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Algebraic mesh quality metrics

Description: Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.
Date: April 24, 2000
Creator: Knupp, Patrick
Partner: UNT Libraries Government Documents Department

The Graft Tool: An All-Hexahedral Transition Algorithm for Creating a Multi-Directional Swept Volume Mesh

Description: Sweeping algorithms have become very mature and can create a semi-structured mesh on a large set of solids. However, these algorithms require that all linking surfaces be mappable or submappable. This restriction excludes solids with imprints or protrusions on the linking surfaces. The grafting algorithm allows these solids to be swept. It then locally modifies the position and connectivity of the nodes on the linking surfaces to align with the graft surfaces. Once a high-quality surface mesh is formed on the graft surface, it is swept along the branch creating a 2 3/4-D mesh.
Date: September 27, 1999
Partner: UNT Libraries Government Documents Department

The generation of hexahedral meshes for assembly geometries: A survey

Description: The finite element method is being used today to model component assemblies in a wide variety of application areas, including structural mechanics, fluid simulations, and others. Generating hexahedral meshes for these assemblies usually requires the use of geometry decomposition, with different meshing algorithms applied to different regions. While the primary motivation for this approach remains the lack of an automatic, reliable all-hexahedral meshing algorithm, requirements in mesh quality and mesh configuration for typical analyses are also factors. For these reasons, this approach is also sometimes required when producing other types of unstructured meshes. This paper will review progress to date in automating many parts of the hex meshing process, which has halved the time to produce all-hex meshes for large assemblies. Particular issues which have been exposed due to this progress will also be discussed, along with their applicability to the general unstructured meshing problem.
Date: February 14, 2000
Partner: UNT Libraries Government Documents Department

Methods for Multisweep Automation

Description: Sweeping has become the workhorse algorithm for creating conforming hexahedral meshes of complex models. This paper describes progress on the automatic, robust generation of MultiSwept meshes in CUBIT. MultiSweeping extends the class of volumes that may be swept to include those with multiple source and multiple target surfaces. While not yet perfect, CUBIT's MultiSweeping has recently become more reliable, and been extended to assemblies of volumes. Sweep Forging automates the process of making a volume (multi) sweepable: Sweep Verification takes the given source and target surfaces, and automatically classifies curve and vertex types so that sweep layers are well formed and progress from sources to targets.
Date: September 14, 2000
Partner: UNT Libraries Government Documents Department

A Method for Controlling Skew on Linked Surfaces

Description: A new method for lessening skew in mapped meshes is presented. This new method involves progressive subdivision of a surface into loops consisting of four sides. Using these loops, constraints can then be set on the curves of the surface, which will propagate interval assignments across the surface, allowing a mesh with a better skew metric to be generated.
Date: September 27, 1999
Partner: UNT Libraries Government Documents Department

Curved mesh generation and mesh refinement using Lagrangian solid mechanics

Description: We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final configuration is determined by solving for the equilibrium configuration. The deformations are represented using piecewise polynomials within each element of the original mesh. When the mesh is sufficiently fine to resolve the solid deformation, this method guarantees non-intersecting elements even for highly distorted or anisotropic initial meshes. We describe the method and the solution procedures, and we show a number of examples of two and three dimensional simplex meshes with curved boundaries. We also demonstrate how to use the technique for local refinement of non-curved meshes in the presence of curved boundaries.
Date: December 31, 2008
Creator: Persson, P.-O. & Peraire, J.
Partner: UNT Libraries Government Documents Department

An Improved Linear Tetrahedral Element for Plasticity

Description: A stabilized, nodally integrated linear tetrahedral is formulated and analyzed. It is well known that linear tetrahedral elements perform poorly in problems with plasticity, nearly incompressible materials, and acute bending. For a variety of reasons, linear tetrahedral elements are preferable to quadratic tetrahedral elements in most nonlinear problems. Whereas, mixed methods work well for linear hexahedral elements, they don't for linear tetrahedrals. On the other hand, automatic mesh generation is typically not feasible for building many 3D hexahedral meshes. A stabilized, nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity, nearly incompressible materials and acute bending. Furthermore, the formulation is analytically and numerically shown to be stable and optimally convergent. The element is demonstrated to perform well in several standard linear and nonlinear benchmarks.
Date: April 25, 2005
Creator: Puso, M
Partner: UNT Libraries Government Documents Department

Hexahedron Projection for Curvilinear Grids

Description: This paper presents a method of dividing into triangle fans the most common projections of hexahedra from curvilinear meshes, so that they can be volume rendered in hardware, with a fragment program for 32-bit floating point compositing.
Date: June 13, 2006
Creator: Max, N
Partner: UNT Libraries Government Documents Department

Visualization Tools for Adaptive Mesh Refinement Data

Description: Adaptive Mesh Refinement (AMR) is a highly effective method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations that must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between general-purpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR visualization research and tools and describe how VisIt currently handles AMR data.
Date: May 9, 2007
Creator: Weber, Gunther H.; Beckner, Vincent E.; Childs, Hank; Ligocki,Terry J.; Miller, Mark C.; Van Straalen, Brian et al.
Partner: UNT Libraries Government Documents Department

