An integrated approach, combining the continuum theory of sintering and Potts model based mesostructure evolution analysis, is used to solve the problem of bi-layered structure sintering. Two types of bi-layered structures are considered: layers of the same material with different initial porosity, and layers of two different materials. The effective sintering stress for the bi-layer powder sintering is derived, both at the meso- and the macroscopic levels. Macroscopic shape distortions and spatial distributions of porosity are determined as functions of the dimensionless specific time of sintering. The effect of the thickness of the layers on shrinkage, warpage, and pore-grain structure is studied. Ceramic ZnO powders are employed as a model experimental system to assess the model predictions.
A theory is developed for the response of moderately porous solids (no more than {approximately}20% void space) to high-strain-rate deformations. The model is consistent because each feature is incorporated in a manner that is mathematically compatible with the other features. Unlike simple p-{alpha} models, the onset of pore collapse depends on the amount of shear present. The user-specifiable yield function depends on pressure, effective shear stress, and porosity. The elastic part of the strain rate is linearly related to the stress rate, with nonlinear corrections from changes in the elastic moduli due to pore collapse. Plastically incompressible flow of the matrix material allows pore collapse and an associated macroscopic plastic volume change. The plastic strain rate due to pore collapse/growth is taken normal to the yield surface. If phase transformation and/or pore nucleation are simultaneously occurring, the inelastic strain rate will be non-normal to the yield surface. To permit hardening, the yield stress of matrix material is treated as an internal state variable. Changes in porosity and matrix yield stress naturally cause the yield surface to evolve. The stress, porosity, and all other state variables vary in a consistent manner so that the stress remains on the yield surface throughout any quasistatic interval of plastic deformation. Dynamic loading allows the stress to exceed the yield surface via an overstress ordinary differential equation that is solved in closed form for better numerical accuracy. The part of the stress rate that causes no plastic work (i.e-, the part that has a zero inner product with the stress deviator and the identity tensor) is given by the projection of the elastic stressrate orthogonal to the span of the stress deviator and the identity tensor.The model, which has been numerically implemented in MIG format, has been exercised under a wide array of extremal loading and unloading paths. As will be discussed in a companion sequel report, the CKP model is capable of closely matching plate impact measurements for porous materials.
A numerical flow model is developed to simulate two-dimensional fluid flow past immersed, elastically supported tube arrays. This work is motivated by the objective of predicting forces and motion associated with both deep-water drilling and production risers in the oil industry. This work has other engineering applications including simulation of flow past tubular heat exchangers or submarine-towed sensor arrays and the flow about parachute ribbons. In the present work, a vortex method is used for solving the unsteady flow field. This method demonstrates inherent advantages over more conventional grid-based computational fluid dynamics. The vortex method is non-iterative, does not require artificial viscosity for stability, displays minimal numerical diffusion, can easily treat moving boundaries, and allows a greatly reduced computational domain since vorticity occupies only a small fraction of the fluid volume. A gridless approach is used in the flow sufficiently distant from surfaces. A Lagrangian remap scheme is used near surfaces to calculate diffusion and convection of vorticity. A fast multipole technique is utilized for efficient calculation of velocity from the vorticity field. The ability of the method to correctly predict lift and drag forces on simple stationary geometries over a broad range of Reynolds numbers is presented.
The moduli used in RSA (see [5]) can be generated by many different sources. The generator of that modulus (assuming a single entity generates the modulus) knows its factorization. They would have the ability to forge signatures or break any system based on this moduli. If a moduli and the RSA parameters associated with it were generated by a reputable source, the system would have higher value than if the parameters were generated by an unknown entity. So for tracking, security, confidence and financial reasons it would be beneficial to know who the generator of the RSA modulus was. This is where digital marking comes in. An RSA modulus ia digitally marked, or digitally trade marked, if the generator and other identifying features of the modulus (such as its intended user, the version number, etc.) can be identified and possibly verified by the modulus itself. The basic concept of digitally marking an RSA modulus would be to fix the upper bits of the modulus to this tag. Thus anyone who sees the public modulus can tell who generated the modulus and who the generator believes the intended user/owner of the modulus is.
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.
