Publications

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Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level GDSW (Generalized Dryja–Smith–Widlund) type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the MPI-parallel implementation of multi-level Schwarz preconditioners provided by the package FROSch (Fast and Robust Schwarz)from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To our knowledge, this is the first time two-level Schwarz preconditioners are applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The pre-conditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the sub-domains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as non uniform meshes for the Greenland ice sheet are considered. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32 K processor cores (8 K MPI-ranks and 4 OpenMP threads) and 566 M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4 K processor cores (and MPI-ranks) and 68 M degrees of freedom for the coupled problem.

This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.

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This report presents the results of a collaborative effort under the Verification, Validation, and Uncertainty Quantification (VVUQ) thrust area of the North American Energy Resilience Model (NAERM) program. The goal of the effort described in this report was to integrate the Dakota software with the NAERM software framework to demonstrate sensitivity analysis of a co-simulation for NAERM.

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CSPlib is an open source software library for analyzing general ordinary differential equation (ODE) systems and detailed chemical kinetic ODE systems. It relies on the computational singular perturbation (CSP) method for the analysis of these systems. The software provides support for: General ODE models (gODE model class) for computing source terms and Jacobians for a generic ODE system; TChem model (ChemElemODETChem model class) for computing source term, Jacobian, other necessary chemical reaction data, as well as the rates of progress for a homogenous batch reactor using an elementary step detailed chemical kinetic reaction mechanism. This class relies on the TChem [2] library; A set of functions to compute essential elements of CSP analysis (Kernel class). This includes computations of the eigensolution of the Jacobian matrix, CSP basis vectors and co-vectors, time scales (reciprocals of the magnitudes of the Jacobian eigenvalues), mode amplitudes, CSP pointers, and the number of exhausted modes. This class relies on the Tines library; A set of functions to compute the eigensolution of the Jacobian matrix using Tines library GPU eigensolver; A set of functions to compute CSP indices (Index Class). This includes participation indices and both slow and fast importance indices.

In this study, a complete inelastic equation of state (IEOS) for solids is developed based on a superposition of thermodynamic energy potentials. The IEOS allows for a tensorial stress state by including an isochoric hyperelastic Helmholtz potential in addition to the zero-kelvin isotherm and lattice vibration energy contributions. Inelasticity is introduced through the nonlinear equations of finite strain plasticity which utilize the temperature dependent Johnson–Cook yield model. Material failure is incorporated into the model by a coupling of the damage history variable to the energy potentials. The numerical evaluation of the IEOS requires a nonlinear solution of stress, temperature and history variables associated with elastic trial states for stress and temperature. The model is implemented into the ALEGRA shock and multi-physics code and the applications presented include single element deformation paths, the Taylor anvil problem and an energetically driven thermo-mechanical problem.

Heterojunctions of semiconductors and metals are the fundamental building blocks of modern electronics. Coherent heterostructures between dissimilar materials can be achieved by composition, doping, or heteroepitaxy of chemically different elements. Here, we report the formation of coherent single-layer 1H-1T MoS2 heterostructures by mechanical exfoliation on Au(111), which are chemically homogeneous with matched lattices but show electronically distinct semiconducting (1H phase) and metallic (1T phase) character, with the formation of these heterojunctions attributed to a combination of lattice strain and charge transfer. The exfoliation approach employed is free of tape residues usually found in many exfoliation methods and yields single-layer MoS2 with millimeter (mm) size on the Au surface. Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM), scanning tunneling microscopy (STM), and scanning tunneling spectroscopy (STS) have collectively been employed to elucidate the structural and electronic properties of MoS2 monolayers on Au substrates. Bubbles in the MoS2 formed by the trapping of ambient adsorbates beneath the single layer during deposition, have also been observed and characterized. Our work here provides a basis to produce two-dimensional heterostructures which represent potential candidates for future electronic devices.

We present a new evaluation framework for implicit and explicit (IMEX) Runge-Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge-Kutta methods with a high Courant-Friedrichs-Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.

