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At least 469 records · Page 26

Gradient-based constrained optimization using a database of linear reduced-order models

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential Equation (PDE). A key component of this methodology is the construction, during an offline phase, of a database of pointwise, linear, Projection-based Reduced-Order Models (PROM)s associated with a design parameter space and the linear PDE(s). A parameter sampling procedure based on an appropriate saturation assumption is proposed to maximize the efficiency of such a database of PROMs. A real-time method is also presented for interpolating at any queried but unsampled parameter vector in the design parameter space the relevant sensitivities of a PROM. The practical feasibility, computational advantages, and performance of the proposed methodology are demonstrated for several realistic, nonlinear, aerodynamic shape optimization problems governed by linear aeroelastic constraints.

97 MATHEMATICS AND COMPUTING↗

High-resolution CH stretch spectroscopy of jet-cooled cyclopentyl radical: First insights into equilibrium structure, out-of-plane puckering, and IVR dynamics

First, high-resolution sub-Doppler infrared spectroscopic results for cyclopentyl radical (C 5 H 9 ) are reported on the α-CH stretch fundamental with suppression of spectral congestion achieved by adiabatic cooling to T rot ≈ 19(4) K in a slit jet expansion. Surprisingly, cyclopentyl radical exhibits a rotationally assignable infrared spectrum, despite 3N – 6 = 36 vibrational modes and an upper vibrational state density (ρ ≈ 40–90 #/cm –1 ) in the critical regime (ρ ≈ 100 #/cm –1 ) necessary for onset of intramolecular vibrational relaxation (IVR) dynamics. Such high-resolution data for cyclopentyl radical permit detailed fits to a rigid-rotor asymmetric top Hamiltonian, initial structural information for ground and vibrationally excited states, and opportunities for detailed comparison with theoretical predictions. Specifically, high level ab initio calculations at the coupled-cluster singles, doubles, and perturbative triples (CCSD(T))/ANO0, 1 level are used to calculate an out-of-plane bending potential, which reveals a C 2 symmetry double minimum 1D energy surface over a C 2v transition state. Here, the inversion barrier [V barrier ≈ 3.7(1) kcal/mol] is much larger than the effective moment of inertia for out-of-plane bending, resulting in localization of the cyclopentyl wavefunction near its C 2 symmetry equilibrium geometry and tunneling splittings for the ground state too small (<1 MHz) to be resolved under sub-Doppler slit jet conditions. The persistence of fully resolved high-resolution infrared spectroscopy for such large cyclic polyatomic radicals at high vibrational state densities suggests a “deceleration” of IVR for a cycloalkane ring topology, much as low frequency torsion/methyl rotation degrees of freedom have demonstrated a corresponding “acceleration” of IVR processes in linear hydrocarbons.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CHARACTERIZATION OF RADIATION DAMAGES TO POSITRON SOURCE MATERIALS

The secondary beam production target at future positron sources at the Continuous Electron Beam Accelerator Facility (CEBAF), the International Linear Collider (ILC) or the Future Circular Collider (FCC), features unprecedented mechanical and thermal stresses which may compromise sustainable and reliable operation. Candidate materials are required to possess high melting temperature together with excellent thermal conductivity, elasticity and radiation hardness properties. In order to substantiate the material choice for the CEBAF and ILC positron sources, the response of candidate materials such as titanium alloys, tungsten, and tantalum to electron beam irradiation was experimentally investigated. CEBAF and ILC expected operating conditions were mimicked using the 3.5 MeV electron beam of the MAMI facility injector. The material degradations were precisely analyzed via high energy X-ray diffraction at the HEMS beamline operated by the Helmholtz-Zentrum Hereon at the PETRA III synchrotron facility. This work reports the results of these measurements and their interpretation.

Lengler, T.↗

Bryan Mound Abandoned Cavern 3 Stability Analysis - 2021 Review

The U.S. Strategic Petroleum Reserve is moving towards employing an expanded enhanced monitoring program. In doing so it has become apparent that there is a need for a better project wide understanding of the current state of Bryan Mound abandoned Cavern 3 stability. Cavern 3 has been inaccessible since 1988 when it was plugged and abandoned and thus this comprehensive report is structured by focusing on 1) a summarization of what can be discerned from historical records prior to 1988 and 2) a presentation and discussion of our current understanding of Cavern 3 based solely on surface monitoring and geomechanical analyses. Historical literature state the cavern was deemed unsuitable for oil storage, as it could not be definitively determined if fluid pressure could be maintained in the borehole. Current surface monitoring indicates the largest surface subsidence rates are occurring above Cavern 3. The subsidence rates are linear with no evidence of acceleration. Cavern collapse could occur if there is insufficient pressure holding up the roof. Next steps are to implement a microseismic system that will lend to a better understanding of cavern stability, as well as provide an improved early warning system for loss of integrity.