Volume Decomposition and Feature Recognition for Hexahedral Mesh Generation

Description: Considerable progress has been made on automatic hexahedral mesh generation in recent years. Several automatic meshing algorithms have proven to be very reliable on certain classes of geometry. While it is always worth pursuing general algorithms viable on more general geometry, a combination of the well-established algorithms is ready to take on classes of complicated geometry. By partitioning the entire geometry into meshable pieces matched with appropriate meshing algorithm the original geometry becomes meshable and may achieve better mesh quality. Each meshable portion is recognized as a meshing feature. This paper, which is a part of the feature based meshing methodology, presents the work on shape recognition and volume decomposition to automatically decompose a CAD model into meshable volumes. There are four phases in this approach: (1) Feature Determination to extinct decomposition features, (2) Cutting Surfaces Generation to form the ''tailored'' cutting surfaces, (3) Body Decomposition to get the imprinted volumes; and (4) Meshing Algorithm Assignment to match volumes decomposed with appropriate meshing algorithms. The feature determination procedure is based on the CLoop feature recognition algorithm that is extended to be more general. Results are demonstrated over several parts with complicated topology and geometry.
Date: September 27, 1999
Partner: UNT Libraries Government Documents Department

Pamgen, a library for parallel generation of simple finite element meshes.

Description: Generating finite-element meshes is a serious bottleneck for large parallel simulations. When mesh generation is limited to serial machines and element counts approach a billion, this bottleneck becomes a roadblock. Pamgen is a parallel mesh generation library that allows on-the-fly scalable generation of hexahedral and quadrilateral finite element meshes for several simple geometries. It has been used to generate more that 1.1 billion elements on 17,576 processors. Pamgen generates an unstructured finite element mesh on each processor at the start of a simulation. The mesh is specified by commands passed to the library as a 'C'-programming language string. The resulting mesh geometry, topology, and communication information can then be queried through an API. pamgen allows specification of boundary condition application regions using sidesets (element faces) and nodesets (collections of nodes). It supports several simple geometry types. It has multiple alternatives for mesh grading. It has several alternatives for the initial domain decomposition. Pamgen makes it easy to change details of the finite element mesh and is very useful for performance studies and scoping calculations.
Date: April 1, 2008
Creator: Foucar, James G.; Drake, Richard Roy; Hensinger, David M. & Gardiner, Thomas Anthony
Partner: UNT Libraries Government Documents Department

Adaptive anisotropic meshing for steady convection-dominated problems

Description: Obtaining accurate solutions for convection–diffusion equations is challenging due to the presence of layers when convection dominates the diffusion. To solve this problem, we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution. Three main ingredients are used. First, the streamline upwind Petrov–Galerkin method is used to produce a stabilized solution. Second, an adapted metric tensor is computed from the approximate solution. Third, optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal Voronoi tessellation algorithm. Our algorithm is tested on a variety of two-dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non-physical oscillations in the numerical approximation.
Date: January 1, 2009
Creator: Nguyen, Hoa; Gunzburger, Max; Ju, Lili & Burkardt, John
Partner: UNT Libraries Government Documents Department

Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

Description: Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.
Date: January 1, 2006
Creator: Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N. & Kennedy, Christopher A.
Partner: UNT Libraries Government Documents Department

Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

Description: This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.
Date: December 1, 2005
Creator: Turner, C. David; Kotulski, Joseph Daniel & Pasik, Michael Francis
Partner: UNT Libraries Government Documents Department

An improved bi-level algorithm for partitioning dynamic grid hierarchies.

Description: Structured adaptive mesh refinement methods are being widely used for computer simulations of various physical phenomena. Parallel implementations potentially offer realistic simulations of complex three-dimensional applications. But achieving good scalability for large-scale applications is non-trivial. Performance is limited by the partitioner's ability to efficiently use the underlying parallel computer's resources. Designed on sound SAMR principles, Nature+Fable is a hybrid, dedicated SAMR partitioning tool that brings together the advantages of both domain-based and patch-based techniques while avoiding their drawbacks. But the original bi-level partitioning approach in Nature+Fable is insufficient as it for realistic applications regards frequently occurring bi-levels as ''impossible'' and fails. This document describes an improved bi-level partitioning algorithm that successfully copes with all possible bi-levels. The improved algorithm uses the original approach side-by-side with a new, complementing approach. By using a new, customized classification method, the improved algorithm switches automatically between the two approaches. This document describes the algorithms, discusses implementation issues, and presents experimental results. The improved version of Nature+Fable was found to be able to handle realistic applications and also to generate less imbalances, similar box count, but more communication as compared to the native, domain-based partitioner in the SAMR framework AMROC.
Date: May 1, 2006
Creator: Deiterding, Ralf; Johansson, Henrik; Steensland, Johan & Ray, Jaideep
Partner: UNT Libraries Government Documents Department