We present a new evaluation framework for implicit and explicit (IMEX) Runge–Kutta time-stepping schemes. The new framework uses a linearized nonhydrostatic system of normal modes. We utilize the framework to investigate the stability of IMEX methods and their dispersion and dissipation of gravity, Rossby, and acoustic waves. We test the new framework on a variety of IMEX schemes and use it to develop and analyze a set of second-order low-storage IMEX Runge–Kutta methods with a high Courant–Friedrichs–Lewy (CFL) number. We show that the new framework is more selective than the 2-D acoustic system previously used in the literature. Schemes that are stable for the 2-D acoustic system are not stable for the system of normal modes.

Accurate and timely weather predictions are critical to many aspects of society with a profound impact on our economy, general well-being, and national security. In particular, our ability to forecast severe weather systems is necessary to avoid injuries and fatalities, but also important to minimize infrastructure damage and maximize mitigation strategies. The weather community has developed a range of sophisticated numerical models that are executed at various spatial and temporal scales in an attempt to issue global, regional, and local forecasts in pseudo real time. The accuracy however depends on the time period of the forecast, the nonlinearities of the dynamics, and the target spatial resolution. Significant uncertainties plague these predictions including errors in initial conditions, material properties, data, and model approximations. To address these shortcomings, a continuous data collection occurs at an effort level that is even larger than the modeling process. It has been demonstrated that the accuracy of the predictions depends on the quality of the data and is independent to a certain extent on the sophistication of the numerical models. Data assimilation has become one of the more critical steps in the overall weather prediction business and consequently substantial improvements in the quality of the data would have transformational benefits. This paper describes the use of infrasound inversion technology, enabled through exascale computing, that could potentially achieve orders of magnitude improvement in data quality and therefore transform weather predictions with significant impact on many aspects of our society.

Chris Saunders and three technologists are in high demand from Sandia’s deep learning teams, and they’re kept busy by building new clusters of computer nodes for researchers who need the power of supercomputing on a smaller scale. Sandia researchers working on Laboratory Directed Research & Development (LDRD) projects, or innovative ideas for solutions on short timeframes, formulate new ideas on old themes and frequently rely on smaller cluster machines to help solve problems before introducing their code to larger HPC resources. These research teams need an agile hardware and software environment where nascent ideas can be tested and cultivated on a smaller scale.

After decades of R&D, quantum computers comprising more than 2 qubits are appearing. If this progress is to continue, the research community requires a capability for precise characterization (“tomography”) of these enlarged devices, which will enable benchmarking, improvement, and finally certification as mission-ready. As world leaders in characterization -- our gate set tomography (GST) method is the current state of the art – the project team is keenly aware that every existing protocol is either (1) catastrophically inefficient for more than 2 qubits, or (2) not rich enough to predict device behavior. GST scales poorly, while the popular randomized benchmarking technique only measures a single aggregated error probability. This project explored a new insight: that the combinatorial explosion plaguing standard GST could be avoided by using an ansatz of few-qubit interactions to build a complete, efficient model for multi-qubit errors. We developed this approach, prototyped it, and tested it on a cutting-edge quantum processor developed by Rigetti Quantum Computing (RQC), a US-based startup. We implemented our new models within Sandia’s PyGSTi open-source code, and tested them experimentally on the RQC device by probing crosstalk. We found two major results: first, our schema worked and is viable for further development; second, while the Rigetti device is indeed a “real” 8-qubit quantum processor, its behavior fluctuated significantly over time while we were experimenting with it and this drift made it difficult to fit our models of crosstalk to the data.

The review was conducted on May 8-9, 2017 at the University of Utah. Overall the review team was impressed with the work presented and found that the CCMSC had met or exceeded the Year 3 milestones. Specific details, comments, and recommendations are included in this document.

