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DOE OSTI2023

Scaled ILU Smoothers for Navier-Stokes Pressure Projection

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) V-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill-level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong-scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu-Wind and PeleLM pressure solvers. For large problem sizes, GMRES+AMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

algebraic multigrid↗

DOE OSTI2020

Estimating posterior quantity of interest expectations in a multilevel scalable framework

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large-scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element-agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state-of-the-art scalable AMG. To illustrate the applicability of this approach, numerical tests are performed on two 3D examples-a unit cube and an egg-shaped domain with an irregular boundary-where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

A Unified Analytical Method Greenness Score ( uAMGS ) Quantifies How Microscopic Imaging Is Greener Than Conventional Liquid Chromatography

Green chemistry is a set of principles for assessing, developing, and implementing methods that are safer, more efficient, and less detrimental to the environment. The analytical method greenness score (AMGS) is one of many metrics that attempt to evaluate traditional liquid chromatography (LC) based on the energy consumption of the instrument and the safety, health risks, and environmental impact of the solvents employed. Unfortunately, in practice, the AMGS is primarily focused on traditional separation methods in the pharmaceutical industry and is not amenable to cutting-edge separation science, including miniaturization. To broaden this scope, the unified Analytical Method Greenness Score (uAMGS) is presented here, which clarifies and expands on the underlying mathematics and incorporates both dimensional and uncertainty analysis, enabling its application to a broader range of analytical techniques. The uAMGS is used to compare the greenness of two distinct methods: single-molecule microscopy (SMM) and high-performance liquid chromatography (HPLC), which were used to collect equivalent data. uAMGS determines that SMM is significantly greener than HPLC due primarily to decreased solvent consumption. Overall, the uAMGS should allow chemists ranging from undergraduates to industrial PhDs to assess the greenness of a wide range of separations.

chemical separations↗

DOE OSTI2021

Viral community analysis in a marine oxygen minimum zone indicates increased potential for viral manipulation of microbial physiological state

Microbial communities in oxygen minimum zones (OMZs) are known to have significant impacts on global biogeochemical cycles, but viral influence on microbial processes in these regions are much less studied. Here we provide baseline ecological patterns using microscopy and viral metagenomics from the Eastern Tropical North Pacific (ETNP) OMZ region that enhance our understanding of viruses in these climate-critical systems. While extracellular viral abundance decreased below the oxycline, viral diversity and lytic infection frequency remained high within the OMZ, demonstrating that viral influences on microbial communities were still substantial without the detectable presence of oxygen. Viral community composition was strongly related to oxygen concentration, with viral populations in low-oxygen portions of the water column being distinct from their surface layer counterparts. However, this divergence was not accompanied by the expected differences in viral-encoded auxiliary metabolic genes (AMGs) relating to nitrogen and sulfur metabolisms that are known to be performed by microbial communities in these low-oxygen and anoxic regions. Instead, several abundant AMGs were identified in the oxycline and OMZ that may modulate host responses to low-oxygen stress. We hypothesize that this is due to selection for viral-encoded genes that influence host survivability rather than modulating host metabolic reactions within the ETNP OMZ. Together, this study shows that viruses are not only diverse throughout the water column in the ETNP, including the OMZ, but their infection of microorganisms has the potential to alter host physiological state within these biogeochemically important regions of the ocean.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Population ecology and biogeochemical implications of ssDNA and dsDNA viruses along a permafrost thaw gradient

Anthropogenic-driven climate change is accelerating permafrost thaw, threatening to release vast carbon stores through increased microbial activity. While microbial roles are increasingly studied, the contributions of viruses remain largely unexplored, in part due to soil-associated technical challenges that have hindered their detection and characterization. Here, we applied an optimized virion enrichment workflow along a permafrost thaw gradient, identifying 9,963 viral populations (vOTUs), including single- and double-stranded DNA viruses, with 99.9% novelty compared to other soils. Hosts were predicted for 38% of vOTUs, spanning nine archaeal, and 36 bacterial phyla, 22% of which were linked to metagenome-assembled genomes, including key carbon-cycling taxa. Genomic analyses revealed 811 putative auxiliary metabolic genes (AMGs) from 658 vOTUs, nearly half involved in carbon processing. These included 59 glycoside hydrolases (GH) across nine GH families, 45 for monosaccharide degradation, and seven involved in short-chain fatty acid and C1 metabolism, linking viruses to both early and late stages of carbon turnover. Additionally, six vOTUs carried racD, which may stabilize microbial necromass and promote long-term carbon storage. Viral and AMG functional diversity increased with thaw stage, indicating that viruses might participate in a broadening range of microbial metabolic processes as permafrost thaws. These findings expand our understanding of virus contributions in microbial carbon processing and suggest their important role in deciphering soil carbon fate under changing climate conditions.

