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DOE OSTI2020

Algebraic multigrid preconditioning of the Hessian in optimization constrained by a partial differential equation

Summary We construct an algebraic multigrid (AMG) based preconditioner for the reduced Hessian of a linear‐quadratic optimization problem constrained by an elliptic partial differential equation. While the preconditioner generalizes a geometric multigrid preconditioner introduced in earlier works, its construction relies entirely on a standard AMG infrastructure built for solving the forward elliptic equation, thus allowing for it to be implemented using a variety of AMG methods and standard packages. Our analysis establishes a clear connection between the quality of the preconditioner and the AMG method used. The proposed strategy has a broad and robust applicability to problems with unstructured grids, complex geometry, and varying coefficients. The method is implemented using the Hypre package and several numerical examples are presented.

Barker, Andrew T.↗

DOE OSTI2020

Viral elements and their potential influence on microbial processes along the permanently stratified Cariaco Basin redoxcline

Little is known about viruses in oxygen-deficient water columns (ODWCs). In surface ocean waters, viruses are known to act as gene vectors among susceptible hosts. Some of these genes may have metabolic functions and are thus termed auxiliary metabolic genes (AMGs). AMGs introduced to new hosts by viruses can enhance viral replication and/or potentially affect biogeochemical cycles by modulating key microbial pathways. Here we identify 748 viral populations that cluster into 94 genera along a vertical geochemical gradient in the Cariaco Basin, a permanently stratified and euxinic ocean basin. The viral communities in this ODWC appear to be relatively novel as 80 of these viral genera contained no reference viral sequences, likely due to the isolation and unique features of this system. We identify viral elements that encode AMGs implicated in distinctive processes, such as sulfur cycling, acetate fermentation, signal transduction, [Fe–S] formation, and N-glycosylation. These AMG-encoding viruses include two putative Mu-like viruses, and viral-like regions that may constitute degraded prophages that have been modified by transposable elements. Our results provide an insight into the ecological and biogeochemical impact of viruses oxygen-depleted and euxinic habitats.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Ecology of inorganic sulfur auxiliary metabolism in widespread bacteriophages

Microbial sulfur metabolism contributes to biogeochemical cycling on global scales. Sulfur metabolizing microbes are infected by phages that can encode auxiliary metabolic genes (AMGs) to alter sulfur metabolism within host cells but remain poorly characterized. Here we identified 191 phages derived from twelve environments that encoded 227 AMGs for oxidation of sulfur and thiosulfate ( dsrA , dsrC/tusE , soxC , soxD and soxYZ ). Evidence for retention of AMGs during niche-differentiation of diverse phage populations provided evidence that auxiliary metabolism imparts measurable fitness benefits to phages with ramifications for ecosystem biogeochemistry. Gene abundance and expression profiles of AMGs suggested significant contributions by phages to sulfur and thiosulfate oxidation in freshwater lakes and oceans, and a sensitive response to changing sulfur concentrations in hydrothermal environments. Overall, our study provides fundamental insights on the distribution, diversity, and ecology of phage auxiliary metabolism associated with sulfur and reinforces the necessity of incorporating viral contributions into biogeochemical configurations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Structural characterization of a soil viral auxiliary metabolic gene product – a functional chitosanase

Metagenomics is unearthing the previously hidden world of soil viruses. Many soil viral sequences in metagenomes contain putative auxiliary metabolic genes (AMGs) that are not associated with viral replication. Here, we establish that AMGs on soil viruses actually produce functional, active proteins. We focus on AMGs that potentially encode chitosanase enzymes that metabolize chitin – a common carbon polymer. We express and functionally screen several chitosanase genes identified from environmental metagenomes. One expressed protein showing endo-chitosanase activity (V-Csn) is crystalized and structurally characterized at ultra-high resolution, thus representing the structure of a soil viral AMG product. This structure provides details about the active site, and together with structure models determined using AlphaFold, facilitates understanding of substrate specificity and enzyme mechanism. Our findings support the hypothesis that soil viruses contribute auxiliary functions to their hosts.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

A call for caution in the biological interpretation of viral auxiliary metabolic genes

Virus-encoded auxiliary metabolic genes (AMGs) are non-essential genes that increase viral fitness by maintaining or manipulating host metabolism during infection. AMGs are intriguing from an evolutionary perspective, as most viral genomes are highly compact and have limited coding capacity for accessory genes. Advances in viral (meta)genomics have expanded the detection of putative AMGs from viruses in diverse environments. However, this has also led to many instances of misannotation due to the limitations of annotation tools, resulting in misinterpretations about the roles of some viral genes. Here, we highlight studies that support claims about AMGs with more than just function predictions for guidance on best practices. We then propose the adoption of an expanded, inclusive view of all genes auxiliary to core viral functions with the term ‘auxiliary viral genes’ (AVGs), alongside an associated eco-evolutionary framework for considering the types of analyses that can better support claims made about AVGs.