If quantum information processors are to fulfill their potential, the diverse errors that affect them must be understood and suppressed. But errors typically fluctuate over time, and the most widely used tools for characterizing them assume static error modes and rates. This mismatch can cause unheralded failures, misidentified error modes, and wasted experimental effort. Here, we demonstrate a spectral analysis technique for resolving time dependence in quantum processors. Our method is fast, simple, and statistically sound. It can be applied to time-series data from any quantum processor experiment. We use data from simulations and trapped-ion qubit experiments to show how our method can resolve time dependence when applied to popular characterization protocols, including randomized benchmarking, gate set tomography, and Ramsey spectroscopy. In the experiments, we detect instability and localize its source, implement drift control techniques to compensate for this instability, and then demonstrate that the instability has been suppressed.

Parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes and more heterogeneous compute architectures make load balancing and the design of low latency network interconnects that are able to satisfy the communication requirements of linear solvers very challenging tasks. In particular, global communication patterns such as inner products become increasingly limiting at scale. We explore the use of asynchronous communication based on one-sided Message Passing Interface primitives in the context of domain decomposition solvers. In particular, a scalable asynchronous two-level Schwarz method is presented. We discuss practical issues encountered in the development of a scalable solver and show experimental results obtained on a state-of-the-art supercomputer system that illustrate the benefits of asynchronous solvers in load balanced as well as load imbalanced scenarios. Using the novel method, we can observe speedups of up to four times over its classical synchronous equivalent.

Additive Manufacturing (AM), commonly referred to as 3D printing, offers the ability to not only fabricate geometrically complex lattice structures but parts in which lattice topologies in-fill volumes bounded by complex surface geometries. However, current AM processes produce defects on the strut and node elements which make up the lattice structure. This creates an inherent difference between the as-designed and as-fabricated geometries, which negatively affects predictions (via numerical simulation) of the lattice's mechanical performance. Although experimental and numerical analysis of an AM lattice's bulk structure, unit cell and struts have been performed, there exists almost no research data on the mechanical response of the individual as-manufactured lattice node elements. This research proposes a methodology that, for the first time, allows non-destructive quantification of the mechanical response of node elements within an as-manufactured lattice structure. A custom-developed tool is used to extract and classify each individual node geometry from micro-computed tomography scans of an AM fabricated lattice. Voxel-based finite element meshes are generated for numerical simulation and the mechanical response distribution is compared to that of the idealised computer-aided design model. The method demonstrates compatibility with Uncertainty Quantification methods that provide opportunities for efficient prediction of a population of nodal responses from sampled data. Overall, the non-destructive and automated nature of the node extraction and response evaluation is promising for its application in qualification and certification of additively manufactured lattice structures.

One of the most severe obstacles to increasing the longevity of tungsten-based plasma facing components, such as divertor tiles, is the surface deterioration driven by sub-surface helium bubble formation and rupture. Supported by experimental observations at PISCES, this work uses molecular dynamics simulations to identify the microscopic mechanisms underlying suppression of helium bubble formation by the introduction of plasma-borne beryllium. Simulations of the initial surface material (crystalline W), early-time Be exposure (amorphous W-Be) and final WBe2 intermetallic surfaces were used to highlight the effect of Be. Significant differences in He retention, depth distribution and cluster size were observed in the cases with beryllium present. Helium resided much closer to the surface in the Be cases with nearly 80% of the total helium inventory located within the first 2 nm. Moreover, coarsening of the He depth profile due to bubble formation is suppressed due to a one-hundred fold decrease in He mobility in WBe2, relative to crystalline W. This is further evidenced by the drastic reduction in He cluster sizes even when it was observed that both the amorphous W-Be and WBe2 intermetallic phases retain nearly twice as much He during cumulative implantation studies.