Biological and medical sciences↗

DOE OSTI2020

DRAM for distilling microbial metabolism to automate the curation of microbiome function

Abstract Microbial and viral communities transform the chemistry of Earth's ecosystems, yet the specific reactions catalyzed by these biological engines are hard to decode due to the absence of a scalable, metabolically resolved, annotation software. Here, we present DRAM (Distilled and Refined Annotation of Metabolism), a framework to translate the deluge of microbiome-based genomic information into a catalog of microbial traits. To demonstrate the applicability of DRAM across metabolically diverse genomes, we evaluated DRAM performance on a defined, in silico soil community and previously published human gut metagenomes. We show that DRAM accurately assigned microbial contributions to geochemical cycles and automated the partitioning of gut microbial carbohydrate metabolism at substrate levels. DRAM-v, the viral mode of DRAM, established rules to identify virally-encoded auxiliary metabolic genes (AMGs), resulting in the metabolic categorization of thousands of putative AMGs from soils and guts. Together DRAM and DRAM-v provide critical metabolic profiling capabilities that decipher mechanisms underpinning microbiome function.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Identification of hidden N4-like viruses and their interactions with hosts

The N4-like viruses, which were recently assigned to the novel viral family Schitoviridae in 2021, belong to a podoviral-like viral lineage and possess conserved genomic characteristics and a unique replication mechanism. Despite their significance, our understanding of N4-like viruses is primarily based on viral isolates. To address this knowledge gap, this study has established a comprehensive N4-like viral data sets comprising 342 high-quality N4-like viruses/proviruses (144 viral isolates, 158 uncultured viruses, and 40 integrated N4-like proviruses). These viruses were classified into 97 subfamilies (89 of which are newly identified), 148 genera (100 of which are newly identified), and 253 species (177 of which are newly identified). The study reveals that N4-like viruses inhibit the polar region, oligotrophic open oceans, and the human gut, where they infect various bacterial lineages, such as Alpha/Beta/Gamma/Epsilon-proteobacteria in the Proteobacteria phylum. Although N4-like viral endogenization appears to be prevalent in Proteobacteria, it has also been observed in Firmicutes. Additionally, the phylogenetic analysis has identified evolutionary divergence within the hallmark genes of N4-like viruses, indicating a complex origin of the different conserved parts of viral genomes. Moreover, 1,101 putative auxiliary metabolic genes (AMGs) were identified in the N4-like viral pan-proteome, which mainly participate in nucleotide and cofactor/vitamin metabolisms. Of these AMGs, 27 were found to be associated with virulence, suggesting their potential involvement in the spread of bacterial pathogenicity. The findings of this study are significant, as N4-like viruses represent a unique viral lineage with a distinct replication mechanism and a conserved core genome. This work has resulted in a comprehensive global map of the entire N4-like viral lineage, including information on their distribution in different biomes, evolutionary divergence, genomic diversity, and the potential for viral-mediated host metabolic reprogramming. As such, this work significantly contributes to our understanding of the ecological function and viral-host interactions of bacteriophages.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗

DOE OSTI2020

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↗

DOE OSTI2023

Parallel Algebraic Multigrid for Fusion and Higher-Order PDEs

Multigrid methods play a key role in large-scale scientific simulation because they are among the fastest and most scalable approaches for solving the underlying sparse linear systems of equations that arise from a wide array of Partial Differential Equation (PDE) discretizations. Algebraic multigrid (AMG) is a special type of multigrid method that depends only on the description of the linear system, giving it better portability and broader applicability than geometric multigrid, as it requires no explicit knowledge of the problem geometry. Even though these methods are widely used today, there are still applications where further development is needed. In this report, we focus on PDEs with higher-order terms (e.g., fourth order), concentrating on a PDE that arises in tokamak edge plasma simulations (a tokamak is a machine that confines a plasma using magnetic fields and is believed to be the leading plasma confinement concept for future fusion power plants). General multigrid relaxes a linear system on coarser grids and reverses this process with interpolation, but standard AMG methods struggle with the aforementioned higher-order PDEs. We investigate cyclic coarsening and interpolation heuristics, as well as new iterative approximation methods of refining the solution at each grid to improve the existing multigrid approach. To this end, we ensure that these techniques are transferable to a parallelized setting with LLNL’s supercomputers.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Algebraic multigrid

The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

Ruge, J. W.↗

DOE OSTI2022

Novel Solver Algorithms for Nearly Singular Linear Systems Arising in Combustion Modelling