Environmental microbiology↗

DOE OSTI2024

Constrained Local Approximate Ideal Restriction for Advection-Diffusion Problems

Herein this paper focuses on developing a reduction-based algebraic multigrid (AMG) method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure advection to pure diffusion. Initial motivation comes from a new reduction-based AMG approach, $\ell \text{AIR}$ (local approximate ideal restriction), that was developed for solving advection-dominated problems. Though this new solver is very effective in the advection-dominated regime, its performance degrades in cases where diffusion becomes dominant. This is consistent with the fact that in general, reduction-based AMG methods tend to suffer from growth in complexity and/or convergence rates as the problem size is increased, especially for diffusion-dominated problems in two or three dimensions. Motivated by the success of $\ell \text{AIR}$ in the advective regime, our aim in this paper is to generalize the AIR framework with the goal of improving the performance of the solver in diffusion-dominated regimes. To do so, we propose a novel way to combine mode constraints as used commonly in energy-minimization AMG methods with the local approximation of ideal operators used in $\ell \text{AIR}$. The resulting constrained $\ell \text{AIR}$ algorithm is able to achieve fast scalable convergence on advective and diffusive problems. In addition, it is able to achieve standard low complexity hierarchies in the diffusive regime through aggressive coarsening, something that was previously difficult for reduction-based methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Algebraic Multigrid with Optimal Interpolation and Adaptive Smoothers (Final Report)

The project team continued with work on developing new bootstrap AMG techniques for solving symmetric and non-symmetric PDE systems. The focus of this work is to derive more reliable measures of the quality of the coarse space set than the convergence rate of the standard F-relaxation form of CR and a more robust form of interpolation than the so-called ideal form. We have successfully derived a sharp variant of CR that gives the precise convergence rate of the two-grid method using this optimal interpolation and, in addition, we derived a new Generalized Bootstrap AMG setup algorithm that uses as its main tool a multilevel eigensolver for the generalized eigenvalue problem involving the system matrix and the symmetrized smoother. In addition, the approach allows for general block smoothers with overlap. We have applied the method to scalar diffusion problems, linear elasticity, and Maxwell’s and the method shows marked improvements over existing AMG methods for these problems. In addition, the team worked with CASC members on new forms of ideal AMG interpolation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Antarctic lake viromes reveal potential virus associated influences on nutrient cycling in ice-covered lakes

The McMurdo Dry Valleys (MDVs) of Antarctica are a mosaic of extreme habitats which are dominated by microbial life. The MDVs include glacial melt holes, streams, lakes, and soils, which are interconnected through the transfer of energy and flux of inorganic and organic material via wind and hydrology. For the first time, we provide new data on the viral community structure and function in the MDVs through metagenomics of the planktonic and benthic mat communities of Lakes Bonney and Fryxell. Viral taxonomic diversity was compared across lakes and ecological function was investigated by characterizing auxiliary metabolic genes (AMGs) and predicting viral hosts. Our data suggest that viral communities differed between the lakes and among sites: these differences were connected to microbial host communities. AMGs were associated with the potential augmentation of multiple biogeochemical processes in host, most notably with phosphorus acquisition, organic nitrogen acquisition, sulfur oxidation, and photosynthesis. Viral genome abundances containing AMGs differed between the lakes and microbial mats, indicating site specialization. Using procrustes analysis, we also identified significant coupling between viral and bacterial communities (p = 0.001). Finally, host predictions indicate viral host preference among the assembled viromes. Collectively, our data show that: (i) viruses are uniquely distributed through the McMurdo Dry Valley lakes, (ii) their AMGs can contribute to overcoming host nutrient limitation and, (iii) viral and bacterial MDV communities are tightly coupled.

