We present algorithmic techniques for parallel PDE solvers that leverage numerical smoothness properties of physics simulation to detect and correct silent data corruption within local computations. We initially model such silent hardware errors (which are of concern for extreme scale) via injected DRAM bit flips. Our mitigation approach generalizes previously developed "robust stencils" and uses modified linear algebra operations that spatially interpolate to replace large outlier values. Prototype implementations for 1D hyperbolic and 3D elliptic solvers, tested on up to 2048 cores, show that this error mitigation enables tolerating orders of magnitude higher bit-flip rates. The runtime overhead of the approach generally decreases with greater solver scale and complexity, becoming no more than a few percent in some cases. A key advantage is that silent data corruption can be handled transparently with data in cache, reducing the cost of false-positive detections compared to rollback approaches.
Post-Moore's law scaling is creating a disruptive shift in simulation workflows, as saving the entirety of raw data to persistent storage becomes expensive. We are moving away from a post-process centric data analysis paradigm towards a concurrent analysis framework, in which raw simulation data is processed as it is computed. Algorithms must adapt to machines with extreme concurrency, low communication bandwidth, and high memory latency, while operating within the time constraints prescribed by the simulation. Furthermore, in- put parameters are often data dependent and cannot always be prescribed. The study of sublinear algorithms is a recent development in theoretical computer science and discrete mathematics that has significant potential to provide solutions for these challenges. The approaches of sublinear algorithms address the fundamental mathematical problem of understanding global features of a data set using limited resources. These theoretical ideas align with practical challenges of in-situ and in-transit computation where vast amounts of data must be processed under severe communication and memory constraints. This report details key advancements made in applying sublinear algorithms in-situ to identify features of interest and to enable adaptive workflows over the course of a three year LDRD. Prior to this LDRD, there was no precedent in applying sublinear techniques to large-scale, physics based simulations. This project has definitively demonstrated their efficacy at mitigating high performance computing challenges and highlighted the rich potential for follow-on re- search opportunities in this space.
Metal particle beds have recently become a major technique for hydrogen storage. In order to extract hydrogen from such beds, it is crucial to understand the decomposition kinetics of the metal hydride. We are interested in obtaining a a better understanding of the uranium hydride (UH3) decomposition kinetics. We first developed an empirical model by fitting data compiled from different experimental studies in the literature and quantified the uncertainty resulting from the scattered data. We found that the decomposition time range predicted by the obtained kinetics was in a good agreement with published experimental results. Secondly, we developed a physics based mathematical model to simulate the rate of hydrogen diffusion in a hydride particle during the decomposition. We used this model to simulate the decomposition of the particles for temperatures ranging from 300K to 1000K while propagating parametric uncertainty and evaluated the kinetics from the results. We compared the kinetics parameters derived from the empirical and physics based models and found that the uncertainty in the kinetics predicted by the physics based model covers the scattered experimental data. Finally, we used the physics-based kinetics parameters to simulate the effects of boundary resistances and powder morphological changes during decomposition in a continuum level model. We found that the species change within the bed occurring during the decomposition accelerates the hydrogen flow by increasing the bed permeability, while the pressure buildup and the thermal barrier forming at the wall significantly impede the hydrogen extraction.
Modeling of reacting flows in porous media has become particularly important with the increased interest in hydrogen solid-storage beds. An advanced type of storage bed has been proposed that utilizes oxidation of uranium hydride to heat and decompose the hydride, releasing the hydrogen. To reduce the cost and time required to develop these systems experimentally, a valid computational model is required that simulates the reaction of uranium hydride and oxygen gas in a hydrogen storage bed using multiphysics finite element modeling. This SAND report discusses the advancements made in FY12 (since our last SAND report SAND2011-6939) to the model developed as a part of an ASC-P&EM project to address the shortcomings of the previous model. The model considers chemical reactions, heat transport, and mass transport within a hydride bed. Previously, the time-varying permeability and porosity were considered uniform. This led to discrepancies between the simulated results and experimental measurements. In this work, the effects of non-uniform changes in permeability and porosity due to phase and thermal expansion are accounted for. These expansions result in mechanical stresses that lead to bed deformation. To describe this, a simplified solid mechanics model for the local variation of permeability and porosity as a function of the local bed deformation is developed. By using this solid mechanics model, the agreement between our reacting bed model and the experimental data is improved. Additionally, more accurate uranium hydride oxidation kinetics parameters are obtained by fitting the experimental results from a pure uranium hydride oxidation measurement to the ones obtained from the coupled transport-solid mechanics model. Finally, the coupled transport-solid mechanics model governing equations and boundary conditions are summarized and recommendations are made for further development of ARIA and other Sandia codes in order for them to sufficiently implement the model.