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At least 145 records · Page 8

Space-Time Block Preconditioning for Incompressible Flow

Parallel-in-time methods have become increasingly popular in the simulation of time-dependent numerical PDEs, allowing for the efficient use of additional message passing interface processes when spatial parallelism saturates. Most methods treat the solution and parallelism in space and time separately. In contrast, all-at-once methods solve the full space-time system directly, largely treating time as simply another spatial dimension. All-at-once methods offer a number of benefits over separate treatment of space and time, most notably significantly increased parallelism and faster time to solution (when applicable). However, the development of fast, scalable all-at-once methods has largely been limited to time-dependent (advection-)diffusion problems. This paper introduces the concept of space-time block preconditioning for the all-at-once solution of incompressible flow. By extending well-known concepts of spatial block preconditioning to the space-time setting, we develop a block preconditioner whose application requires the solution of a space-time (advection-)diffusion equation in the velocity block, coupled with a pressure Schur complement approximation consisting of independent spatial solves at each time-step, and a space-time matrix-vector multiplication. The new method is tested on four classical models in incompressible flow. Finally, the results indicate perfect scalability in refinement of spatial and temporal mesh spacing, perfect scalability in nonlinear Picard iteration count when applied to a nonlinear Navier--Stokes problem, and minimal overhead in terms of number of preconditioner applications compared with sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

Machine Learning-Driven Conservative-to-Primitive Conversion in Hybrid Piecewise Polytropic and Tabulated Equations of State

We present a novel machine learning (ML)-based method to accelerate conservative-to-primitive inversion, focusing on hybrid piecewise polytropic and tabulated equations of state. Traditional root-finding techniques are computationally expensive, particularly for large-scale relativistic hydrodynamics simulations. To address this, we employ feedforward neural networks (NNC2PS and NNC2PL), trained in PyTorch (2.0+) and optimized for GPU inference using NVIDIA TensorRT (8.4.1), achieving significant speedups with minimal accuracy loss. The NNC2PS model achieves 𝐿 1 and 𝐿 ∞ errors of 4.54 × 10 −7 and 3.44 × 10−6, respectively, while the NNC2PL model exhibits even lower error values. TensorRT optimization with mixed-precision deployment substantially accelerates performance compared to traditional root-finding methods. Specifically, the mixed-precision TensorRT engine for NNC2PS achieves inference speeds approximately 400 times faster than a traditional single-threaded CPU implementation for a dataset size of 1,000,000 points. Ideal parallelization across an entire compute node in the Delta supercomputer (dual AMD 64-core 2.45 GHz Milan processors and 8 NVIDIA A100 GPUs with 40 GB HBM2 RAM and NVLink) predicts a 25-fold speedup for TensorRT over an optimally parallelized numerical method when processing 8 million data points. Moreover, the ML method exhibits sub-linear scaling with increasing dataset sizes. We release the scientific software developed, enabling further validation and extension of our findings. By exploiting the underlying symmetries within the equation of state, these findings highlight the potential of ML, combined with GPU optimization and model quantization, to accelerate conservative-to-primitive inversion in relativistic hydrodynamics simulations.

conservative-to-primitive conversion↗

A study of potential energy curves from the model space quantum Monte Carlo method

We report on the first application of the model space quantum Monte Carlo (MSQMC) to potential energy curves (PECs) for the excited states of C{sub 2}, N{sub 2}, and O{sub 2} to validate the applicability of the method. A parallel MSQMC code is implemented with the initiator approximation to enable efficient sampling. The PECs of MSQMC for various excited and ionized states are compared with those from the Rydberg-Klein-Rees and full configuration interaction methods. The results indicate the usefulness of MSQMC for precise PECs in a wide range obviating problems concerning quasi-degeneracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improved scaling of temperature-accelerated dynamics using localization