In this paper we introduce by means of examples a new technique for formulating compact (i.e. polynomial-size) LP relaxations in place of exponential-size models requiring separation algorithms. In the same vein as a celebrated theorem by Groetschel, Lovasz and Schrijver, we state the equivalence of compact separation and compact optimization. Among the examples used to illustrate our technique, we introduce a new formulation for the Traveling Salesman Problem, whose relaxation we show equivalent to the subtour elimination relaxation.
In this paper the authors present the current status of an unsteady 3D parachute simulation code which is being developed at Sandia National Laboratories under the Department of Energy's Accelerated Strategic Computing Initiative (ASCI). The Vortex Inflation PARachute code (VIPAR) which embodies this effort will eventually be able to perform complete numerical simulations of ribbon parachute deployment, inflation, and steady descent. At the present time they have a working serial version of the uncoupled fluids code which can simulate unsteady 3D incompressible flows around bluff bodies made up of triangular membrane elements. A parallel version of the code has just been completed which will allow one to compute flows over complex geometries utilizing several thousand processors on one of the new DOE teraFLOP computers.
The authors understanding of multiphase physics and the associated predictive capability for multi-phase systems are severely limited by current continuum modeling methods and experimental approaches. This research will deliver an unprecedented modeling capability to directly simulate three-dimensional multi-phase systems at the particle-scale. The model solves the fully coupled equations of motion governing the fluid phase and the individual particles comprising the solid phase using a newly discovered, highly efficient coupled numerical method based on the discrete-element method and the Lattice-Boltzmann method. A massively parallel implementation will enable the solution of large, physically realistic systems.
Combinatorial Chemistry is a powerful new technology in drug design and molecular recognition. It is a wet-laboratory methodology aimed at ``massively parallel'' screening of chemical compounds for the discovery of compounds that have a certain biological activity. The power of the method comes from the interaction between experimental design and computational modeling. Principles of ``rational'' drug design are used in the construction of combinatorial libraries to speed up the discovery of lead compounds with the desired biological activity. This paper presents algorithms, software development and computational complexity analysis for problems arising in the design of combinatorial libraries for drug discovery. The authors provide exact polynomial time algorithms and intractability results for several Inverse Problems-formulated as (chemical) graph reconstruction problems-related to the design of combinatorial libraries. These are the first rigorous algorithmic results in the literature. The authors also present results provided by the combinatorial chemistry software package OCOTILLO for combinatorial peptide design using real data libraries. The package provides exact solutions for general inverse problems based on shortest-path topological indices. The results are superior both in accuracy and computing time to the best software reports published in the literature. For 5-peptoid design, the computation is rigorously reduced to an exhaustive search of about 2% of the search space; the exact solutions are found in a few minutes.
A gridless technique for the solution of the integral form of the radiative heat flux equation for emitting and absorbing media is presented. Treatment of non-uniform absorptivity and gray boundaries is included. As part of this work, the authors have developed fast multipole techniques for extracting radiative heat flux quantities from the temperature fields of one-dimensional and three-dimensional geometries. Example calculations include those for one-dimensional radiative heat transfer through multiple flame sheets, a three-dimensional enclosure with black walls, and an axisymmetric enclosure with black walls.
The weld solidification and cracking behavior of sulfur bearing free machining austenitic stainless steel was investigated for both gas-tungsten arc (GTA) and pulsed laser beam weld processes. The GTA weld solidification was consistent with those predicted with existing solidification diagrams and the cracking response was controlled primarily by solidification mode. The solidification behavior of the pulsed laser welds was complex, and often contained regions of primary ferrite and primary austenite solidification, although in all cases the welds were found to be completely austenite at room temperature. Electron backscattered diffraction (EBSD) pattern analysis indicated that the nature of the base metal at the time of solidification plays a primary role in initial solidification. The solid state transformation of austenite to ferrite at the fusion zone boundary, and ferrite to austenite on cooling may both be massive in nature. A range of alloy compositions that exhibited good resistance to solidification cracking and was compatible with both welding processes was identified. The compositional range is bounded by laser weldability at lower Cr{sub eq}/Ni{sub eq} ratios and by the GTA weldability at higher ratios. It was found with both processes that the limiting ratios were somewhat dependent upon sulfur content.
