tangled, there are local submeshes for which the free node is out of the feasible region, or this does not exist. In this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all R 3. With these modifications, the optimisation process is also directly applicable to meshes with inverted elements, making a previous untangling procedure unnecessary. This simultaneous procedure allows to reduce the number of iterations for reaching a prescribed quality. To illustrate the effectiveness of our approach, we present several applications where it can be seen that our results clearly improve those obtained by other authors.
Quality Encoding for Tetrahedral Mesh Optimization
, 2009
"... We define quality differential coordinates (QDC) for pervertex encoding of the quality of a tetrahedral mesh. QDC measures the deviation of a mesh vertex from a position which maximizes the combined quality of the set of tetrahedra incident at that vertex. Our formulation allows the incorporation o ..."
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Cited by 3 (1 self)
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We define quality differential coordinates (QDC) for pervertex encoding of the quality of a tetrahedral mesh. QDC measures the deviation of a mesh vertex from a position which maximizes the combined quality of the set of tetrahedra incident at that vertex. Our formulation allows the incorporation of different choices of element quality metrics into QDC construction to penalize badly shaped and inverted tetrahedra. We develop an algorithm for tetrahedral mesh optimization through energy minimization driven by QDC. The variational problem is solved efficiently and robustly using gradient flow based on a stable semiimplicit integration scheme. To ensure quality boundary of the resulting tetrahedral mesh, we propose a harmonicguided optimization scheme which leads to consistent handling of both the interior and boundary tetrahedra.
Program Development Environments and Tools Center for Component Technology for Terascale Simulation Software
"... models that are widely used in industry⎯such as CORBA, DCOM, and Enterprise JavaBeans⎯do not address parallelism and other needs of highperformance scientific software. The Common Component Architecture (CCA) component approach specifically targets the needs of largescale, complex, highperformanc ..."
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models that are widely used in industry⎯such as CORBA, DCOM, and Enterprise JavaBeans⎯do not address parallelism and other needs of highperformance scientific software. The Common Component Architecture (CCA) component approach specifically targets the needs of largescale, complex, highperformance, scientific simulations. We have demonstrated the basic principles of such a system. This proposal establishes a distributed Center, comprised of researchers from six DOE laboratories and two universities, focused on taking the CCA from a conceptual prototype to a fullfledged, highperformance component architecture for the scientific community.
Sandia National Laboratories
"... 1 Introduction Local mesh smoothing algorithms are commonly used for simplicial mesh improvement. These methods relocate a set of adjustable vertices, one at a time, to improve mesh quality in a neighborhood of that vertex. The new grid point position is determined by considering a local submesh con ..."
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1 Introduction Local mesh smoothing algorithms are commonly used for simplicial mesh improvement. These methods relocate a set of adjustable vertices, one at a time, to improve mesh quality in a neighborhood of that vertex. The new grid point position is determined by considering a local submesh containing the adjustable, or free vertex, v, and its incident vertices and elements. For example, in Figure 1, we show a twodimensional local submesh with three possible locations for v. The leftmost local submesh shows a valid but poorquality mesh, the middle submesh shows a higherquality valid mesh, and the rightmost shows an invalid mesh with inverted elements. Overall improvement in the mesh is obtained by performing some number of sweeps over the set of adjustable vertices.
J.M. GonzálezYuste
"... The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. The objective function is derived from some quality measure of the local ..."
Abstract
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(Show Context)
The quality improvement in mesh optimisation techniques that preserve its connectivity are obtained by an iterative process in which each node of the mesh is moved to a new position that minimises a certain objective function. The objective function is derived from some quality measure of the local submesh, that is, the set of tetrahedra connected to the adjustable or free node. Although these objective functions are suitable to improve the quality of a mesh in which there are non inverted elements, they are not when the mesh is tangled. This is due to the fact that usual objective functions are not defined on all R 3 and they present several discontinuities and local minima that prevent the use of conventional optimisation procedures. Otherwise, when the mesh is tangled, there are local submeshes for which the free node is out of the feasible region, or this does not exist. In this paper we propose the substitution of objective functions having barriers by modified versions that are defined and regular on all R 3. With these modifications, the optimisation process is also directly applicable to meshes with inverted elements, making a previous untangling procedure unnecessary. This simultaneous procedure allows to reduce the number of iterations for reaching a prescribed quality. To illustrate the effectiveness of our approach, we present several applications where it can be seen that our results clearly improve those obtained by other authors.
Quality Encoding for Tetrahedral Mesh Optimization
"... We define quality differential coordinates (QDC) for pervertex encoding of the quality of a tetrahedral mesh. QDC measures the deviation of a mesh vertex from a position which maximizes the combined quality of the set of tetrahedra incident at that vertex. Our formulation allows the incorporation o ..."
Abstract
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We define quality differential coordinates (QDC) for pervertex encoding of the quality of a tetrahedral mesh. QDC measures the deviation of a mesh vertex from a position which maximizes the combined quality of the set of tetrahedra incident at that vertex. Our formulation allows the incorporation of different choices of element quality metrics into QDC construction to penalize badly shaped and inverted tetrahedra. We develop an algorithm for tetrahedral mesh optimization through energy minimization driven by QDC. The variational problem is solved efficiently and robustly using gradient flow based on a stable semiimplicit integration scheme. To ensure quality boundary of the resulting tetrahedral mesh, we propose a harmonicguided optimization scheme which leads to consistent handling of both the interior and boundary tetrahedra.
Automatic Construction of Boundary Parametrizations for Geometric Multigrid Solvers
, 2004
"... We present an algorithm that constructs parametrizations of boundary and interface surfaces automatically. Starting with highresolution triangulated surfaces describing the computational domains, we iteratively simplify the surfaces yielding a coarse approximation of the boundaries with the same ..."
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We present an algorithm that constructs parametrizations of boundary and interface surfaces automatically. Starting with highresolution triangulated surfaces describing the computational domains, we iteratively simplify the surfaces yielding a coarse approximation of the boundaries with the same topological type. While simplifying we construct a function that is dened on the coarse surface and whose image is the original surface. This function allows access to the correct shape and surface normals of the original surface as well as to any kind of data dened on it. Such information can be used by geometric multigrid solvers doing adaptive mesh renement. Our algorithm runs stable on all types of input surfaces, including those that describe domains consisting of several materials. We have used our method with success in dierent elds and we discuss examples from structural mechanics and biomechanics. 2 Figure 1: Using parametrized boundaries increases the geometric accuracy of local mesh renements. 1