Publications

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The parallel strong-scaling of iterative methods is often determined by the number of global reductions at each iteration. Low-synch Gram–Schmidt algorithms are applied here to the Arnoldi algorithm to reduce the number of global reductions and therefore to improve the parallel strong-scaling of iterative solvers for nonsymmetric matrices such as the GMRES and the Krylov–Schur iterative methods. In the Arnoldi context, the QR factorization is “left-looking” and processes one column at a time. Among the methods for generating an orthogonal basis for the Arnoldi algorithm, the classical Gram–Schmidt algorithm, with reorthogonalization (CGS2) requires three global reductions per iteration. A new variant of CGS2 that requires only one reduction per iteration is presented and applied to the Arnoldi algorithm. Delayed CGS2 (DCGS2) employs the minimum number of global reductions per iteration (one) for a one-column at-a-time algorithm. The main idea behind the new algorithm is to group global reductions by rearranging the order of operations. DCGS2 must be carefully integrated into an Arnoldi expansion or a GMRES solver. Numerical stability experiments assess robustness for Krylov–Schur eigenvalue computations. Performance experiments on the ORNL Summit supercomputer then establish the superiority of DCGS2 over CGS2.

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Exterior solar glaze was added to a 3 foot x 3 foot x 3 foot aluminum solar collector that had six triangular dimpled fins for enhanced heat transfer. The interior vertical wall on the south side was also dimpled. The solar glaze was added to compare its solar collection performance with unglazed solar collector experiments conducted at Sandia in 2021. The east, west, front, and top sides of the solar collector were encased with solar glaze glass. Because the solar incident heat on the north and bottom sides was minimal, they were insulated to retain the heat that was collected by the other four sides. The advantages of the solar glaze include the entrapment of more solar heat, as well as insulation from the wind. The disadvantages are that it increases the cost of the solar collector and has fragile structural properties when compared to the aluminum walls. Nevertheless, prior to conducting experiments with the glazed solar collector, it was not clear if the benefits outweighed the disadvantages. These issues are addressed herein, with the conclusion that the additional amount of heat collected by the glaze justifies the additional cost. The solar collector glaze design, experimental data, and costs and benefits are documented in this report.

Chemical engineering systems often involve a functional porous medium, such as in catalyzed reactive flows, fluid purifiers, and chromatographic separations. Ideally, the flow rates throughout the porous medium are uniform, and all portions of the medium contribute efficiently to its function. The permeability is a property of a porous medium that depends on pore geometry and relates flow rate to pressure drop. Additive manufacturing techniques raise the possibilities that permeability can be arbitrarily specified in three dimensions, and that a broader range of permeabilities can be achieved than by traditional manufacturing methods. Using numerical optimization methods, we show that designs with spatially varying permeability can achieve greater flow uniformity than designs with uniform permeability. We consider geometries involving hemispherical regions that distribute flow, as in many glass chromatography columns. By several measures, significant improvements in flow uniformity can be obtained by modifying permeability only near the inlet and outlet.

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This report documents a method for the quantitative identification of radionuclides of potential interest for accident consequence analysis involving advanced nuclear reactors. Based on previous qualitative assessments of radionuclide inventories for advanced reactors coupled with the review of a radiological inventory developed for a heat pipe reactor, a 1 Ci activity airborne release was calculated for 137 radionuclides using the MACCS 4.1 code suite. Several assumptions regarding release conditions were made and discussed herein. The potential release of a heat pipe reactor inventory was also modeled following the same assumptions. Results provide an estimation of the relative EARLY and CHRONC phase dose contribution from advanced reactor radionuclides and are normalized to doses from equivalent releases of I-131 and Cs-137, respectively. Ultimately, a list of 69 radionuclides with EARLY or CHRONC dose contributions at least 1/100th that of I-131 or Cs-137, respectively – 48 of which are currently considered for LWR consequence analyses – was identified of being of potential importance for analyses involving a heat pipe reactor.

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The paper presents a collection of results on continuous dependence for solutions to nonlocal problems under perturbations of data and system parameters. The integral operators appearing in the systems capture interactions via heterogeneous kernels that exhibit different types of weak singularities, space dependence, even regions of zero-interaction. The stability results showcase explicit bounds involving the measure of the domain and of the interaction collar size, nonlocal Poincaré constant, and other parameters. In the nonlinear setting, the bounds quantify in different Lp norms the sensitivity of solutions under different nonlinearity profiles. The results are validated by numerical simulations showcasing discontinuous solutions, varying horizons of interactions, and symmetric and heterogeneous kernels.

Modeling real-world phenomena to any degree of accuracy is a challenge that the scientific research community has navigated since its foundation. Lack of information and limited computational and observational resources necessitate modeling assumptions which, when invalid, lead to model-form error (MFE). The work reported herein explored a novel method to represent model-form uncertainty (MFU) that combines Bayesian statistics with the emerging field of universal differential equations (UDEs). The fundamental principle behind UDEs is simple: use known equational forms that govern a dynamical system when you have them; then incorporate data-driven approaches – in this case neural networks (NNs) – embedded within the governing equations to learn the interacting terms that were underrepresented. Utilizing epidemiology as our motivating exemplar, this report will highlight the challenges of modeling novel infectious diseases while introducing ways to incorporate NN approximations to MFE. Prior to embarking on a Bayesian calibration, we first explored methods to augment the standard (non-Bayesian) UDE training procedure to account for uncertainty and increase robustness of training. In addition, it is often the case that uncertainty in observations is significant; this may be due to randomness or lack of precision in the measurement process. This uncertainty typically manifests as “noisy” observations which deviate from a true underlying signal. To account for such variability, the NN approximation to MFE is endowed with a probabilistic representation and is updated using available observational data in a Bayesian framework. By representing the MFU explicitly and deploying an embedded, data-driven model, this approach enables an agile, expressive, and interpretable method for representing MFU. In this report we will provide evidence that Bayesian UDEs show promise as a novel framework for any science-based, data-driven MFU representation; while emphasizing that significant advances must be made in the calibration of Bayesian NNs to ensure a robust calibration procedure.

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