The authors have discussed the three factors that they believe are the most important in determining the difficulty of a beam shaping problem: scaling, smoothness, and coherence. The arguments have been almost completely based on considering how these factors influence beam shaping lenses that were designed using geometrical optics. However, they believe that these factors control the difficulty of beam shaping problems even if one does not base ones design strategy on geometrical optics. For example, they have shown that a lens designed using geometrical optics will not work well unless {beta} is large. However, they have also shown that if {beta} is small the uncertainty principle shows that it is impossible to do a good job of beam shaping no matter how one designs ones lens.
An unconstrained minimization algorithm for electronic structure calculations using density functional for systems with a gap is developed to solve for nonorthogonal Wannier-like orbitals in the spirit of E. B. Stechel, A. R. Williams, and P. J. Feibelman, Phys. Rev. B 49, 10,008 (1994). The search for the occupied sub-space is a Grassmann conjugate gradient algorithm generalized from the algorithm of A. Edelman, T.A. Arias, and S. T. Smith, SIAM J. on Matrix Anal. Appl. 20, 303 (1998). The gradient takes into account the nonorthogonality of a local atom-centered basis, gaussian in their implementation. With a localization constraint on the Wannier-like orbitals, well-constructed sparse matrix multiplies lead to O(N) scaling of the computationally intensive parts of the algorithm. Using silicon carbide as a test system, the accuracy, convergence, and implementation of this algorithm as a quantitative alternative to diagonalization are investigated. Results up to 1,458 atoms on a single processor are presented.
The authors present the results of molecular dynamics simulations of n-butane and isobutane in silicalite. They begin with a comparison of the bulk adsorption and diffusion properties for two different parameterizations of the interaction potential between the hydrocarbon species, both of which have been shown to reproduce experimental gas-liquid coexistence curves. They examine diffusion as a function of the loading of the zeolite, as well as the temperature dependence of the diffusion constant at loading and for infinite dilution. They continue with simulations in which interfaces are formed between single component gases and the zeolite. After reaching equilibrium, they examine the dynamics of exchange between the bulk gas and the zeolite. Finally, they calculate the permeability of the zeolite for n-butane and isobutane as a function of pressure. Their simulations are performed for a number of different gas temperatures and pressures, covering a wide range of state points.
The authors describe a convergence theory for evolutionary pattern search algorithms (EPSAs) on a broad class of unconstrained and linearly constrained problems. EPSAs adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAs is inspired by recent analyses of pattern search methods. The analysis significantly extends the previous convergence theory for EPSAs. The analysis applies to a broader class of EPSAs,and it applies to problems that are nonsmooth, have unbounded objective functions, and which are linearly constrained. Further, they describe a modest change to the algorithmic framework of EPSAs for which a non-probabilistic convergence theory applies. These analyses are also noteworthy because they are considerably simpler than previous analyses of EPSAs.
A procedure for code Verification by the Method of Manufactured Solutions (MMS) is presented. Although the procedure requires a certain amount of creativity and skill, we show that MMS can be applied to a variety of engineering codes which numerically solve partial differential equations. This is illustrated by detailed examples from computational fluid dynamics. The strength of the MMS procedure is that it can identify any coding mistake that affects the order-of-accuracy of the numerical method. A set of examples which use a blind-test protocol demonstrates the kinds of coding mistakes that can (and cannot) be exposed via the MMS code Verification procedure. The principle advantage of the MMS procedure over traditional methods of code Verification is that code capabilities are tested in full generality. The procedure thus results in a high degree of confidence that all coding mistakes which prevent the equations from being solved correctly have been identified.
Many parallel applications require periodic redistribution of workloads and associated data. In a distributed memory computer, this redistribution can be difficult if limited memory is available for receiving messages. The authors propose a model for optimizing the exchange of messages under such circumstances which they call the minimum phase remapping problem. They first show that the problem is NP-Complete, and then analyze several methodologies for addressing it. First, they show how the problem can be phrased as an instance of multi-commodity flow. Next, they study a continuous approximation to the problem. They show that this continuous approximation has a solution which requires at most two more phases than the optimal discrete solution, but the question of how to consistently obtain a good discrete solution from the continuous problem remains open. Finally, they devise a simple and practical approximation algorithm for the problem with a bound of 1.5 times the optimal number of phases.