The Message Passing Interface (MPI) standard allows user-level threads to concurrently call into an MPI library. While this feature is currently rarely used, there is considerable interest from developers in adopting it in the near future. There is reason to believe that multithreaded communication may incur additional message processing overheads in terms of number of items searched during demultiplexing and amount of time spent searching because it has the potential to increase the number of messages exchanged and to introduce non-deterministic message ordering. Therefore, understanding the implications of adding multithreading to MPI applications is important for future application development.One strategy for advancing this understanding is through 'low-cost' benchmarks that emulate full communication patterns using fewer resources. For example, while a complete, 'real-world' multithreaded halo exchange requires 9 or 27 nodes, the low-cost alternative needs only two, making it deployable on systems where acquiring resources is difficult because of high utilization (e.g., busy capacity-computing systems), or impossible because the necessary resources do not exist (e.g., testbeds with too few nodes). While such benchmarks have been proposed, the reported results have been limited to a single architecture or derived indirectly through simulation, and no attempt has been made to confirm that a low-cost benchmark accurately captures features of full (non-emulated) exchanges. Moreover, benchmark code has not been made publicly available.The purpose of the study presented in this paper is to quantify how accurately the low-cost benchmark captures the matching behavior of the full, real-world benchmark. In the process, we also advocate for the feasibility and utility of the low-cost benchmark. We present a 'real-world' benchmark implementing a full multithreaded halo exchange on 9 and 27 nodes, as defined by 5-point and 9-point 2D stencils, and 7-point and 27-point 3D stencils. Likewise, we present a 'low-cost' benchmark that emulates these communication patterns using only two nodes. We then confirm, across multiple architectures, that the low-cost benchmark gives accurate estimates of both number of items searched during message processing, and time spent processing those messages. Finally, we demonstrate the utility of the low-cost benchmark by using it to profile the performance impact of state-of-The-Art Mellanox ConnectX-5 hardware support for offloaded MPI message demultiplexing. To facilitate further research on the effects of multithreaded MPI on message matching behavior, the source of our two benchmarks is to be included in the next release version of the Sandia MPI Micro-Benchmark Suite.

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We present evidence of inverse Hall-Petch behavior for a single-phase high entropy alloy (CoCrFeMnNi) in ultra-high vacuum and show that it is associated with low friction coefficients (~0.3). Grain size measurements by STEM validate a recently proposed dynamic amorphization model that accurately predicts grain size-dependent shear strength in the inverse Hall-Petch regime. Wear rates in the initially soft (coarse grained) material were shown to be remarkably low (~10–6 mm3/N-m), the lowest for any HEA tested in an inert environment where oxidation and the formation of mixed metal-oxide films is mitigated. The combined high wear resistance and low friction are linked to the formation of an ultra-nanocrystalline near-surface layer. The dynamic amorphization model was also used to predict an average high angle grain boundary energy (0.87 J/m2). This value was used to explain cavitation-induced nanoporosity found in the highly deformed surface layer, a phenomenon that has been linked to superplasticity.

This article concerns modeling unsaturated deformable porous media as an equivalent single-phase and single-force state peridynamic material through the effective force state. The balance equations of linear momentum and mass of unsaturated porous media are presented by defining relevant peridynamic states. The energy balance of unsaturated porous media is utilized to derive the effective force state for the solid skeleton that is an energy conjugate to the nonlocal deformation state of the solid, and the suction force state. Through an energy equivalence, a multiphase constitutive correspondence principle is built between classical unsaturated poromechanics and peridynamic unsaturated poromechanics. The multiphase correspondence principle provides a means to incorporate advanced constitutive models in classical unsaturated porous theory directly into unsaturated peridynamic poromechanics. Numerical simulations of localized failure in unsaturated porous media under different matric suctions are presented to demonstrate the feasibility of modeling the mechanical behavior of such three-phase materials as an equivalent single-phase peridynamic material through the effective force state concept.

This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. We propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.

This report details work to study trade-offs in topology and network bandwidth for potential interconnects in the exascale (2021-2022) timeframe. The work was done using multiple interconnect models across two parallel discrete event simulators. Results from each independent simulator are shown and discussed and the areas of agreement and disagreement are explored.

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