Solution-Verified Reliability Analysis and Design of Bistable MEMS Using Error Estimation and Adaptivity
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"An important component of verification and validation of computational models is solution verification, which focuses on the convergence of the desired solution quantities as one refines the spatial and temporal discretizations and iterative controls. Uncertainty analyses often treat solution verification as a separate issue, hopefully through the use of a priori grid convergence studies and selection of models with acceptable discretization errors. In this paper, a tighter connection between solution verification and uncertainty quantification is investigated. In particular, error estimation techniques, using global norm and quantity of interest error estimators, are applied to the nonlinear structural analysis of microelectromechanical systems (MEMS). Two primary approaches for uncertainty quantification are then developed: an error-corrected approach, in which simulation results are directly corrected for discretization errors, and an error-controlled approach, in which estimators are used to drive adaptive h-refinement of mesh discretizations. The former requires quantity of interest error estimates that are quantitatively accurate, whereas the latter can employ any estimator that is qualitatively accurate. Combinations of these error-corrected and error-controlled approaches are also explored. Each of these techniques treats solution verification and uncertainty analysis as a coupled problem, recognizing that the simulation errors may be influenced by, for example, conditions present in the tails of input probability distributions. The most effective and affordable of these approaches are carried forward in probabilistic design studies for robust and reliable operation of a bistable MEMS device. Computational results show that on-line and parameter-adaptive solution verification can lead to uncertainty quantification and design under uncertainty studies that are more accurate, efficient, reliable, and convenient." (Read the PDF)
Multilevel parallel optimization using massively parallel structural dynamics
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"A large-scale structural optimization of an electronics package has been completed using a massively parallel structural dynamics code. The optimization goals were to maximize safety margins for stress and acceleration resulting from transient impulse loads, while remaining within strict mass limits. The optimization process utilized non-gradient, gradient, and approximate optimization methods in succession to modify shell thickness and foam density values within the electronics package. This combination of optimization methods was successful in improving the performance from an infeasible design which violated response allowables by a factor of two to a completely feasible design with positive design margins, while remaining within the mass limits. In addition, a tradeoff curve of mass versus safety margin was developed to facilitate the design decision process. These studies employed the ASCI Red supercomputer and utilized multiple levels of parallelism on up to 2560 processors. In total, a series of calculations were performed on ASCI Red in five days, where an equivalent calculation on a single desktop computer would have taken greater than 12 years to complete. This paper conveys the approaches, results, and lessons learned from this large-scale production design application." (Read the PDF)
Computational Analysis and Optimization of a Chemical Vapor Deposition Reactor with Large-Scale Computing
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"A computational analysis and optimization is presented for the chemical vapor deposition (CVD) of silicon in a horizontal rotating disk reactor. A three-dimensional reactor-scale model for the gas flow, heat transfer, and mass transfer in a CVD reactor is coupled to a simple transport-limited surface reaction mechanism for the deposition of epitaxial silicon from trichlorosilane. The model is solved to steady-state for the deposition rate profile over the 8-inch silicon wafer using an unstructured grid finite element method and a fully coupled in-exact Newton method on parallel computers. Since a high degree of spatial uniformity in the deposition rate is desired, parameter continuation runs for 6 key operating parameters, including the inlet flow rate and the rotation rate of the substrate, were performed and their individual effects analyzed. Finally, optimization runs were performed that located operating conditions that predict non-uniformity as low as 0:1%." (Read the PDF)