Microbiology↗

DOE OSTI2025

Scalable multilevel Monte Carlo methods exploiting parallel redistribution on coarse levels

Here, we study an element agglomeration coarsening strategy that requires data redistribution at coarse levels when the number of coarse elements becomes smaller than the number of MPI processes used on the finest level. The overall procedure generates coarse elements (general unstructured unions of fine grid elements) within the framework of element-based algebraic multigrid methods (or AMGe) studied previously. The AMGe-generated coarse spaces have the ability to exhibit approximation properties of the same order as the fine-level spaces since by construction they contain the piecewise polynomials of the same order as on the fine level. These approximation properties are key for the successful use of AMGe in multilevel solvers for nonlinear partial differential equations as well as for multilevel Monte Carlo (MLMC) simulations. The ability to coarsen without being constrained by the number of MPI processes, as described in the present paper, allows to improve the scalability of these solvers as well as the overall MLMC method. The paper illustrates this latter fact with detailed scalability study of MLMC simulations applied to model Darcy equations with a stochastic log-normal permeability field.

AMGe↗

DOE OSTI2024

Physical origins of the varying performance and unusual transport behaviors among thermoelectric A Mg 2 Sb 2 materials ( A = Ca, Sr, Sm, Yb, and Mg)

Contrary to the similar thermoelectric performance among both AZn 2 Sb 2 and AMg 2 Bi 2 compounds, their isostructural counterparts, AMg 2 Sb 2 , can exhibit thermoelectric figure of merit values that vary by orders of magnitude with different A elements. Here, we reveal physical origins accounting for the significantly differing performance among AMg 2 Sb 2 -based compounds (A = Ca, Sr, Sm, Yb, and Mg) through comprehensive analyses, where it is shown that the dispar- ities in performance at the macroscale essentially originate from the widely varying activation energies that equal amounts of dopant can induce. Meanwhile, a few unusual transport behaviors regarding electrical conductivity, carrier concentration, or lattice thermal con- ductivity among these compounds have been identified, and we also present their rationales in depth. Furthermore, this mechanism-focused study can not only promote further understanding of the complex transport behaviors in condensed matter but be instrumental in rationally tun- ing the physical properties of materials as well.

36 MATERIALS SCIENCE↗

DOE OSTI2022

A Comparison of Linear Solvers for Resolving Flow in Three-Dimensional Discrete Fracture Networks

We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.

58 GEOSCIENCES↗

DOE OSTI2020

Investigation of the process of mixing reagents in the laser chamber of active medium generators of continuous-wave chemical lasers with promising nozzle arrays

It is shown that the use of a toothed nozzle array in the active medium generator (AMG) of continuous-wave chemical lasers (CWCLs) allows more efficient mixing of reagents to be achieved in the laser chamber than in an AMG with a slit nozzle array. The results of calculations of parameters of the active medium of a DF CWCL operating in the gain regime for the AMG with traditional and promising nozzle array designs are presented. A kinetic model of processes in the DF CWCL active medium is proposed, which allows obtaining a good agreement with the results of measurements of the small-signal gain. (paper)

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

DNA Viral Diversity, Abundance, and Functional Potential Vary across Grassland Soils with a Range of Historical Moisture Regimes

Soil viruses are abundant, but the influence of the environment and climate on soil viruses remains poorly understood. Here, we addressed this gap by comparing the diversity, abundance, lifestyle, and metabolic potential of DNA viruses in three grassland soils with historical differences in average annual precipitation, low in eastern Washington (WA), high in Iowa (IA), and intermediate in Kansas (KS). Bioinformatics analyses were applied to identify a total of 2,631 viral contigs, including 14 complete viral genomes from three deep metagenomes (1 terabase [Tb] each) that were sequenced from bulk soil DNA. An additional three replicate metagenomes (~0.5 Tb each) were obtained from each location for statistical comparisons. Identified viruses were primarily bacteriophages targeting dominant bacterial taxa. Both viral and host diversity were higher in soil with lower precipitation. Viral abundance was also significantly higher in the arid WA location than in IA and KS. More lysogenic markers and fewer clustered regularly interspaced short palindromic repeats (CRISPR) spacer hits were found in WA, reflecting more lysogeny in historically drier soil. More putative auxiliary metabolic genes (AMGs) were also detected in WA than in the historically wetter locations. The AMGs occurring in 18 pathways could potentially contribute to carbon metabolism and energy acquisition in their hosts. Structural equation modeling (SEM) suggested that historical precipitation influenced viral life cycle and selection of AMGs. The observed and predicted relationships between soil viruses and various biotic and abiotic variables have value for predicting viral responses to environmental change.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

A Fast Algebraic Multigrid Solver and Accurate Discretization for Highly Anisotropic Heat Flux I: Open Field Lines