While temperature-accelerated dynamics (TAD) is a powerful method for carrying out non-equilibrium simulations of systems over extended time scales, the computational cost of serial TAD increases approximately as N{sup 3} where N is the number of atoms. In addition, although a parallel TAD method based on domain decomposition [Y. Shim et al., Phys. Rev. B 76, 205439 (2007)] has been shown to provide significantly improved scaling, the dynamics in such an approach is only approximate while the size of activated events is limited by the spatial decomposition size. Accordingly, it is of interest to develop methods to improve the scaling of serial TAD. As a first step in understanding the factors which determine the scaling behavior, we first present results for the overall scaling of serial TAD and its components, which were obtained from simulations of Ag/Ag(100) growth and Ag/Ag(100) annealing, and compare with theoretical predictions. We then discuss two methods based on localization which may be used to address two of the primary “bottlenecks” to the scaling of serial TAD with system size. By implementing both of these methods, we find that for intermediate system-sizes, the scaling is improved by almost a factor of N{sup 1/2}. Some additional possible methods to improve the scaling of TAD are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Parallel diffusion operator for magnetized plasmas with improved spectral fidelity

Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge for describing non-grid-aligned magnetic structures in Eulerian (grid-based) simulations. Here, the present paper describes and validates a new method for parallel diffusion in magnetized plasmas based on the anti-symmetry representation [Halpern and Waltz, Phys. Plasmas 25, 060703 (2018)]. In the anti-symmetry formalism, diffusion manifests as a flow operator involving the logarithmic derivative of the transported quantity. Qualitative plane wave analysis shows that the new operator naturally yields better discrete spectral resolution compared to its conventional counterpart. Numerical simulations comparing the new method against existing finite difference methods are carried out, showing significant improvement. In particular, we find that combining anti-symmetry with finite differences in diagonally staggered grids essentially eliminates the so-called “artificial numerical diffusion” that affects conventional finite difference and finite volume methods.

Anisotropic diffusion↗

On the performance of exponential integrators for problems in magnetohydrodynamics

Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and their performance was evaluated using a range of test problems. While the results of these investigations showed that exponential integrators can provide significant computational savings, the research on validating this hypothesis for large scale systems and understanding what classes of problems can particularly benefit from the use of the new techniques is in its initial stages. Resistive magnetohydrodynamic (MHD) modeling is widely used in studying large scale behavior of laboratory and astrophysical plasmas. In many problems numerical solution of MHD equations is a challenging task due to the temporal stiffness of this system in the parameter regimes of interest. In this paper we evaluate the performance of exponential integrators on large MHD problems and compare them to a state-of-the-art implicit time integrator. Both the variable and constant time step exponential methods of EPIRK-type are used to simulate magnetic reconnection and the Kevin–Helmholtz instability in plasma. Performance of these methods, which are part of the EPIC software package, is compared to the variable time step variable order BDF scheme included in the CVODE (part of SUNDIALS) library. We study performance of the methods on parallel architectures and with respect to magnitudes of important parameters such as Reynolds, Lundquist, and Prandtl numbers. We find that the exponential integrators provide superior or equal performance in most circumstances and conclude that further development of exponential methods for MHD problems is warranted and can lead to significant computational advantages for large scale stiff systems of differential equations such as MHD.

97 MATHEMATICS AND COMPUTING↗

Parallelized multiple nozzle system and method to produce layered droplets and fibers for microencapsulation

The present disclosure relates to a nozzle system for use in a microfluidic production application for producing at least one of particles, capsules or fibers. The system has a main body portion having a compressed fluid inlet and a core fluid inlet, and a plurality of parallel arranged core fluid nozzles that receive the core fluid and create a plurality of core fluid streams. At least one compressed fluid inlet associated with the main body channels compressed fluid to areas adjacent ends of the core fluid nozzles. An apertured plate having a plurality of apertures is arranged near the ends of the core fluid nozzles, with each aperture being uniquely associated with a single one of the core fluid nozzles. The compressed fluid acts on the core fluid streams exiting the core fluid nozzles to help create, with the apertures, at least one of core fluid droplets or core fluid fibers from the core fluid streams.

