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At least 1,423 records · Page 79

Semi-analytic solutions to the Noh problem with a black box EoS

The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.

97 MATHEMATICS AND COMPUTING↗

MatCal Users Guide: Release 1.3.0

Any continuum mechanics model will require three components: (1) a discretized geometry of the boundary value problem being studied, (2) the partial differential equations to be solved, and (3) the initial conditions and boundary conditions for the problem. To describe material behavior in these computational models, material models contribute to (2) the underlying equations and, occasionally, to (3) the initial conditions for the simulation. These material models can exhibit a mathematical form that is empirically based, based on first principles, or developed from both empirical observations and known physics. In general, these models are meant to represent a class of materials with well understood behavior. As a result, material models have parameters that must be tuned or calibrated so that the model response matches characterization data available for the specific material it is intended to represent when used to simulate a specific system. For simple models, such as isotropic, linear elastic materials in solid mechanics, this calibration process can be a simple analytical calculation directly extracting the parameters from experimental measurements. For complex models that have many inputs and require many characterization datasets to adequately identify the material behavior, the model calibration process can require an inverse problem approach where an optimization is performed to tune the model parameters to the available data.

36 MATERIALS SCIENCE↗

Accelerating computing for the future electric grid (CRADA Final Report)

As a participant in the Cyclotron Road Lab-Embedded Entrepreneurship Program (LEEP), Vellex Computing, Inc. has successfully validated the "Vellex Computing Stack," a breakthrough Analog Neural Computer (ANC) specifically designed for high-performance edge optimization. This project achieved critical milestones in mixed-signal circuit stability and software-hardware co-design, directly addressing national priorities in semiconductor resiliency. The success of this work is deeply rooted in the support from the Cyclotron Road LEEP, which provided the essential "hard tech" runway—funding, mentorship, and access to Lawrence Berkeley National Laboratory’s world-class characterization facilities—allowing Vellex to overcome the "Valley of Death" often faced by deep-tech hardware startups. By leveraging LBNL’s advanced testing infrastructure, Vellex was able to rigorously benchmark the ANC architecture against state-of-the-art digital solutions, a feat that would have been resource-prohibitive independently. This collaboration has not only advanced American leadership in analog computing but has also matured Vellex’s technology to a stage ripe for private sector commercialization.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A continuous proportional low-thrust propulsion system

Helium gas flows continuously from a low-temperature dewar supplying propellant for satellite thrusters. Thrust is obtained by movement of a spool located between two opposing nozzles, thus differentially restricting the helium flow. The design procedure and test results of a high bandwidth, low power, linear electromagnetic actuator for the pool movement are presented. Two mathematical models are used to describe the helium flow through the thruster under different flow conditions. The experimental data measured in the vacuum chamber and the computational results from the mathematical models are compared. The models agree with the experiment to 3 percent except near a Knudsen number of 1.

Chen, J.-H.↗

Scalable Plug-and-Play ADMM with Convergence Guarantees

Plug-and-play priors (PnP) is a broadly applicable methodology for solving inverse problems by exploiting statistical priors specified as denoisers. Recent work has reported the state-of-the-art performance of PnP algorithms using pre-trained deep neural nets as denoisers in a number of imaging applications. However, current PnP algorithms are impractical in large-scale settings due to their heavy computational and memory requirements. This work addresses this issue by proposing an incremental variant of the widely used PnP-ADMM algorithm, making it scalable to problems involving a large number measurements. Here, we theoretically analyze the convergence of the algorithm under a set of explicit assumptions, extending recent theoretical results in the area. Additionally, we show the effectiveness of our algorithm with nonsmooth data-fidelity terms and deep neural net priors, its fast convergence compared to existing PnP algorithms, and its scalability in terms of speed and memory.

97 MATHEMATICS AND COMPUTING↗

The virtual element method for linear elastodynamics models: Design, analysis, and implementation

We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the L 2 norm. The performance of the virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally seen in the p-refinement setting.