We present a novel solver technique for the anisotropic heat flux equation, aimed at the high level of anisotropy seen in magnetic confinement fusion plasmas. Such problems pose two major challenges: (i) discretization accuracy and (ii) efficient implicit linear solvers. We simultaneously address each of these challenges by constructing a new finite element discretization with excellent accuracy properties, tailored to a novel solver approach based on algebraic multigrid (AMG) methods designed for advective operators. We pose the problem in a mixed formulation, introducing the directional temperature gradient as an auxiliary variable. The temperature and auxiliary fields are discretized in a scalar discontinuous Galerkin space with upwinding principles used for discretizations of advection. We demonstrate the proposed discretization’s superior accuracy over other discretizations of anisotropic heat flux, achieving error 1000x smaller for anisotropy ratio of 10 9 , for closed field lines. The block matrix system is reordered and solved in an approach where the two advection operators are inverted using AMG solvers based on approximate ideal restriction, which is particularly efficient for upwind discontinuous Galerkin discretizations of advection. To ensure that the advection operators are nonsingular, in this paper we restrict ourselves to considering open (acyclic) magnetic field lines for the linear solvers. We demonstrate fast convergence of the proposed iterative solver in highly anisotropic regimes where other diffusion-based AMG methods fail.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

On Compatible Transfer Operators in Nonsymmetric Algebraic Multigrid

The standard goal for an effective algebraic multigrid (AMG) algorithm is to develop relaxation and coarse-grid correction schemes that attenuate complementary error modes. In the nonsymmetric setting, coarse-grid correction Π will almost certainly be nonorthogonal (and divergent) in any known standard product, meaning ∥Π∥ > 1. This introduces a new consideration, that one wants coarse-grid correction to be as close to orthogonal as possible, in an appropriate norm. In addition, due to nonorthogonality, Π may actually amplify certain error modes that are in the range of interpolation. Relaxation must then not only be complementary to interpolation, but also rapidly eliminate any error amplified by the nonorthogonal correction, or the algorithm may diverge. Here this paper develops analytic formulae on how to construct “compatible” transfer operators in nonsymmetric AMG such that ∥Π∥ = 1 in some standard matrix-induced norm. Discussion is provided on different options for the norm in the nonsymmetric setting, the relation between “ideal” transfer operators in different norms, and insight into the convergence of nonsymmetric reduction-based AMG.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Expanding standards in viromics: in silico evaluation of dsDNA viral genome identification, classification, and auxiliary metabolic gene curation

Viruses influence global patterns of microbial diversity and nutrient cycles. Though viral metagenomics (viromics), specifically targeting dsDNA viruses, has been critical for revealing viral roles across diverse ecosystems, its analyses differ in many ways from those used for microbes. To date, viromics benchmarking has covered read pre-processing, assembly, relative abundance, read mapping thresholds and diversity estimation, but other steps would benefit from benchmarking and standardization. Here we use in silico-generated datasets and an extensive literature survey to evaluate and highlight how dataset composition (i.e., viromes vs bulk metagenomes) and assembly fragmentation impact (i) viral contig identification tool, (ii) virus taxonomic classification, and (iii) identification and curation of auxiliary metabolic genes (AMGs). The in silico benchmarking of five commonly used virus identification tools show that gene-content-based tools consistently performed well for long (≥3 kbp) contigs, while k -mer- and blast-based tools were uniquely able to detect viruses from short (≤3 kbp) contigs. Notably, however, the performance increase of k -mer- and blast-based tools for short contigs was obtained at the cost of increased false positives (sometimes up to ~5% for virome and ~75% bulk samples), particularly when eukaryotic or mobile genetic element sequences were included in the test datasets. Furthermore, for viral classification, variously sized genome fragments were assessed using gene-sharing network analytics to quantify drop-offs in taxonomic assignments, which revealed correct assignations ranging from ~95% (whole genomes) down to ~80% (3 kbp sized genome fragments). A similar trend was also observed for other viral classification tools such as VPF-class, ViPTree and VIRIDIC, suggesting that caution is warranted when classifying short genome fragments and not full genomes. Finally, we highlight how fragmented assemblies can lead to erroneous identification of AMGs and outline a best-practices workflow to curate candidate AMGs in viral genomes assembled from metagenomes. Together, these benchmarking experiments and annotation guidelines should aid researchers seeking to best detect, classify, and characterize the myriad viruses ‘hidden’ in diverse sequence datasets.

59 BASIC BIOLOGICAL SCIENCES↗

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↗