Ye, Congwang↗

Markov Chain Monte Carlo Predictions of Neutron-rich Lanthanide Properties as a Probe of r -process Dynamics

Lanthanide element signatures are key to understanding many astrophysical observables, from merger kilonova light curves to stellar and solar abundances. To learn about the lanthanide element synthesis that enriched our solar system, we apply the statistical method of Markov Chain Monte Carlo to examine the nuclear masses capable of forming the r-process rare-earth abundance peak. We describe the physical constraints we implement with this statistical approach and demonstrate the use of the parallel chains method to explore the multidimensional parameter space. We apply our procedure to three moderately neutron-rich astrophysical outflows with distinct types of r-process dynamics. We show that the mass solutions found are dependent on outflow conditions and are related to the r-process path. We describe in detail the mechanism behind peak formation in each case. We then compare our mass predictions for neutron-rich neodymium and samarium isotopes to the latest experimental data from the CPT at CARIBU. Here, we find our mass predictions given outflows that undergo an extended (n,γ)⇌(γ,n) equilibrium to be those most compatible with both observational solar abundances and neutron-rich mass measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Parallel beamlet dose calculation via beamlet contexts in a distributed multi‐GPU framework

Purpose Dose calculation is one of the most computationally intensive, yet essential tasks in the treatment planning process. With the recent interest in automatic beam orientation and arc trajectory optimization techniques, there is a great need for more efficient model‐based dose calculation algorithms that can accommodate hundreds to thousands of beam candidates at once. Foundational work has shown the translation of dose calculation algorithms to graphical processing units ( GPU s), lending to remarkable gains in processing efficiency. But these methods provide parallelization of dose for only a single beamlet, serializing the calculation of multiple beamlets and under‐utilizing the potential of modern GPU s. In this paper, the authors propose a framework enabling parallel computation of many beamlet doses using a novel beamlet context transformation and further embed this approach in a scalable network of multi‐ GPU computational nodes. Methods The proposed context‐based transformation separates beamlet‐local density and TERMA into distinct beamlet contexts that independently provide sufficient data for beamlet dose calculation. Beamlet contexts are arranged in a composite context array with dosimetric isolation, and the context array is subjected to a GPU collapsed‐cone convolution superposition procedure, producing the set of beamlet‐specific dose distributions in a single pass. Dose from each context is converted to a sparse representation for efficient storage and retrieval during treatment plan optimization. The context radius is a new parameter permitting flexibility between the speed and fidelity of the dose calculation process. A distributed manager‐worker architecture is constructed around the context‐based GPU dose calculation approach supporting an arbitrary number of worker nodes and resident GPU s. Phantom experiments were executed to verify the accuracy of the context‐based approach compared to Monte Carlo and a reference CPU ‐ CCCS implementation for single beamlets and broad beams composed by addition of beamlets. Dose for representative 4 π beam sets was calculated in lung and prostate cases to compare its efficiency with that of an existing beamlet‐sequential GPU ‐ CCCS implementation. Code profiling was also performed to evaluate the scalability of the framework across many networked GPU s. Results The dosimetric accuracy of the context‐based method displays <1.35% and 2.35% average error from the existing serialized CPU ‐ CCCS algorithm and Monte Carlo simulation for beamlet‐specific PDD s in water and slab phantoms, respectively. The context‐based method demonstrates substantial speedup of up to two orders of magnitude over the beamlet‐sequential GPU ‐ CCCS method in the tested configurations. The context‐based framework demonstrates near linear scaling in the number of distributed compute nodes and GPU s employed, indicating that it is flexible enough to meet the performance requirements of most users by simply increasing the hardware utilization. Conclusions The context‐based approach demonstrates a new expectation of performance for beamlet‐based dose calculation methods. This approach has been successful in accelerating the dose calculation process for very large‐scale treatment planning problems ‐ such as automatic 4 π IMRT beam orientation and VMAT arc trajectory selection, with hundreds of thousands of beamlets ‐ in clinically feasible timeframes. The flexibility of this framework makes it as a strong candidate for use in a variety of other very large‐scale treatment planning tasks and clinical workflows.

