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At least 91 records · Page 5

Replicated Computational Results (RCR) Report for “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software”

The article by Flegar et al. titled “Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software” presents a novel, practical implementation of an adaptive precision block-Jacobi preconditioner. Performance results using state-of-the-art GPU architectures for the block-Jacobi preconditioner generation and application demonstrate the practical usability of the method, compared to a traditional full-precision block-Jacobi preconditioner. A production-ready implementation is provided in the Ginkgo numerical linear algebra library. In this report, the Ginkgo library is reinstalled and performance results are generated to perform a comparison to the original results when using Ginkgo’s Conjugate Gradient solver with either the full or the adaptive precision block-Jacobi preconditioner for a suite of test problems on an NVIDIA GPU accelerator. After completing this process, the published results are deemed reproducible.

97 MATHEMATICS AND COMPUTING↗

Preconditioning of overcast-to-broken cloud transitions by riming in marine cold air outbreaks

Marine cold air outbreaks (CAOs) commonly form overcast cloud decks that transition into broken cloud fields downwind, dramatically altering the local radiation budget. In this study, we investigate the impact of frozen hydrometeors on these transitions. We focus on a CAO case in the NW Atlantic, the location of the multi-year flight campaign ACTIVATE (Aerosol Cloud meTeorology Interactions oVer the western ATlantic Experiment). We use MERRA-2 (Modern-Era Retrospective analysis for Research and Applications, version 2) reanalysis fields to drive large eddy simulations with mixed-phase two-moment microphysics in a Lagrangian framework. We find that transitions are triggered by substantial rain (rainwater paths >25 g m−2), and only simulations that allow for aerosol depletion result in sustained breakups, as observed. Using a range of diagnostic ice nucleating particle concentrations, Ninp, we find that increasing ice progressively accelerates transitions, thus abbreviating the overcast state. Ice particles affect the cloud-topped boundary layer evolution, primarily through riming-related processes prior to substantial rain, leading to (1) a reduction in cloud liquid water, (2) early consumption of cloud condensation nuclei, and (3) early and light precipitation cooling and moistening below cloud. We refer to these three effects collectively as “preconditioning by riming”. Greater boundary layer aerosol concentrations available as cloud condensation nuclei (CCN) delay the onset of substantial rain. However, cloud breakup and low CCN concentration final stages are found to be inevitable in this case, due, primarily, to liquid water path buildup. An ice-modulated cloud transition speed suggests the possibility of a negative cloud–climate feedback. To address prevailing uncertainties in the model representation of mixed-phase processes, the magnitude of ice formation and riming impacts and, thereby, the strength of an associated negative cloud–climate feedback process, requires further observational evaluation by targeting riming hot spots with in situ imaging probes that allow for both the characterization of ice particles and abundance of supercooled droplets.

Marine cold air outbreaks↗

Matrix-free preconditioning for high-order H (curl) discretizations

The greater arithmetic intensity of high-order finite element discretizations makes them attractive for implementation on next-generation hardware, but assembly of high-order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix-free application of high-order operators has received significant attention in the literature in the context of Poisson-type problems, but preconditioners and solvers for inverting more general operators are not very well-developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high-order H 1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor-product basis functions on an unstructured mesh of quadrilaterals. Overall, our approach uses a sparsified H 1 solver constructed on a low-order mesh of the nodal points of the underlying high-order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two-dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(p d+1 ) floating point operation count and optimal O(p d ) memory transfer requirements, outperforming existing Maxwell preconditioners in the high-order regime.

97 MATHEMATICS AND COMPUTING↗

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗

Block triangular preconditioning for stochastic Galerkin method

Here, in this paper, we develop a new block triangular preconditioner for solving partial differential equations with random coefficients. We prove spectral bounds for the preconditioned system. Several numerical examples are provided to demonstrate the efficiency of this preconditioner, especially for stochastic problems with large variance.

97 MATHEMATICS AND COMPUTING↗

Dexmedetomidine preconditioning ameliorates lung injury induced by pulmonary ischemia/reperfusion by upregulating promoter histone H3K4me3 modification of KGF-2