Direct Numerical Simulations of realistic combustion devices are extremely challenging due to the wide separation of scales in the simulation, for example an internal combustion (IC) engine chamber, and the flame thickness of a high-pressure flame. The PeleLMeX solver uses adaptive mesh refinement (AMR) to evolve multi-species reacting flows in the low Mach number limit at the Exascale and relies on an embedded boundary (EB) approach to represent complex geometries. In that framework, the EB geometries often give rise to very small cut-cells along the boundary, which translate into extreme ill-conditioning of the pressure-projection, with eigenvalues that span 15-16 orders of magnitude. In this talk, we focus on the case of a typical IC piston bowl geometry for which we present on a novel approach towards solving these nearly singular linear systems with ILU-based, C-AMG smoothers on massively parallel architectures. In particular, we use scaling and equilibration algorithms to handle the non-normality of the upper triangular factors. This enables us to approximate the highly sequential triangular solve algorithm, embedded in the AMG smoothing-solve phase, with Jacobi iterations. This approximation can be written as a convergent Neumann series whose terms are composed of highly parallel sparse matrix vector multiplications. The result is an algorithm that substantially decreases setup and solve time, compared to state-of-the-art, for these challenging linear systems.

combustion modelling↗

DOE OSTI2023

Parallel Element-based Algebraic Multigrid for H (c url ) and H (div) Problems Using the ParELAG Library

This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H (c url ) and H (div) formulations. ParELAG constructs hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

On ParELAG's Parallel Element-based Algebraic Multigrid and its MFEM Miniapps for H(curl) and H(div) Problems: a report including lowest and next to the lowest order numerical results

This paper presents the utilization of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and solvers for H(curl) and H(div) formulations. This involves the construction of hierarchies of compatible nested spaces, forming an exact de Rham sequence on each level. This allows the application of hybrid smoothers on all levels and AMS (Auxiliary-space Maxwell Solver) or ADS (Auxiliary-space Divergence Solver) on the coarsest levels, obtaining complete multigrid cycles. Numerical results are presented, showing the parallel performance of the proposed methods. As a part of the exposition, this paper demonstrates some of the capabilities of ParELAG and outlines some of the components and procedures within the library.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Two-Stage Gauss-Seidel Preconditioners and Smoothers for Krylov Solvers on a GPU Cluster: Preprint

Gauss-Seidel (GS) relaxation is often employed as a preconditioner for a Krylov solver or as a smoother for Algebraic Multigrid (AMG). However, the requisite sparse triangular solve is difficult to parallelize on many-core architectures such as graphics processing units (GPUs). In the present study, the performance of the sequential GS relaxation based on a triangular solve is compared with two-stage variants, replacing the direct triangular solve with a fixed number of inner Jacobi-Richardson (JR) iterations. When a small number of inner iterations is sufficient to maintain the Krylov convergence rate, the two-stage GS (GS2) often outperforms the sequential algorithm on many-core architectures. The GS2 algorithm is also compared with JR. When they perform the same number of ops for SpMV (e.g. three JR sweeps compared to two GS sweeps with one inner JR sweep), the GS2 iterations, and the Krylov solver preconditioned with GS2, may converge faster than the JR iterations. Moreover, for some problems (e.g. elasticity), it was found that JR may diverge with a damping factor of one, whereas two-stage GS may improve the convergence with more inner iterations. Finally, to study the performance of the two-stage smoother and preconditioner for a practical problem, these were applied to incompressible uid ow simulations on GPUs.

algebraic multigrid↗

DOE OSTI2024

ytopt: Autotuning Scientific Applications for Energy Efficiency at Large Scales

As we enter the exascale computing era, efficiently utilizing power and optimizing the performance of scientific applications under power and energy constraints has become critical and challenging. We propose a low-overhead autotuning framework to autotune performance and energy for various hybrid MPI/OpenMP scientific applications at large scales and to explore the tradeoffs between application runtime and power/energy for energy efficient application execution, then use this framework to autotune four ECP proxy applications—XSBench, AMG, SWFFT, and SW4lite. Our approach uses Bayesian optimization with a Random Forest surrogate model to effectively search parameter spaces with up to 6 million different configurations on two large-scale HPC production systems, Theta at Argonne National Laboratory and Summit at Oak Ridge National Laboratory. The experimental results show that our autotuning framework at large scales has low overhead and achieves good scalability. Using the proposed autotuning framework to identify the best configurations, we achieve up to 91.59% performance improvement, up to 21.2% energy savings, and up to 37.84% EDP (energy delay product) improvement on up to 4096 nodes.

Autotuning↗

DOE OSTI2022

Smoothed aggregation for difficult stretched mesh and coefficient variation problems

Abstract Four adaptations of the smoothed aggregation algebraic multigrid (SA‐AMG) method are proposed with an eye toward improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak connections. These weak connections can cause higher than expected levels of fill‐in within the coarse discretization matrices and can also give rise to suboptimal smoothing within the prolongator smoothing phase. These smoothing drawbacks are due to the relatively small size of some diagonal entries within the filtered matrix that one obtains after dropping the weak connections. The new algorithms consider modifications to the Jacobi‐like step that defines the prolongator smoother, modifications to the filtered matrix, and also direct modifications to the resulting grid transfer operators. Numerical results are given illustrating the potential benefits of the proposed adaptations.

Hu, Jonathan J.↗