Neph, Ryan↗

Biasing Smarter, Not Harder, by Partitioning Collective Variables into Families in Parallel Bias Metadynamics

Molecular simulations of systems with multiple copies of identical atoms or molecules may require the biasing of numerous, degenerate collective variables (CVs) to accelerate sampling. Recently, a variation of metadynamics (MetaD) named parallel bias metadynamics (PBMetaD) has been shown to make biasing of many CVs more tractable. We extended the PBMetaD scheme so that it partitions degenerate CVs into families that share the same bias potential, consequently expediting convergence of the free-energy landscape. We tested our method, named parallel bias metadynamics with partitioned families, on 3, 21, and 78 CV systems and obtained an approximately proportional increase in convergence speed compared to standard PBMetaD.

Prakash, Arushi↗

Elucidating the challenges in extracting ultra-slow flame speeds in a closed vessel - A CH 2 F 2 microgravity case study using optical and pressure-rise data

Refrigerants with a low global warming potential (GWP) possess mild flammability. Hence, a fundamental understanding of their combustion characteristics is required to assess their fire-hazardous potential. The laminar burning velocity is one fundamental property to describe these under safety evaluation aspects. However, measuring laminar burning velocities for slow-burning components, such as low-GWP alternatives, is challenging. This is due to influencing effects such as buoyant flame deformation, stretch, radiation, and confinement, especially at the flammability limits. Here, in the present study, we investigated near-limit flames of the representative refrigerant difluoromethane (CH 2 F 2 ) with nitrogen-enriched oxidizer mixtures to elucidate the potentials and limitations at ultra-slow flame speeds of two widely used flame speed measurement methods in the closed vessel configuration: the optical flame speed measurement in the early quasi-isobaric regime and the flame speed determination from the pressure-rise during the later phase of the isochoric combustion process. Experiments were performed under terrestrial- and microgravity, conducted in a specially designed setup suitable for drop tower applications, using both methods in parallel. Recommendations for the extraction of flame speed data are derived from the non-buoyant reference investigations under microgravity and transferred to ultra-slow flames at terrestrial gravity. Near-limit flames under microgravity were found to be significantly affected by stretch effects for the optical method so that flame speed extrapolations to unstretched conditions are prone to errors. Stretch also affects the pressure method’s lower evaluation limit, and errors can be estimated by combining flame speed data from the pressure method and Markstein lengths from optical experiments.

42 ENGINEERING↗

In situ particle advection via parallelizing over particles

We extend the method for particle advection that parallelizes over particles to work in an in situ setting. We then compare our method with the typical method for in situ, parallelizing over data. Our experiments consist of parallelism at 512 cores, a data set with 67 million cells, and ten billion total advection steps. Our findings show that parallelizing over particles can be more than ten times faster for some workloads, for reasonable memory cost. Overall, the significance of these findings is to demonstrate that moving data can be worthwhile in some in situ settings.

Pugmire, Dave↗

Calculation of the state-to-state S-matrix for tetra-atomic reactions with transition-state wave packets: H{sub 2}/D{sub 2} + OH → H/D + H{sub 2}O/HOD

This work is concerned with the calculation of state-to-state S-matrix elements for four-atom reactions using a recently proposed method based on the quantum transition-state theory. In this approach, the S-matrix elements are computed from the thermal flux cross-correlation functions obtained in both the reactant and product arrangement channels. Since transition-state wave packets are propagated with only single arrangement channels, the bases/grids required are significantly smaller than those needed in state-to-state approaches based on a single set of scattering coordinates. Furthermore, the propagation of multiple transition-state wave packets can be carried out in parallel. This method is demonstrated for the H{sub 2}/D{sub 2} + OH → H/D + H{sub 2}O/HOD reactions (J = 0) and the reaction probabilities are in excellent agreement with benchmark results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

LLNL Mercury Project Trinity Open Science Final Report

The Mercury Monte Carlo particle transport code developed at Lawrence Livermore National Laboratory (LLNL) is used to simulate the transport of radiation through urban environments. These challenging calculations include complicated geometries and require significant computational resources to complete. As a result, a question arises as to the level of convergence of the calculations with Monte Carlo simulation particle count. In the Trinity Open Science calculations, one main focus was to investigate convergence of the relevant simulation quantities with Monte Carlo particle count to assess the current simulation methodology. Both for this application space but also of more general applicability, we also investigated the impact of code algorithms on parallel scaling on the Trinity machine as well as the utilization of the Trinity DataWarp burst buffer technology in Mercury via the LLNL Scalable Checkpoint/Restart (SCR) library.