02 PETROLEUM↗

Extreme Longitudinal Compression of Optimized Beams for MEV Ultrafast Electron Diffraction (Final Technical Report)

We worked out the design of a high repetition rate MeV energy ultrafast electron diffraction instrument based on the existing Cornell photoinjector, which can readily be applied to the presented findings. This example is a blueprint of other similarly arranged UED setups. Using particle tracking simulations in conjunction with multiobjective genetic algorithm optimization, we explored the smallest bunch lengths, emittance, and probe spot sizes achievable. As two limits, we defined stroboscopic conditions (with single electrons per pulse) and operation with 10 5 electrons per bunch which may be suitable for single-shot diffraction images. In the stroboscopic case, the flexibility provided by the many cavity bunching and acceleration allows for longitudinal phase space linearization without a higher harmonic field, providing sub-fs bunch lengths at the sample. Given low emittance photoemission conditions, these small bunch lengths can be maintained with probe transverse sizes at the single micron (1 μm) scale and below. In the case of 10 5 electrons per pulse, we simulated state-of-the-art 5D brightness conditions: rms bunch lengths of 10 fs with 3-nm normalized emittances, while permitting repetition rates as high as 1.3 GHz. We showed that in conjunction with collimating apertures, a novel focusing scheme achieves very high-quality emittance compensation for the central core of the beam composing 40% of particles, for a resulting beam size of 5 μm (rms). Finally, to aid in the design of new SRF-based ultrafast electron diffraction machines, we simulated the trade-off between the number of cavities used and achievable bunch length and emittance. In the longitudinal dimension, we made use of the fact that MeV UED requires much lower energy than the 15-MeV maxi mum energy of Cornell’s CBETA injector, and we may therefore use several of the SRF cavities for bunch length compression. In practice, we used a genetic optimization algorithm to choose the phases and amplitudes of the cavities appropriately for optimal bunching. In the zero space charge case, we found that bunching and acceleration are distributed across the six cavities in a way that produces a linearizing effect. And we showed that the ultimate bunch length can be limited by time-of-flight differences arising from transverse size and transverse momentum spread. The space charge code developed and used for this development is now permanent part of the Bmad accelerator simulation code and has already contributed to other developments, e.g., for the EIC electron cooler design.

43 PARTICLE ACCELERATORS↗

On the possibility of footprint compression with one lens in nonlinear accelerator lattice

Electromagnetic interaction of colliding beams along with other nonlinear fields often limits the beams' lifetimes and luminosities. Nonlinearities result in the spread of betatron frequencies (footprint) and, thus, may enhance dynamic diffusion of particles due to high order resonances. One of the possible ways to eliminate nonlinearities and overcome the corresponding difficulties is compensation of nonlinear forces, but, in practice, it is hardly possible to obtain exact linearity of the system. The compensation with a single nonlinear lens cannot cope with distributed nonlinearities, nonlinearities due to parasitic crossings, etc. Here, we present a method to compute parameters of nonlinear element (lens) that eliminates both the footprint and resonance strength without achieving full compensation.

43 PARTICLE ACCELERATORS↗

Hierarchical Optimal Power Flow with Improved Gradient Evaluation

Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which rested on primal-dual gradients evaluated in a linearized distribution power flow model. Specifically, we identify a risk of voltage violation arising from the model linearization, and propose a more accurate gradient evaluation method to eliminate that risk. We further develop a hierarchical primal-dual algorithm to solve OPF based on the proposed gradient evaluation method. Numerical results on IEEE networks show that our algorithm can enhance voltage safety with satisfactory computational efficiency.

distributed algorithm↗

Finite boundary effects on the spherical Rayleigh–Taylor instability between viscous fluids