97 MATHEMATICS AND COMPUTING↗

The Scientific Impact of the Exascale Computing Project

The recent arrival of the Frontier Supercomputer at Oak Ridge National Laboratory officially marked the dawn of the exascale computing era. Its successful deployment coincided with the culmination of the U.S. Department of Energy Exascale Computing Project (ECP), an ambitious, complex, and risky research and development effort that integrated contributions from a broad and diverse subset of the high-performance computing community. The success of ECP will ultimately be judged by the scientific and engineering advances that it enabled. In conclusion, this Special Issue is focused on showcasing early successes in the use of exascale resources to enable breakthroughs in key areas of science in engineering.

97 MATHEMATICS AND COMPUTING↗

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗

Reproduced Computational Results Report for “Ginkgo: A Modern Linear Operator Algebra Framework for High Performance Computing”

The article titled “Ginkgo: A Modern Linear Operator Algebra Framework for High Performance Computing” by Anzt et al. presents a modern, linear operator centric, C++ library for sparse linear algebra. Experimental results in the article demonstrate that Ginkgo is a flexible and user-friendly framework capable of achieving high-performance on state-of-the-art GPU architectures. In this report, the Ginkgo library is installed and a subset of the experimental results are reproduced. Specifically, the experiment that shows the achieved memory bandwidth of the Ginkgo Krylov linear solvers on NVIDIA A100 and AMD MI100 GPUs is redone and the results are compared to what presented in the published article. Upon completion of the comparison, the published results are deemed reproducible.

97 MATHEMATICS AND COMPUTING↗

Nonoverlapping block smoothers for the Stokes equations

Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computationally expensive. This paper is concentrated on the development and analysis of new block smoothers for the Stokes equations that are discretized on staggered grids. These smoothers are nonoverlapping and therefore desirable due to reduced computational costs. Traditional geometric multigrid methods are based on simple pointwise smoothers. However, using multigrid methods to efficiently solve more difficult problems such as the Stokes equations leads to computationally more expensive smoothers, for example, overlapping block smoothers. Nonoverlapping smoothers are less expensive, but have been considered less efficient in the literature. In this paper, we develop new nonoverlapping smoothers, the so-called triad-wise smoothers, and show their efficiency within multigrid methods to solve the Stokes equations. In addition, we compare overlapping and nonoverlapping smoothers by measuring their computational costs and analyzing their behavior by the use of local Fourier analysis.

97 MATHEMATICS AND COMPUTING↗

HTESP (High-throughput electronic structure package): A package for high-throughput ab initio calculations

High-throughput ab initio calculations are the indispensable parts of data-driven discovery of new materials with desirable properties, as reflected in the establishment of several online material databases. The accumulation of extensive theoretical data through computations enables data-driven discovery by constructing machine learning and artificial intelligence models to predict novel compounds and forecast their properties. Efficient usage and extraction of data from these existing online material databases can accelerate the next stage materials discovery that targets different and more advanced properties, such as electron–phonon coupling for phonon-mediated superconductivity. However, extracting data from these databases, generating tailored input files for different ab initio calculations, performing such calculations, and analyzing new results can be demanding tasks. Here, in this work, we introduce a software package named “HTESP” (High-Throughput Electronic Structure Package) written in Python and Bash languages, which automates the entire workflow including data extraction, input file generation, calculation submission, result collection and plotting. Our HTESP will help speed up future computational materials discovery processes.

