Beall M.W., Shephard M.S. "A General Topology-Based Mesh Data Structure." International Journal for Numerical Methods in Engineering, vol. 40, no. 9, 1573--1596, May 1997  Home/Search   Document Not in Database   Summary   Related Articles   Check

....can arise, allowing templates to be constructed for the partition of unity functions on the octants. Last but not least, the structure of the octree reduces the memory consumption compared to a finite element mesh. For the same spatial discretization size the finite element mesh structure [4] needs about four times as much memory than the octree structure [14] The paper is organized as follows: in section 2 we introduce the octree structure used as the basic building block for the partition of unity and the integration cells. Sections 3 and 4 describe how the open cover and the ....

....far less rules than a finite element mesh. Furthermore, the octree has very good localization capabilities allowing refinement of the discretization in areas of singularities if necessary. Last but not least, the memory consumption is about four times smaller compared to a finite element structure [4] since the high structure of the octree allows it to calculate needed information fast rather than storing it, e.g. the coordinates of the corners of an octant can be computed from the coordinate of the center and the size of the octant. For methods constructing the partition of unity based on ....

Beall, MW; Shephard, MS (1997): A General Topology-Based Mesh Data Structure. Int. J. Numer. Meth. Eng. 40, 1573 - 1596.

....mathematical framework for handling triangle (tetrahedron) insertion and removal into unstructured meshes becomes an important issue. Effective representation of unstructured meshes is also critical, and several data structures to represent and manipulate them have been published over the years [5][6] 7] Such structures usually offer efficient solutions to represent and recover mesh topology and modify its geometric parameters. To insert new elements into the mesh, or to remove existing elements, some data structures define operators that ensure the topological consistency of the resulting ....

....the topological consistency while manipulating elements during the mesh construction process. A topological data structure should meet some fundamental requirements in order to hold the complete topological information and support effective representation and manipulation of meshes. Beall et al. [5] point out some of such requirements and propose several implementation alternatives for three dimensional meshes. They also offer an interesting analysis of storage requirements with comparative results, but do not discuss topological operators to manage the data structures presented. Some ....

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Beall, M.W.; Shephard M. (1997) A general topology-based mesh data structure. Int. J. for Numerical Methods in Engineering, 40:1573-1596.

....on the use of parallel computers using the MPI library for interprocessor communication. Details of the parallel communication structures used here may be found in Whiting, et al. The hierarchical basis that we have chosen is based on the abstract mesh data structure of Beall and Shephard [2], where basis functions are considered to be attached to the individual topological entities of the finite element mesh. Mesh entity based hierarchical basis functions support nonuniform k refinement of meshes of arbitrary element type, e.g. tetrahedral, hexahedral, and pyramid. To gain this ....

.... the basis functions that contribute to the element level matrices appearing in the finite element formulation, it is necessary to first make precise the concept of a topological hierarchy of mesh entities (more details of the mesh data structures may be found in the work of Beall and Shephard [2]) The basis functions will then be defined in terms of parametric coordinate systems associated with these individual structures. This is in contrast to the Lagrange basis functions which are defined in terms of traditional element parametric coordinates. The finite element mesh, denoted by TM, ....

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M. W. Beall and M. S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meth. Engng., 40(9):1573-1596, 1997.

....3 Meshing of topological entities Our approach to meshing general domains consists of a traversal of the B Rep tree in a bottom up fashion, with the edges being meshed first, then the faces and finally the sub bodies. This hierarchical approach aims at ensuring the validity of the final mesh [57, 3]. An underlying element size distribution function h(x) is assumed to be defined throughout the domain Omega to be meshed. For convenience, we define the size h of a tetrahedron as p 2=3 the radius of its circumscribed sphere. By this convention, for a regular tetrahedron h equals one half of ....

M.W. Beall and M. S. Shephard. A general topology-based mesh data structure. International Journal for Numerical Methods in Engineering, 40:1573--1596, 1997.