High-Fidelity Geometric Modelling for Biomedical Applications

Description: We describe a combination of algorithms for high fidelity geometric modeling and mesh generation. Although our methods and implementations are application-neutral, our primary target application is multiscale biomedical models that range in scales across the molecular, cellular, and organ levels. Our software toolchain implementing these algorithms is general in the sense that it can take as input a molecule in PDB/PQR forms, a 3D scalar volume, or a user-defined triangular surface mesh that may have very low quality. The main goal of our work presented is to generate high quality and smooth surface triangulations from the aforementioned inputs, and to reduce the mesh sizes by mesh coarsening. Tetrahedral meshes are also generated for finite element analysis in biomedical applications. Experiments on a number of bio-structures are demonstrated, showing that our approach possesses several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). The availability of this software toolchain will give researchers in computational biomedicine and other modeling areas access to higher-fidelity geometric models.
Date: April 1, 2008
Creator: Zeyun Yu, Michael Holst, and J.A. McCammon
Partner: UNT Libraries Government Documents Department

Computer simulation with CaPS of an aluminum plate casting

Description: A simulation of a benchmark test casting has been performed with the CaPS-3D casting process simulator software. The test casting was made at the University of Birmingham in the UK for the 7th International Conference on the Modeling of Casting, Welding and Advanced Solidification Processes. The measured results were not available prior to the simulation, hence the simulation is a blind prediction.
Date: December 31, 1995
Creator: Domanus, H.M.; Schmitt, R.C.; Chuzhoy, L. & Nastac, L.
Partner: UNT Libraries Government Documents Department

Overture: an objectoriented framework for solving partial differential equations on overlapping grids

Description: The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It merges geometry, grid generation, difference operators, boundary conditions, data-base access and graphics into an easy to use high level interface.
Date: September 22, 1998
Creator: Brown, D L; Henshaw, W D & Quinlan , D J
Partner: UNT Libraries Government Documents Department

Overture: The grid classes

Description: Overture is a library containing classes for grids, overlapping grid generation and the discretization and solution of PDEs on overlapping grids. This document describes the Overture grid classes, including classes for single grids and classes for collections of grids.
Date: January 1, 1997
Creator: Brislawn, K.; Brown, D.; Chesshire, G. & Henshaw, W.
Partner: UNT Libraries Government Documents Department

PMESH: A parallel mesh generator

Description: The Parallel Mesh Generation (PMESH) Project is a joint LDRD effort by A Division and Engineering to develop a unique mesh generation system that can construct large calculational meshes (of up to 10{sup 9} elements) on massively parallel computers. Such a capability will remove a critical roadblock to unleashing the power of massively parallel processors (MPPs) for physical analysis. PMESH will support a variety of LLNL 3-D physics codes in the areas of electromagnetics, structural mechanics, thermal analysis, and hydrodynamics.
Date: October 21, 1994
Creator: Hardin, D.D.
Partner: UNT Libraries Government Documents Department

Efficient second order remapping on arbitrary two dimensional meshes

Description: The authors have developed an efficient method of remapping physical variables from one unstructured grid composed of arbitrary polygons to another, based on the work of Ramshaw and Dukowicz. Eulerian cycles are used to convert the mesh into a single chain of connected edge,s which eliminates grid searching. The error is second order in the zone size. The algorithm handles degenerate meshes well. Computational effort to perform a remap scales linearly with the number of zones in the two grids, which is an improvement over typical N log N methods.
Date: March 18, 1996
Creator: Miller, D.S.; Burton, D.E. & Oliviera, J.S.
Partner: UNT Libraries Government Documents Department

ROAMing terrain (Real-time Optimally Adapting Meshes)

Description: Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and ground-based aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, view-dependent triangle meshes and texture maps that produce good images at the required frame rate. We present an algorithm for constructing triangle meshes that optimizes flexible view-dependent error metrics, produces guaranteed error bounds, achieves specified triangle counts directly, and uses frame-to-frame coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Real-time Optimally Adapting Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from pre-processed bintree triangles. We introduce two additional performance optimizations: incremental triangle stripping and priority-computation deferral lists. ROAM execution time is proportionate to the number of triangle changes per frame, which is typically a few percent of the output mesh size, hence ROAM performance is insensitive to the resolution and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.
Date: July 1, 1997
Creator: Duchaineau, M.; Wolinsky, M.; Sigeti, D.E.; Miller, M.C.; Aldrich, C. & Mineev, M.
Partner: UNT Libraries Government Documents Department

Semicoarsening multigrid for systems

Description: Previously we examined the black box multigrid approach to systems of equations. The approach was a direct extension of the methodology used for scalar equations; that is, interpolation and residual weighting were operator induced, and coarsening employed a Galerkin strategy. The application was to standard coarsening of the unknowns. In this paper we consider a semicoarsening approach and find that there are a few differences in what is generally effective.
Date: April 1, 1997
Creator: Dendy, J.E. Jr.
Partner: UNT Libraries Government Documents Department