36 MATERIALS SCIENCE↗

Customizable adaptive regularization techniques for B-spline modeling

B-spline models are a powerful way to represent scientific data sets with a functional approximation. However, these models can suffer from spurious oscillations when the data to be approximated are not uniformly distributed. Model regularization (i.e., smoothing) has traditionally been used to minimize these oscillations; unfortunately, it is sometimes impossible to sufficiently remove unwanted artifacts without smoothing away key features of the data set. In this article, we present a method of model regularization that preserves significant features of a data set while minimizing artificial oscillations. Our method varies the strength of a smoothing parameter throughout the domain automatically, removing artifacts in poorly-constrained regions while leaving other regions unchanged. Further, the proposed method selectively incorporates regularization terms based on first and second derivatives to maintain model accuracy while minimizing numerical artifacts. The behavior of our method is validated on a collection of two- and three-dimensional data sets produced by scientific simulations. In addition, a key tuning parameter is highlighted and the effects of this parameter are presented in detail. This paper is an extension of our previous conference paper at the 2022 International Conference on Computational Science (ICCS) (Lenz et al., 2022).

97 MATHEMATICS AND COMPUTING↗

Two-dimensional materials for bio-realistic neuronal computing networks

Two-dimensional (2D) van der Waals materials have found broad utility in a diverse range of applications including electronics, optoelectronics, renewable energy, and quantum information technologies. Meanwhile, exponentially growing digital data coupled with the ubiquity of artificial intelligence algorithms have generated significant interest in edge neuromorphic computing as an alternative to centralized cloud computing. The drive to incorporate neuroscience principles into computing hardware is motivated by the low power consumption, parallel processing, and reconfigurability of the human brain. The diverse library of 2D materials with atomic-level thicknesses, exceptional electrostatic tunability, and integration versatility is particularly well-suited for realizing bio-realistic synaptic and neuronal functionality. Here, we summarize past and present work in this field and outline the frontier challenges that have not yet been overcome. Here we also delineate potential solutions and suggest that the neuroscience principles of criticality and synchrony have the potential to inspire breakthrough applications of 2D materials in neuronal computing networks.

36 MATERIALS SCIENCE↗

All-Atom Biomolecular Simulation in the Exascale Era

Exascale supercomputers have opened the door to dynamic simulations, facilitated by AI/ML techniques, that model biomolecular motions over unprecedented length and time scales. This new capability holds the potential to revolutionize our understanding of fundamental biological processes. Herein we report on some of the major advances that were discussed at a recent CECAM workshop in Pisa, Italy, on the topic with a primary focus on atomic-level simulations. First, we highlight examples of current large-scale biomolecular simulations and the future possibilities enabled by crossing the exascale threshold. Next, we discuss challenges to be overcome in optimizing the usage of these powerful resources. Finally, we close by listing several grand challenge problems that could be investigated with this new computer architecture.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum computer-enabled receivers for optical communication

Abstract Optical communication is the standard for high-bandwidth information transfer in today’s digital age. The increasing demand for bandwidth has led to the maturation of coherent transceivers that use phase- and amplitude-modulated optical signals to encode more bits of information per transmitted pulse. Such encoding schemes achieve higher information density, but also require more complicated receivers to discriminate the signaling states. In fact, achieving the ultimate limit of optical communication capacity, especially in the low light regime, requires coherent joint detection of multiple pulses. Despite their superiority, such joint detection receivers are not in widespread use because of the difficulty of constructing them in the optical domain. In this work we describe how optomechanical transduction of phase information from coherent optical pulses to superconducting qubit states followed by the execution of trained short-depth variational quantum circuits can perform joint detection of communication codewords with error probabilities that surpass all classical, individual pulse detection receivers. Importantly, we utilize a model of optomechanical transduction that captures non-idealities such as thermal noise and loss in order to understand the transduction performance necessary to achieve a quantum advantage with such a scheme. We also execute the trained variational circuits on an IBM-Q device with the modeled transduced states as input to demonstrate that a quantum advantage is possible even with current levels of quantum computing hardware noise.

97 MATHEMATICS AND COMPUTING↗

Extending the Frontier of Quantum Computers with Qutrits

Here, we advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the log 2 (3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla - an exponential improvement over the best qubit-only equivalent. Our approach features a 70× improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers.

97 MATHEMATICS AND COMPUTING↗