....when using elements with curved edges or faces (cf. Section 5. 4) If the finite element basis were known at the preprocessing stage, space could be reserved for edge and interior nodes or for a symbolic factorization of the resulting algebraic system (cf. Chapter 11) Beall and Shephard [4] introduced a database and data structure that have great flexibility. It is suitable for use with high order and hierarchical bases, adaptive mesh refinement and or order variation, and arbitrarily complex domains. It has a hierarchical structure with three dimensional elements (regions) having ....

....illustrating the SCOREC mesh database. Faces are indexed as shown at the upper left, edge numbering is shown at the upper right, and vertex numbering is shown at the bottom. 12 Mesh Generation and Assembly Face Edge Edge Edge 1 1 [ 1 ] 7 [ 1 2] 6 [ 1 9] 2 2 [ 2 ] 8 [ 2 3] 7 [ 2 1] 3 8 [ 3 2] 9 [ 3 4] 12 [ 3 6] 4 3 [ 4 ] 10 [ 4 5] 9 [ 4 3] 5 10 [ 5 4] 14 [ 5 7] 13 [ 5 6] 6 12 [ 6 3] 13 [ 6 5] 11 [ 6 11] 7 4 [ 7 ] 15 [ 7 8] 14 [ 7 5] 8 15 [ 8 7] 5 [ 8 ] 16 [ 8 13] 9 6 [ 9 1] 17 [ 9 10] 22 [ 9 ] 10 17 [10 9] 19 [10 11] 18 [10 14] 11 11 [11 6] 20 [11 12] 19 [11 10] 12 20 [12 11] 21 [12 13] 24 [12 ....

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M.W. Beall and M.S. Shephard. A general topology-based mesh data structure. International Journal of Numerical Methods in Engineering, 40:1573--1596, 1997.

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M. W. Beall and M. S. Shephard, "A General Topology-based Mesh Data Structure", International Journal for Numerical Methods in Engineering, Vol. 40, 1573 (1997)

....as mesh library. 1. ALGORITHM ORIENTED MESH DATABASE A mesh is a discretization of a geometrical domain consisting of mesh entities of controlled size and distribution with simple topology (hexahedron, tetrahedron. The topology of a mesh is described with adjacencies between mesh entities [2]. Meshes are used for scienti c computation. Physical parameters, i.e. material properties and boundary conditions, are to be prescribed on the geometrical model which is the most natural representation of the domain [13] and are then related to the mesh with the analysis process. Data structures ....

M. W. Beall and M. S. Shephard, A general topology-based mesh data structure, International Journal for Numerical Methods in Engineering, 40 (1997), pp. 1573 1596.

....support information used to convert the simulation problem definition into a mathematical model form appropriate for simulation. The third structure is needed to house the domain discretizations employed by the simulation procedures. These domain discretizations can include finite element meshes [2], finite di#erence grids, partition of unity discretizations [3] etc. The fourth structure, referred to as a field, links the simulation results, defined on the appropriate discrete models to the problem definition and the product definition. In most cases the solid modelers underlying the CAD ....

....with the domain definition as needed to associate attribute data to the discrete models and to relate the simulation results back to the domain definition. Such a structure has been developed for finite element meshes using an e#ective boundary hierarchy of regions, faces, edges and vertices [2]. To support the proper association of the simulation results with the domain definition more than just result values at a set of discrete points is needed. The field structure [12] stores all the information needed to calculate the represented tensor over the geometric domain. 6 The managers ....

Beall, M.W.; Shephard, M.S. (1997) A general topology-based mesh data structure, International Journal for Numerical Methods in Engineering, 40(9), 1573 -- 1596.

....computers. Adaptivity is central and the completed system will provide highlevel support for unstructured mesh computation. Portions of this system involving tetrahedral element mesh generation for arbitrary geometries, hand p re nement, data management, and parallel load balancing are in place [10,11,13,24]. For the breadth of nite element applications, A may be considered as sparse but, not necessarily symmetric or positive de nite. Our approach must be Preprint submitted to Elsevier Preprint 17 June 1997 conservative in both memory and processing requirements, growing as slowly as possible with ....