An integrated approach, including a continuum theory of sintering and mesostructure evolution analysis, is used for the solution of the problem of bi-layered structure sintering. Two types of bi-layered structures are considered: layers of the same material different by initial porosity, and layers of two different materials. The effective sintering stress and the normalized bulk modulus for the bi-layer powder sintering are derived based on mesoscale simulations. The combined effect of the layers' porosity and differences in sintering rate on shrinkage and warpage is studied for both sintering on a rigid substrate and free sintering.
Most algorithms used in preconditioned iterative methods are generally applicable to complex valued linear systems, with real valued linear systems simply being a special case. However, most iterative solver packages available today focus exclusively on real valued systems, or deal with complex valued systems as an afterthought. One obvious approach to addressing this problem is to recast the complex problem into one of a several equivalent real forms and then use a real valued solver to solve the related system. However, well-known theoretical results showing unfavorable spectral properties for the equivalent real forms have diminished enthusiasm for this approach. At the same time, experience has shown that there are situations where using an equivalent real form can be very effective. In this paper, the authors explore this approach, giving both theoretical and experimental evidence that an equivalent real form can be useful for a number of practical situations. Furthermore, they show that by making good use of some of the advance features of modem solver packages, they can easily generate equivalent real form preconditioners that are computationally efficient and mathematically identical to their complex counterparts. Using their techniques, they are able to solve very ill-conditioned complex valued linear systems for a variety of large scale applications. However, more importantly, they shed more light on the effectiveness of equivalent real forms and more clearly delineate how and when they should be used.
Processes that involve particle-laden fluids are common in geomechanics and especially in the petroleum industry. Understanding the physics of these processes and the ability to predict their behavior requires the development of coupled fluid-flow and particle-motion computational methods. This paper outlines an accurate and robust coupled computational scheme using the lattice-Boltzmann method for fluid flow and the discrete-element method for solid particle motion. Results from several two-dimensional validation simulations are presented. Simulations reported include the sedimentation of an ellipse, a disc and two interacting discs in a closed column of fluid. The recently discovered phenomenon of drafting, kissing, and tumbling is fully reproduced in the two-disc simulation.
The authors describe a naturalistic behavioral model for the simulation of small unit combat. This model, Klein's recognition-primed decision making (RPD) model, is driven by situational awareness rather than a rational process of selecting from a set of action options. They argue that simulated combatants modeled with RPD will have more flexible and realistic responses to a broad range of small-scale combat scenarios. Furthermore, they note that the predictability of a simulation using an RPD framework can be easily controlled to provide multiple evaluations of a given combat scenario. Finally, they discuss computational issues for building an RPD-based behavior engine for fully automated combatants in small conflict scenarios, which are being investigated within Sandia's Next Generation Site Security project.
This report summarizes materials issues associated with advanced micromachines development at Sandia. The intent of this report is to provide a perspective on the scope of the issues and suggest future technical directions, with a focus on computational materials science. Materials issues in surface micromachining (SMM), Lithographic-Galvanoformung-Abformung (LIGA: lithography, electrodeposition, and molding), and meso-machining technologies were identified. Each individual issue was assessed in four categories: degree of basic understanding; amount of existing experimental data capability of existing models; and, based on the perspective of component developers, the importance of the issue to be resolved. Three broad requirements for micromachines emerged from this process. They are: (1) tribological behavior, including stiction, friction, wear, and the use of surface treatments to control these, (2) mechanical behavior at microscale, including elasticity, plasticity, and the effect of microstructural features on mechanical strength, and (3) degradation of tribological and mechanical properties in normal (including aging), abnormal and hostile environments. Resolving all the identified critical issues requires a significant cooperative and complementary effort between computational and experimental programs. The breadth of this work is greater than any single program is likely to support. This report should serve as a guide to plan micromachines development at Sandia.