54 ENVIRONMENTAL SCIENCES↗

Interactive Correlation Analysis and Visualization of Climate Data

The relationship between our ability to analyze and extract insights from visualization of climate model output and the capability of the available resources to make those visualizations has reached a crisis point. The large volume of data currently produced by climate models is overwhelming the current, decades-old visualization workflow. The traditional methods for visualizing climate output also have not kept pace with changes in the types of grids used, the number of variables involved, and the number of different simulations performed with a climate model or the feature-richness of high-resolution simulations. This project has developed new and faster methods for visualization in order to get the most knowledge out of the new generation of high-resolution climate models. While traditional climate images will continue to be useful, there is need for new approaches to visualization and analysis of climate data if we are to gain all the insights available in ultra-large data sets produced by high-resolution model output and ensemble integrations of climate models such as those produced for the Coupled Model Intercomparison Project. Towards that end, we have developed new visualization techniques for performing correlation analysis. We have also introduced highly scalable, parallel rendering methods for visualizing large-scale 3D data. This project was done jointly with climate scientists and visualization researchers at Argonne National Laboratory and NCAR.

54 ENVIRONMENTAL SCIENCES↗

Scalable domain decomposition solvers for stochastic PDEs in high performance computing

Stochastic spectral finite element models of practical engineering systems may involve solutions of linear systems or linearized systems for non-linear problems with billions of unknowns. For stochastic modeling, it is therefore essential to design robust, parallel and scalable algorithms that can efficiently utilize high-performance computing to tackle such large-scale systems. Domain decomposition based iterative solvers can handle such systems. And though these algorithms exhibit excellent scalabilities, significant algorithmic and implementational challenges exist to extend them to solve extreme-scale stochastic systems using emerging computing platforms. Intrusive polynomial chaos expansion based domain decomposition algorithms are extended here to concurrently handle high resolution in both spatial and stochastic domains using an in-house implementation. Sparse iterative solvers with efficient preconditioners are employed to solve the resulting global and subdomain level local systems through multi-level iterative solvers. We also use parallel sparse matrix–vector operations to reduce the floating-point operations and memory requirements. Numerical and parallel scalabilities of these algorithms are presented for the diffusion equation having spatially varying diffusion coefficient modeled by a non-Gaussian stochastic process. Scalability of the solvers with respect to the number of random variables is also investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation

This study proposes an automated calibration procedure for bond parameters in bonded discrete element modelling. By exploring the underlying physical correlations between microscopic parameters of bonds and macroscopic strength parameters of the continuum to be modelled, the microscopic shear strength and tensile strength are identified as independent variables for calibration purpose. Then a physics-informed iterative scheme is proposed to automatically approximate the bond parameters by viewing the micro-macro relation as an implicitly defined mathematical mapping function. As a result of highly non-convex features of this implicit mapping, the adaptive moment estimation (Adam), which is especially suitable for problems with noisy gradients, is adopted as the basic iterative scheme, in conjunction with other numerical techniques to approximately evaluate the partial derivatives involved. The whole procedure offers a simple and effective framework for bond parameter calibration. Finally, a numerical example of SiC ceramic is provided for validation. By compared with some existing calibration methods, the proposed method shows significant advantages in terms of calibration efficiency and accuracy.

42 ENGINEERING↗

An analysis of various solution strategies and perturbations on inputs of the reactor shielding problem - 25584

Previous work focused on the use of automated variance reduction parameters for use in a fixed source reactor shielding problem to solve for ex-core particle transport results. The current work assesses that strategy in light of a fully-coupled Monte Carlo problem run as a critical system with parallel processing and the use of moderate variance reduction parameters set manually. The results from the two strategies compare well. Also, results are compared between the MCNP, Virtual Environment for Reactor Applications (VERA) and Shift computer codes. Shift and VERA deliver similar results and compare well to MCNP. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