....obtained from CAD systems with a hierarchical mesh database [23] 2 This arrangement makes geometric data available during the computation without requiring complete integration of the discrete and physical models. The mesh is a hierarchical structure of region, face, edge and vertex entities [10,23]. Each entity is associated with one or more of its components. For example, a tetrahedral region is associated with its four faces, which, in turn are associated with their three edges, which are associated with their two vertices. The association is bi directional; thus, higher dimensional ....

M. W. Beall and M. S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meths. Engng., 1997. to appear.

....computers. Adaptivity is central and the completed system will provide highlevel support for unstructured mesh computation. Portions of this system involving tetrahedral element mesh generation for arbitrary geometries, hand p refinement, data management, and parallel load balancing are in place [10,11,13,24]. For the breadth of finite element applications, A may be considered as sparse but, not necessarily symmetric or positive definite. Our approach must be Preprint submitted to Elsevier Preprint 23 January 1997 conservative in both memory and processing requirements, growing as slowly as possible ....

....obtained from CAD systems with a hierarchical mesh database [23] 2 This arrangement makes geometric data available during the computation without requiring complete integration of the discrete and physical models. The mesh is a hierarchical structure of region, face, edge and vertex entities [10,23]. Each entity is associated with one or more of its components. For example, a tetrahedral region is associated with its four faces, which, in turn are associated with their three edges, which are associated with their two vertices. The association is bi directional; thus, higher dimensional ....

M. W. Beall and M. S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meths. Engng., 1997. to appear.

....for any Delaunay type triangulation scheme [10] 3. The outside entities are deleted from the cavity mesh by checking classification information. Top down deletion is required for a hierarchical mesh database in which there is up and down inheritance in vertex edge face region entity links [11]. The deletion of outside regions from the cavity mesh is shown for two example cavities in Figure 11 and Figure 12. The algorithm of the first stage can be given in pseudo code form as below: Input: Original cavity boundary mesh faces as Faces For each cavity boundary face M 2 c from faces ....

M. W. Beall and M. S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meth. Engng., 40(19):1573--1596, 1997.

....environment, the octree also serves as a means to partition the domain to be discretized. A parallel octree library supports the creation and distribution of octree structures (Section 4) We use a hierarchical representation of finite element meshes that is appropriate for h or p refinement [3]. A Parallel Mesh Database [22, 45] provides operators to create and manipulate distributed mesh data. Poor partitioning of data across the processors of a parallel computer leads to high communication costs. Several static partitioning algorithms have been developed [5, 20, 38, 27] however, ....

M. W. Beall and M. S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meth. Engng., 40(9):1573--1596, 1997.

....which define the primary topological elements of the mesh domain. Critical to the understanding of the relationship of the mesh with the geometric domain is the concept of classification of a mesh with respect to its geometric model. Definition: Mesh Classification Against the Geometric Model [5,14,15] The unique association of a topological mesh entity of dimension , to a topological geometric model entity of dimension , where , is termed classification and is denoted where the classification symbol, indicates that the left hand entity, or set, is classified on the right hand entity. ....

....region, on the domain face, on the domain edge, or on the domain vertex, on which it lies. Mesh entities are always classified with respect to the lowest order object entity possible. Restrictions on the topology of a mesh which allow the use of only the primary topological entities are [5]: 1. Regions and faces have no interior holes. 2. Each entity of order in a mesh, may use a particular entity of lower order, at most once. 3. For any entity there is a unique set of entities of order , that are on the boundary of if at least one member of is classified on where . The first ....

Beall, M.W. and Shephard, M.S., "A General Topology-Based Mesh Data Structure", Int. J. Num. Meth. Engng., 40(9):1573-1596, 1997.