For the Rayleigh–Taylor unstable arrangement of a viscous fluid sphere embedded in a finite viscous fluid spherical shell with a rigid boundary and a radially directed acceleration, a dispersion relation is developed from a linear stability analysis using the method of normal modes. [Formula: see text] is the radially directed acceleration at the interface. ρ i denotes the density, μ i is the viscosity, and R i is the radius, where i = 1 is the inner sphere and i = 2 is the outer sphere. The dispersion relation is a function of the following dimensionless variables: viscosity ratio [Formula: see text], density ratio [Formula: see text], spherical harmonic mode n, [Formula: see text], [Formula: see text], and the dimensionless growth rate [Formula: see text], where σ is the exponential growth rate. We show that the boundedness provided by the outer spherical shell has a strong influence on the instability behavior, which is reflected not only in the modulation of the growth rate but also in the selection of the most unstable modes that are physically possible. This outer boundary effect is quantified by the relative magnitude of the radius ratio H. We find that when H is close to unity, lower order harmonics are excluded from becoming the most unstable within a vast region of the parameter space. In other words, the effect of H has precedence over the other controlling parameters d, B, and a wide range of s in establishing what the lowest most unstable mode can be. When H ~ 1, low order harmonics can become the most unstable only for s >> 1. However, in the limit when s → ∞, we show that the most unstable mode is n = 1 and derive the dispersion relation in this limit. The exclusion of most unstable low order harmonics caused by a finite outer boundary is not realized when the outer boundary extends beyond a certain threshold length-scale in which case all modes are equally possible depending on the value of B.

74 ATOMIC AND MOLECULAR PHYSICS↗

A survey of numerical linear algebra methods utilizing mixed-precision arithmetic

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications. Especially with the hardware integration of low-precision special-function units designed for machine learning applications, the traditional numerical algorithms community urgently needs to reconsider the floating point formats used in the distinct operations to efficiently leverage the available compute power. In this study, we provide a comprehensive survey of mixed-precision numerical linear algebra routines, including the underlying concepts, theoretical background, and experimental results for both dense and sparse linear algebra problems.

97 MATHEMATICS AND COMPUTING↗

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action–angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant–Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

43 PARTICLE ACCELERATORS↗

Porting the Nonlinear Optimization Library HiOp to Accelerator-Based Hardware Architectures

While interior point method has been the centerpiece of nonlinear programming tools used in science and engineering, its reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement it effectively on hardware accelerators. HiOp optimization package attempts to provide an implementation of the interior point method suitable for hardware accelerators by compressing the original sparse problem to produce an underlying linear problem that is dense and of manageable size. Implementations of dense linear solvers are more mature and utilize hardware accelerators better than their sparse counterparts. There is a number of important domain problems, such as optimal power flow analysis for power grids, where the sparse problem can be effectively compressed and deploying dense linear solver within the interior point method can improve performance. Here we describe a portable implementation of HiOp optimization engine, which uses a linear solver from Magma library and runs entirely on hardware accelerators. To compress the problem, HiOp uses customized mixed dense-sparse linear algebra. All HiOp kernels are implemented using Umpire and RAJA portability libraries. We describe details of the implementation and discuss trade-offs between performance, portability and development cost.

97 MATHEMATICS AND COMPUTING↗

Assessing VQLS for Fluid Dynamics on a Hybrid Quantum-HPC Stack

Recent advances in quantum linear solvers offer a promising direction for accelerating extreme scientific computations such as fluid dynamics. However, the deep and complex circuits required by many quantum algorithms limit their practical use on current quantum hardware. The Variational Quantum Linear Solver (VQLS) presents a viable alternative for near-term quantum devices (NISQ), and initial efforts have explored its application to select fluid dynamics problems. In this work, we evaluate the use of VQLS for canonical fluid dynamics problems, aiming to identify pathways for generalizing its implementation across a broader class of systems. We analyze the impact of various circuit ansatz and classical optimizers on solution quality and convergence behavior. Furthermore, we assess the algorithm's feasibility within a hybrid quantum–high-performance computing (HPC) framework by porting it to QFw, a state-of-the-art quantum-HPC software stack. 11This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US DOE under Contract No. DE-AC05-00OR22725.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗

Implosion dynamics of triple-nozzle gas-puff z pinches on COBRA

Experiments on the 1-MA, 220-ns COBRA generator at Cornell University were conducted to provide detailed measurements of structured cylindrical gas-puff z pinches. In the experiments, a 7 cm diameter triple-nozzle gas valve assembly with concentric outer and inner annular nozzles and a central gas jet initialize the z-pinch load with various working gases, radial density profiles, and externally applied axial magnetic fields. Planar laser-induced fluorescence provides a measure of the initial neutral gas density of the load, while three-frame laser shearing interferometry and multi-frame extreme ultraviolet (XUV) cameras reveal the formation and propagation of a magneto-Rayleigh–Taylor (MRT) unstable shock layer. Implosion trajectories are compared to simple, experimentally informed models and found to be in good agreement. Differences in the structure of the accelerating plasma sheath and evolution of the MRT instability are observed for different gas species and axial magnetic field strengths, correlating with differences in pinch uniformity and x-ray emission. Here, the average instability growth is compared to linear MRT theory predictions using the instantaneous acceleration of the best-fit implosion models and characteristic instability wavelength, with the effective Atwood number and seed perturbation size as fit parameters. For high density argon center jets, ionization prior to the arrival of the imploding plasma sheath suggests a heating mechanism consistent with photoionization by XUV self-emission.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetically Levitated and Constrained Flywheel Energy Storage System