This paper examines the modeling accuracy of finite element interpolation, kriging, and polynomial regression used in conjunction with the Progressive Lattice Sampling (PLS) incremental design-of-experiments approach. PLS is a paradigm for sampling a deterministic hypercubic parameter space by placing and incrementally adding samples in a manner intended to maximally reduce lack of knowledge in the parameter space. When combined with suitable interpolation methods, PLS is a formulation for progressive construction of response surface approximations (RSA) in which the RSA are efficiently upgradable, and upon upgrading, offer convergence information essential in estimating error introduced by the use of RSA in the problem. The three interpolation methods tried here are examined for performance in replicating an analytic test function as measured by several different indicators. The process described here provides a framework for future studies using other interpolation schemes, test functions, and measures of approximation quality.
This case study presents initial results from research targeted at the development of cost-effective scalable visualization and rendering technologies. The implementations of two 3D graphics libraries based on the popular sort-last and sort-middle parallel rendering techniques are discussed. An important goal of these implementations is to provide scalable rendering capability for extremely large datasets (>> 5 million polygons). Applications can use these libraries for either run-time visualization, by linking to an existing parallel simulation, or for traditional post-processing by linking to an interactive display program. The use of parallel, hardware-accelerated rendering on commodity hardware is leveraged to achieve high performance. Current performance results show that, using current hardware (a small 16-node cluster), they can utilize up to 85% of the aggregate graphics performance and achieve rendering rates in excess of 20 million polygons/second using OpenGL{reg_sign} with lighting, Gouraud shading, and individually specified triangles (not t-stripped).
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.
This paper analyzes the scalability limitations of networking technologies based on the Virtual Interface Architecture (VIA) in supporting the runtime environment needed for an implementation of the Message Passing Interface. The authors present an overview of the important characteristics of VIA and an overview of the runtime system being developed as part of the Computational Plant (Cplant) project at Sandia National Laboratories. They discuss the characteristics of VIA that prevent implementations based on this system to meet the scalability and performance requirements of Cplant.
As computational needs for structural finite element analysis increase, a robust implicit structural dynamics code is needed which can handle millions of degrees of freedom in the model and produce results with quick turn around time. A parallel code is needed to avoid limitations of serial platforms. Salinas is an implicit structural dynamics code specifically designed for massively parallel platforms. It computes the structural response of very large complex structures and provides solutions faster than any existing serial machine. This paper gives a current status of Salinas and uses demonstration problems to show Salinas' performance.
A lattice-Monte Carlo approach was developed to simulate ferroelectric domain behavior. The model utilizes a Hamiltonian for the total energy that includes electrostatic terms (involving dipole-dipole interactions, local polarization gradients, and applied electric field), and elastic strain energy. The contributions of these energy components to the domain structure and to the overall applied field response of the system were examined. In general, the model exhibited domain structure characteristics consistent with those observed in a tetragonally distorted ferroelectric. Good qualitative agreement between the appearance of simulated electrical hysteresis loops and those characteristic of real ferroelectric materials was found.
Computational materials simulations have traditionally focused on individual phenomena: grain growth, crack propagation, plastic flow, etc. However, real materials behavior results from a complex interplay between phenomena. In this project, the authors explored methods for coupling mesoscale simulations of microstructural evolution and micromechanical response. In one case, massively parallel (MP) simulations for grain evolution and microcracking in alumina stronglink materials were dynamically coupled. In the other, codes for domain coarsening and plastic deformation in CuSi braze alloys were iteratively linked. this program provided the first comparison of two promising ways to integrate mesoscale computer codes. Coupled microstructural/micromechanical codes were applied to experimentally observed microstructures for the first time. In addition to the coupled codes, this project developed a suite of new computational capabilities (PARGRAIN, GLAD, OOF, MPM, polycrystal plasticity, front tracking). The problem of plasticity length scale in continuum calculations was recognized and a solution strategy was developed. The simulations were experimentally validated on stockpile materials.
This case study provides examples of how some simple decisions the authors made in structuring their algorithms for handling cell-centered data can dramatically influence the results. Although they all know that these decisions produce variations in results, they think that they underestimate the potential magnitude of the differences. More importantly, the users of the codes may not be aware that these choices have been made or what they mean to the resulting visualizations of their data. This raises the question of whether or not these decisions are inadvertently distorting user interpretations of data sets.
