Solution Methods for Multi-Time-Scale Multiphysics Systems
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Since 1998, the Department of Energy/NNSA National Laboratories have invested millions in strategies for assessing the credibility of computational science and engineering (CSE) models used in high consequence decision making. The answer? There is no answer. There's a process--and a lot of politics. The importance of model evaluation (verification, validation, uncertainty quantification, and assessment) increases in direct proportion to the significance of the model as input to a decision. Other fields, including computational social science, can learn from the experience of the national laboratories. Some implications for evaluating 'low cognition agents'. Epistemology considers the question, How do we know what we [think we] know? What makes Western science special in producing reliable, predictive knowledge about the world? V&V takes epistemology out of the realm of thought and puts it into practice. What is the role of modeling and simulation in the production of reliable, credible scientific knowledge about the world? What steps, investments, practices do I pursue to convince myself that the model I have developed is producing credible knowledge?
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In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of the Navier-Stokes system first presented in [25]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code.
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Proposed for publication in Computer Methods in Applied Mechanics and Engineering.
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Sandia journal manuscript; Not yet accepted for publication
In this work, we examine the formation energies of interstitials in semiconductors obtained with four different pure functionals. Explicitely we investigate three silicon self-interstitials. All functionals give the same trend among those interstitials; the lowest energy being for formation of the <110>-split, somewhat higher energy for the formation of the hexagonal interstitial, while highest energy among the three is obtained for the meta-stable tetragonal configuration. However, the value for the formation energy for a specific interstitial differs substantially in calculations using different functionals. It is shown that the main contribution to these differences is stemming from the functionals different surface intrinsic errors. We also discuss the puzzle that the values obtained with the surface intrisic error free AM05 functional (Armiento and Mattsson, Phys. Rev. B 72, 085108 (2006)) gives values substantially lower than Quantum Monte Carlo results
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Journal of Control and Vibratio
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Proposed for publication in SIAM Journal on Scientific Computing.
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Low Temperature Cofired Ceramic (LTCC) has proven to be an enabling medium for microsystem technologies, because of its desirable electrical, physical, and chemical properties coupled with its capability for rapid prototyping and scalable manufacturing of components. LTCC is viewed as an extension of hybrid microcircuits, and in that function it enables development, testing, and deployment of silicon microsystems. However, its versatility has allowed it to succeed as a microsystem medium in its own right, with applications in non-microelectronic meso-scale devices and in a range of sensor devices. Applications include silicon microfluidic ''chip-and-wire'' systems and fluid grid array (FGA)/microfluidic multichip modules using embedded channels in LTCC, and cofired electro-mechanical systems with moving parts. Both the microfluidic and mechanical system applications are enabled by sacrificial volume materials (SVM), which serve to create and maintain cavities and separation gaps during the lamination and cofiring process. SVMs consisting of thermally fugitive or partially inert materials are easily incorporated. Recognizing the premium on devices that are cofired rather than assembled, we report on functional-as-released and functional-as-fired moving parts. Additional applications for cofired transparent windows, some as small as an optical fiber, are also described. The applications described help pave the way for widespread application of LTCC to biomedical, control, analysis, characterization, and radio frequency (RF) functions for macro-meso-microsystems.
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