The concept of using linear induction motors to lift, constrain, accelerate, and decelerate a large-scale flywheel is proposed, and some of the advantages are investigated. Calculations for a Magnetically Levitated Energy Storage System (MLES) are performed that compare a single large scale MLES with a current state of the art flywheel energy storage system in order to show the relative differences and advantages of such a system. The system that is used for comparison is a typical Beacon Power flywheel energy system. This is currently one of the state-of-the-art flywheel energy storage systems and so it can be used to provide a basic data set to compare to an MLES system.

VanOsdol, John↗

Data-driven acceleration of thermal radiation transfer calculations with the dynamic mode decomposition and a sequential singular value decomposition

In this work, we present a method for accelerating discrete ordinates radiative transfer calculations for radiative transfer. Our method works with nonlinear positivity fixes, in contrast to most acceleration schemes. The method is based on the dynamic mode decomposition (DMD) and using a sequence of rank-one updates to compute the singular value decomposition needed for DMD. Using a sequential method allows us to automatically determine the number of solution vectors to include in the DMD acceleration. We present results for slab geometry discrete ordinates calculations with the standard temperature linearization. Compared with positive source iteration, our results demonstrate that our acceleration method reduces the number of transport sweeps required to solve the problem by a factor of about 3 on a standard diffusive Marshak wave problem, a factor of several thousand on a cooling problem where the effective scattering ratio approaches unity, and a factor of 20 improvement in a realistic, multimaterial radiating shock problem.

97 MATHEMATICS AND COMPUTING↗

Advanced Modeling of Plasma-based Particle Accelerators

Plasma-based acceleration (PBA) driven by an intense laser (LWFA) or particle beam (PWFA) can produce ultra-high accelerating fields in excess of a GV/cm. PBA could substantially reduce the size and cost of future linear collider facilities if deployed successfully. PBA enables compact tabletop accelerators that can provide lower energy GeV-class beams in a laboratory setting. PBA enables high quality beam generation suitable for x-ray free electron lasers (XFEL) via controllable methods of self-injection. Challenges in modeling and optimization of multi-stage PBA motivate the need for exascale computing and state-of-the-art PIC codes.

43 PARTICLE ACCELERATORS↗

GPU-resident sparse direct linear solvers for alternating current optimal power flow analysis

Integrating renewable resources within the transmission grid at a wide scale poses significant challenges for economic dispatch as it requires analysis with more optimization parameters, constraints, and sources of uncertainty. This motivates the investigation of more efficient computational methods, especially those for solving the underlying linear systems, which typically take more than half of the overall computation time. In this paper, we present our work on sparse linear solvers that take advantage of hardware accelerators, such as graphical processing units (GPUs), and improve the overall performance when used within economic dispatch computations. We treat the problems as sparse, which allows for faster execution but also makes the implementation of numerical methods more challenging. We present the first GPU-native sparse direct solver that can execute on both AMD and NVIDIA GPUs. We demonstrate significant performance improvements when using high-performance linear solvers within alternating current optimal power flow (ACOPF) analysis. Furthermore, we demonstrate the feasibility of getting significant performance improvements by executing the entire computation on GPU-based hardware. Finally, we identify outstanding research issues and opportunities for even better utilization of heterogeneous systems, including those equipped with GPUs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

High-order matrix-free incompressible flow solvers with GPU acceleration and low-order refined preconditioners

In this work, we present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems resulting from the finite element discretization can be prohibitively expensive, both in terms of computational complexity and memory. For this reason, it is necessary to develop matrix-free operators and preconditioners, which can be used to efficiently solve these linear systems without access to the matrix entries themselves. The matrix-free operator evaluations utilize GPU-accelerated sum-factorization techniques to minimize memory movement and maximize throughput. The preconditioners developed in this work are based on a low-order refined methodology with parallel subspace corrections, as described for diffusion problems in [1]. The saddle-point Stokes system is solved using block-preconditioning techniques, which are robust in mesh size, polynomial degree, time step, and viscosity. For the incompressible Navier-Stokes equations, we make use of projection (fractional step) methods, which require Helmholtz and Poisson solves at each time step. The performance of our flow solvers is assessed on several benchmark problems in two and three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