US infrastructures provide essential services that support the economic prosperity and quality of life. Today, the latest threat to these infrastructures is the increasing complexity and interconnectedness of the system. On balance, added connectivity will improve economic efficiency; however, increased coupling could also result in situations where a disturbance in an isolated infrastructure unexpectedly cascades across diverse infrastructures. An understanding of the behavior of complex systems can be critical to understanding and predicting infrastructure responses to unexpected perturbation. Sandia National Laboratories has developed an agent-based model of critical US infrastructures using time-dependent Monte Carlo methods and a genetic algorithm learning classifier system to control decision making. The model is currently under development and contains agents that represent the several areas within the interconnected infrastructures, including electric power and fuel supply. Previous work shows that agent-based simulations models have the potential to improve the accuracy of complex system forecasting and to provide new insights into the factors that are the primary drivers of emergent behaviors in interdependent systems. Simulation results can be examined both computationally and analytically, offering new ways of theorizing about the impact of perturbations to an infrastructure network.
This report describes Salvo, a three-dimensional seismic-imaging software for complex geologies. Regions of complex geology, such as overthrusts and salt structures, can cause difficulties for many seismic-imaging algorithms used in production today. The paraxial wave equation and finite-difference methods used within Salvo can produce high-quality seismic images in these difficult regions. However this approach comes with higher computational costs which have been too expensive for standard production. Salvo uses improved numerical algorithms and methods, along with parallel computing, to produce high-quality images and to reduce the computational and the data input/output (I/O) costs. This report documents the numerical algorithms implemented for the paraxial wave equation, including absorbing boundary conditions, phase corrections, imaging conditions, phase encoding, and reduced-source migration. This report also describes I/O algorithms for large seismic data sets and images and parallelization methods used to obtain high efficiencies for both the computations and the I/O of seismic data sets. Finally, this report describes the required steps to compile, port and optimize the Salvo software, and describes the validation data sets used to help verify a working copy of Salvo.
This research effort focuses on methodology for quantifying the effects of model uncertainty and discretization error on computational modeling and simulation. The work is directed towards developing methodologies which treat model form assumptions within an overall framework for uncertainty quantification, for the purpose of developing estimates of total prediction uncertainty. The present effort consists of work in three areas: framework development for sources of uncertainty and error in the modeling and simulation process which impact model structure; model uncertainty assessment and propagation through Bayesian inference methods; and discretization error estimation within the context of non-deterministic analysis.
The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.
Electrical test structures of the type known as cross-bridge resistors have been patterned in (100) epitaxial silicon material that was grown on Bonded and Etched-Back Silicon-on-Insulator (BESOI) substrates. The CDs (Critical Dimensions) of a selection of their reference segments have been measured electrically, by SEM (Scanning-Electron Microscopy) cross-section imaging, and by lattice-plane counting. The lattice-plane counting is performed on phase-contrast images made by High-Resolution Transmission-Electron Microscopy (HRTEM). The reference-segment features were aligned with <110> directions in the BESOI surface material. They were defined by a silicon micromachining process which results in their sidewalls being atomically-planar and smooth and inclined at 54.737{degree} to the surface (100) plane of the substrate. This (100) implementation may usefully complement the attributes of the previously-reported vertical-sidewall one for selected reference-material applications. The SEM, HRTEM, and electrical CD (ECD) linewidth measurements that are made on BESOI features of various drawn dimensions on the same substrate is being investigated to determine the feasibility of a CD traceability path that combines the low cost, robustness, and repeatability of the ECD technique and the absolute measurement of the HRTEM lattice-plane counting technique. Other novel aspects of the (100) SOI implementation that are reported here are the ECD test-structure architecture and the making of HRTEM lattice-plane counts from both cross-sectional, as well as top-down, imaging of the reference features. This paper describes the design details and the fabrication of the cross-bridge resistor test structure. The long-term goal is to develop a technique for the determination of the absolute dimensions of the trapezoidal cross-sections of the cross-bridge resistors reference segments, as a prelude to making them available for dimensional reference applications.