....of data. Tools developed at the Scientific Computation Research Center (SCOREC) at Rensselaer to facilitate the development and use of parallel adaptive finite element software are described in Section 2. An object oriented, hierarchical mesh database is used to store and manipulate mesh data [3]. Meshes are created by an automatic finite octree procedure [35] Parallel extensions to the mesh database allow operations to be performed on distributed data and provide for the dynamic migration of finite elements [7,30] Parallel mesh enrichment routines are used for spatial refinement and ....

....to demonstrate the advantages of predictive load balancing. The solution of a transient flow in a muzzle brake is shown as Example 3 in Section 4.4. In Section 5, we discuss results and present future research directions. 2 SCOREC Mesh Tools 2. 1 SCOREC Mesh Database The SCOREC Mesh Database (MDB) [3] provides an object oriented hierarchical representation of a finite element mesh. It also includes a set of operators to query and update the mesh data structure. The basic mesh entity hierarchy consists of three dimensional regions, and their bounding faces, edges, and vertices, with ....

M. W. Beall and M. S. Shephard, A general topology-based mesh data structure, to appear Int. J. Numer. Meth. Engng. (1997).

....on issues specific to a given problem rather than the details of the underlying data structures or parallelization issues, a number of tools have been developed. They provide a uniform way to implement reusable parallel adaptive software. 2.1. Mesh data structures The SCOREC Mesh Database (MDB) [2] provides an object oriented representation of a finite element mesh and operators to query and update the mesh data structure. The mesh entity hierarchy consists of threedimensional regions, and their bounding faces, edges, and vertices, with bidirectional links between mesh entities of ....

M. W. Beall and M. S. Shephard. A general topologybased mesh data structure. To appear Int. J. Numer. Meth. Engng., 1997.

....way and enable the programmer to concentrate on issues specific to the problem at hand rather than the details of the underlying mesh structures or parallelization concerns. Initial meshes are created using the SCOREC Finite Octree Automatic Mesh Generator [3] The SCOREC Mesh Database (MDB) [4] provides an object oriented hierarchical representation of a finite element mesh and a set of operators to query and update the mesh data structure. The basic mesh entity hierarchy consists of threedimensional regions, and their bounding faces, edges, and vertices, with bidirectional links ....

M. W. Beall and M. S. Shephard. A general topology-based mesh data structure. To appear Int. J. Numer. Meth. Engng., 1997.

.... (p refinement) Each adaptive process concentrates the computational effort in areas where the solution resolution would otherwise be inadequate [7] Conventional array based data representations, which work well for fixed mesh solutions, are not wellsuited to solutions involving mesh adaptivity [1]. Traversal of the data must be efficient in all cases, but when adaptivity is introduced, modification of the mesh structures and corresponding solution data must also be efficient. Parallel computation introduces complications such as the need to balance processor loading, coordinate ....

....view of the data structures. Two basic paradigms have been used as the underlying structure for these computations. An array based approach, such as the Scalable Distributed Dynamic Array [11] uses the distribution of arrays as the fundamental unit of parallelism. The mesh based approach [1,4,14,21,24 27] uses mesh connectivity and distribution of mesh entities to achieve parallelism. Our recent efforts have focused on implementing a framework for the reliable automated solution of problems in science and engineering over arbitrary domains using scalable parallel adaptive techniques [2] This ....

[Article contains additional citation context not shown here]

M. W. Beall and M. S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meth. Engng., 40(9):1573--1596, 1997.

No context found.

Beall M.W., Shephard M.S. "A General Topology-Based Mesh Data Structure." International Journal for Numerical Methods in Engineering, vol. 40, no. 9, 1573--1596, May 1997

No context found.

M. W. Beall and M. S. Shephard, A general topology-based mesh data structure, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 1573--1596.

No context found.

M. W. Beall and M. S. Shephard, A general topology-based mesh data structure, Internat. J. Numer. Methods Engrg., 40 (1997), pp. 1573--1596.

No context found.

Mark W. Beall and Mark S. Shephard. A general topology-based mesh data structure. Int. J. Numer. Meth. Engng., 40(9):1573--1596, 1997.

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