Mark W. Beall

A GENERAL TOPOLOGY-BASED MESH DATA STRUCTURE

SUMMARY A representation for a mesh based on the topological hierarchy of vertices, edges, faces and regions, is described. The representation is general and easily supports procedures ranging from mesh generation to adaptive analysis processes. Three implementations are given which concentrate on di⁄erent aspects of performance (storage requirements and speed). Comparisons are made to other published representations. ( 1997 by John Wiley & Sons, Ltd.

Automatic p-version mesh generation for curved domains

To achieve the exponential rates of convergence possible with the p-version finite element method requires properly constructed meshes. In the case of piecewise smooth domains, these meshes are characterized by having large curved elements over smooth portions of the domain and geometrically graded curved elements to isolate the edge and vertex singularities that are of interest. This paper presents a procedure under development for the automatic generation of such meshes for general three-dimensional domains defined in solid modeling systems. Two key steps in the procedure are the determination of the singular model edges and vertices, and the creation of geometrically graded elements around those entities. The other key step is the use of general curved element mesh modification procedures to correct any invalid elements created by the curving of mesh entities on the model boundary, which is required to ensure a properly geometric approximation of the domain. Example meshes are included to demonstrate the features of the procedure.

Adaptive boundary layer meshing for viscous flow simulations

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.

An Object-Oriented Framework for Reliable Numerical Simulations

Abstract.An object-oriented framework for general numerical simulations has been developed that is designed to enable the rapid development of new analysis techniques. The framework is currently being used to implement finite element and partition of unity solution techniques. This paper discusses the overall design of the framework and gives details of how finite element procedures are implemented within it.

A hierarchical partition model for adaptive finite element computation

Software tools for the solution of partial differential equations using parallel adaptive finite element methods have been developed. We describe the design and implementation of the parallel mesh structures within an adaptive framework. The most fundamental concept is that of a hierarchical partition model used to distribute finite element meshes and associated data on a parallel computer. The hierarchical model represents heterogeneous processor and network speeds, and may be used to represent processes in any parallel computing environment, including an SMP, a distributed-memory computer, a network of workstations, or some combination of these. Using this model to segment the computation into chunks which can fit into cache memory provides a potential efficiency gain from an increased cache hit rate, even in a single processor environment. The information about different processor speeds, memory sizes, and the corresponding interconnection network can be useful in a dynamic load balancing algorithm which seeks to achieve a good balance with minimal interprocessor communication penalties when a slow interconnection network is involved.

Triangulation of arbitrary polyhedra to support automatic mesh generators

An algorithm is presented for the triangulation of arbitrary non-convex polyhedral regions starting with a prescribed boundary triangulation matching existing mesh entities in the remainder of the domain. The algorithm is designed to circumvent the termination problems of volume meshing algorithms which manifest themselves in the inability to successfully create tetrahedra within small subdomains to be referred to herein as cavities. To address this need, a robust Delaunay algorithm with an eecient and termination guaranteed face recovery method is the most appropriate approach. The algorithm begins with Delaunay vertex insertion followed by a face recovery method that conserves the boundary of the cavity by utilizing local mesh modiication operations such as edge split, collapse and swap and a new set of tools which we call complex splits. The local mesh modiications are performed in such a manner that each original surface triangulation is represented either as was, or as a concatenation of triangles. When done in this manner, it is always possible to split the matching mesh entities, ensuring that a compatible mesh is created. The algorithm is robust and has been tested against complex manifold and non-manifold cavities resulting in a valid mesh of the entire domain.

Attribute Management System for Engineering Analysis

Abstract. This paper presents the design and implementation of an attribute management system that supports the specification of information, past that of the domain definition, needed to qualify an engineering analysis. The information anaged by this system includes various order tensors eeded to specify the analysis attributes of material properties, oads, and boundary conditions as well as additional data constructs used by the analysis such as strings, and references to either other attributes or model entities. The system supports general dependencies and variations of this attribute information as well as its association with the various geometric entities which constitute the geometric domain being analyzed. In addition, since the information is coupled with the model entities themselves, the system can be used to store information needed to control the discretization process of the geometric domain. Since the information can be both spatially and temporally varying, an expression subsystem was also designed into the system. The framework was designed using object-oriented techniques, implemented in C++, and can be easily maintained and extended.

A comparison of techniques for geometry access related to mesh generation

One of the major issues of mesh generation today is access to geometry in an accurate and efficient manner. This paper will review several of the issues associated with accessing geometry for mesh generation. This paper will also evaluate alternative techniques for accessing geometry and review how these techniques address, or do not address, the issues related to geometry access for mesh generation. The techniques for geometry access to be reviewed include: translation and healing, discrete representations, direct geometry access, and unified topology accessing geometry directly. The intent of this paper is to provide an overview to the alternative approaches and how they address the specific issues related to accessing geometry for mesh generation. It is not the intent of this paper to provide detailed algorithms related to accessing or repairing geometry data.

Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method

The adaptive variable p- and hp-version finite element method can achieve exponential convergence rate when a near optimal finite element mesh is provided. For general 3D domains, near optimal p-version meshes require large curved elements over the smooth portions of the domain, geometrically graded curved elements to the singular edges and vertices, and a controlled layer of curved prismatic elements in the thin sections. This paper presents a procedure that accepts a CAD solid model as input and creates a curved mesh with the desired characteristics. One key component of the procedure is the automatic identification of thin sections of the model through a set of discrete medial surface points computed from an Octree-based tracing algorithm and the generation of prismatic elements in the thin directions in those sections. The second key component is the identification of geometric singular edges and the generation of geometrically graded meshes in the appropriate directions from the edges. Curved local mesh modification operations are applied to ensure the mesh can be curved to the geometry to the required level of geometric approximation.

Computer-aided multiscale modeling tools for composite materials and structures☆

Abstract This paper presents recent research efforts at Rensselaer Polytechnic Institute aimed at developing computer-aided multiscale modeling tools for composite materials and structures aimed at predicting the macromechanical (overall) structural response, such as critical deformation, vibration and buckling modes, as well as various failure modes on the mesomechanical (lamina) level, such as delamination and ply buckling, and on the micromechanical (the scale of microconstituents) level, such as debonding, microbuckling, etc. The building blocks of this technology are (i) idealization error estimators aimed at quantifying the quality of the numerical and mathematical models of composites, (ii) multigrid technology aimed at superconvergent solution of the multiscale computational models, (iii) mathematical homogenization theory aimed at constructing inter-scale transfer operators for rapid and reliable information flow between the scales, (iv) system identification for in situ characterization of the phases and their interface, and (v) multiscale model construction and visualization.