Highlights: • DexP alleviates I/R-induced lung injury and endothelial barrier dysfunction in mice. • DexP reduces the inflammatory response and increases KGF-2 expression in I/R. • DexP regulates the H3K4me3 modification of KGF-2 promoter histone. • DexP promotes KGF-2 expression by downregulating the expression of JMJD3. • DexP has the potential to be used as a means of treating I/R-induced lung injury. Keratinocyte growth factor (KGF)-2 has been highlighted to play a significant role in maintaining the endothelial barrier integrity in lung injury induced by ischemia-reperfusion (I/R). However, the underlying mechanism remains largely unknown. The aims of this study were to determine whether dexmedetomidine preconditioning (DexP) modulates pulmonary I/R-induced lung injury through the alteration in KGF-2 expression. In our I/R-modeled mice, DexP significantly inhibited pathological injury, inflammatory response, and inflammatory cell infiltration, while promoted endothelial barrier integrity and KGF-2 promoter activity in lung tissues. Bioinformatics prediction and ChIP-seq revealed that I/R significantly diminished the level of H3K4me3 modification in the KGF-2 promoter, which was significantly reversed by DexP. Moreover, DexP inhibited the expression of histone demethylase JMJD3, which in turn promoted the expression of KGF-2. In addition, overexpression of JMJD3 weakened the protective effect of DexP on lung injury in mice with I/R. Collectively, the present results demonstrated that DexP ameliorates endothelial barrier dysfunction via the JMJD3/KGF-2 axis.

60 APPLIED LIFE SCIENCES↗

Self‐Potential Tomography Preconditioned by Particle Swarm Optimization—Application to Monitoring Hyporheic Exchange in a Bedrock River

Abstract A self‐potential (SP) data‐inversion algorithm was developed and tested on an analytical model of electrical‐potential profile data attributed to single and multiple polarized electrical sources. The developed algorithm was then validated by an application to SP‐monitoring field data measured on the floodplain of East Fork Poplar Creek, Oak Ridge, Tennessee, to image electrical sources in areas conducive to preferential flow into the flood plain from the bedrock‐lined riverbed. The algorithm combined stochastic source‐localization by particle‐swarm‐optimization (PSO) of electrical sources characterized by simplified geometries with source tomography by regularized weighted least‐squares minimization of a quadratic objective function. Prior information was incorporated by preconditioning the tomography algorithm by PSO results. Variable percentages of random noise were added to analytical‐model data to evaluate the algorithm performance. Results indicated that true parameters of single‐source models were inverted and approximated with small residual error, whereas inversion of analytical‐model data representing multiple electrical sources accurately approximated the locations of the sources but miscalculated some parameters because of the non‐uniqueness of the inverse‐model solution. Source tomography applied to analytical model data during testing produced a spatially continuous parameter field that identified the locations of point‐scale synthetic dipole sources of electrical current flow with varying degrees of accuracy depending on the prior information incorporated into the tomography. When applied to SP‐monitoring field data, the algorithm imaged electrical sources within a known fault that intersects the bedrock riverbed and flood plain of East Fork Poplar Creek and depicted dynamic electrical conditions attributed to hyporheic exchange.

54 ENVIRONMENTAL SCIENCES↗

Seven days of ischemic preconditioning augments hypoxic exercise ventilation and muscle oxygenation in recreationally trained males

This investigation sought to assess whether single or repeated bouts of ischemic preconditioning (IPC) could improve oxyhemoglobin saturation ([Formula: see text]) and/or attenuate reductions in muscle tissue saturation index (TSI) during submaximal hypoxic exercise. Fifteen healthy young men completed submaximal graded exercise under four experimental conditions: 1) normoxia (NORM), 2) hypoxia (HYP) [oxygen fraction of inspired air ([Formula: see text]) = 0.14, ∼3,200 m], 3) hypoxia preceded by a single session of IPC (IPC1-HYP), and 4) hypoxia preceded by seven sessions of IPC, one a day for 7 consecutive days (IPC7-HYP). IPC7-HYP heightened minute ventilation (V̇e) at 80% HYP peak cycling power output ( W peak ) (+10.47 ± 3.35 L·min −1 , P = 0.006), compared with HYP, as a function of increased breathing frequency. Both IPC1-HYP (+0.17 ± 0.04 L·min −1 , P < 0.001) and IPC7-HYP (+0.16 ± 0.04 L·min −1 , P < 0.001) elicited greater oxygen consumption (V̇o 2 ) across exercise intensities compared with NORM, whereas V̇o 2 was unchanged with HYP alone. [Formula: see text] was unchanged by either IPC condition at any exercise intensity, yet the reduction of muscle TSI during resting hypoxic exposure was attenuated by IPC7-HYP (+9.9 ± 3.6%, P = 0.040) compared with HYP, likely as a function of reduced local oxygen extraction. Considering all exercise intensities, IPC7-HYP attenuated reductions of TSI with HYP (+6.4 ± 1.8%, P = 0.001). Seven days of IPC heightens ventilation, posing a threat to ventilatory efficiency, during high-intensity submaximal hypoxic exercise and attenuates reductions in hypoxic resting and exercise muscle oxygenation in healthy young men. A single session of IPC may be capable of modulating hypoxic ventilation; however, our present population was unable to demonstrate this with certainty.

Physiology↗

Smoothers for Matrix-Free Algebraic Multigrid Preconditioning of High-Order Finite Elements

We investigate smoothers for use in matrix-free algebraic multigrid (AMG) preconditioning of high-order finite element problems. These AMG preconditioners are matrix-free in the sense that they are built from a related low-order refined finite element problem whose system matrix can be much more rapidly assembled than the high-order problem. Our proposed smoother, which we call distributive relaxation, is more robust to the anisotropy present in many low-order refined meshes which feature a clustering of nodes near the boundaries between high-order finite elements. For solving the low-order refined problem, we show that this new distributive relaxation smoother possesses significantly improved performance compared to more traditional smoothers.

97 MATHEMATICS AND COMPUTING↗

Replicated Computational Results (RCR) Report for "Adaptive Precision Block-Jacobi for High Performance Preconditioning in the Ginkgo Linear Algebra Software''

In, a practical implementation of a novel adaptive precision block-Jacobi preconditioner is introduced. In particular, the authors present a heavily-tuned GPU implementation of the adaptive precision block-Jacobi preconditioner within the Ginkgo numerical linear algebra library. The performance of the methodology and implementation is demonstrated using the proposed preconditioning scheme within Ginkgo’s high-performance Conjugate Gradient (CG) implementation on an NVIDIA Volta GPU. In this report, we replicate a subset of the computational results presented in. The focus is generating results from Fig. 9 to evaluate the performance of using Ginkgo’s CG solver integrated with either the full or the adaptive precision block-Jacobi preconditioner applied to a variety of test cases

97 MATHEMATICS AND COMPUTING↗

Preconditioning for Hyper-reduction in Reduced Order Models

Many projection-based reduced order models (pROM) that utilize the governing equation and data to accelerate physical simulations can be applied to nonlinear dynamical systems. To avoid full order model (FOM) scale update for each time step, hyperreduction techniques are developed to sample high dimensional nonlinear terms. Our study aims to investigate if preconditioning the least-squares problem used for the nonlinear approximation can improve the robustness of the condition number of the problem while achieving high accuracy. In our study, we use the row-normalization matrix motivated by the Christoffel function as the preconditioner and solve the corresponding weighted least-squares problem. Numerical results for Lagrangian hydrodynamics examples are analyzed to explore how the preconditioner works compared to existing hyper-reduction techniques.

97 MATHEMATICS AND COMPUTING↗

Multi-physics Preconditioning for Thermally Activated Batteries

Thermal batteries, also known as molten-salt batteries, are single-use reserve power systems activated by pyrotechnic heat generation, which transitions the solid electrolyte into a molten state. The simulation of these batteries relies on multiphysics modeling to evaluate performance and behavior under various conditions. This paper presents advancements in scalable preconditioning strategies for the Thermally Activated Battery Simulator (TABS) tool, enabling efficient solutions to the coupled electrochemical systems that dominate computational costs in thermal battery simulations. We propose a hierarchical block Gauss-Seidel preconditioner implemented through the Teko package in Trilinos, which effectively addresses the challenges posed by tightly coupled physics, including charge transport, porous flow, and species diffusion. The preconditioner leverages scalable subblock solvers, including smoothed aggregation algebraic multigrid (SA-AMG) methods and domain-decomposition techniques, to achieve robust convergence and parallel scalability. Strong and weak scaling studies demonstrate the solver’s ability to handle problem sizes up to 51.3 million degrees of freedom on 2048 processors, achieving near sub-second setup and solve times for the end-to-end electrochemical solve. These advancements significantly improve the computational efficiency and turnaround time of thermal battery simulations, paving the way for higher-resolution models and enabling the transition from 2D axisymmetric to full 3D simulations.

25 ENERGY STORAGE↗

M-step preconditioned conjugate gradient methods

Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

Adams, L.↗

An M-step preconditioned conjugate gradient method for parallel computation

This paper describes a preconditioned conjugate gradient method that can be effectively implemented on both vector machines and parallel arrays to solve sparse symmetric and positive definite systems of linear equations. The implementation on the CYBER 203/205 and on the Finite Element Machine is discussed and results obtained using the method on these machines are given.

Adams, L.↗

Stratospheric sudden coolings and the role of nonlinear wave interactions in preconditioning the circumpolar flow

The mechanisms responsible for the transition of the circumpolar flow from its normal midwinter state to the preconditioned state that should evolve before a wavenumber-2 major warming are investigated, through a combination of observational, numerical and theoretical studies. Observations of Eliassen-Palm flux cross sections indicate that while wave zonal mean flow interaction theory could account for the qualitative evolution of the circumpolar flow during the warming, substantial nonlinear wave interactions were active during the cooling period, and these interactions significantly influenced the evolution of the circumpolar flow. Numerical experiments employing a truncated, semispectral model indicate that this cooling phenomenon is realistically reproducible in an idealized integration in which wave-wave interactions are present. Two different mechanisms are proposed to account for these nonlinearities.

Palmer, T. N.↗