AMG Preconditioner for Multiphase Flow in Engineered Simulation Domains.
Abstract not provided.
Park, HeeHo Daniel↗
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Space-time block preconditioning for incompressible flow, and nonsymmetric AMG
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Southworth, Benjamin Scott↗
Performance of AMG-based preconditioners for fully-coupled Newton-Krylov methods for implicit continuum plasma simulations.
Abstract not provided.
Lin, Paul↗
A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows
This paper presents a comparison of parallel strong scaling performance of classical and aggregation algebraic multigrid (AMG) preconditioners in the context of wind turbine simulations. Fluid motion is governed by the incompressible Navier--Stokes equations, discretized in space with control-volume finite elements and in time with an inexact projection scheme using an implicit integrator. A discontinuous-Galerkin sliding-mesh algorithm captures rotor motion. The momentum equations are solved with iterative Krylov methods, preconditioned by symmetric Gauss--Seidel (SGS) in Trilinos and $\ell_1$ SGS in hypre. The mass-continuity equation is solved with GMRES preconditioned by AMG and can account for the majority of simulation time. Reducing this continuity solve time is crucial. Wind turbine simulations present two unique challenges for AMG preconditioned solvers: the computational meshes include strongly anisotropic elements, and mesh motion requires matrix reinitialization and computation of preconditioners at each time step. Detailed timing profiles are presented and analyzed, and best practices are discussed for both classical and aggregation-based AMG. Results are presented for simulations of two different wind turbines with up to 6 billion grid points on two different computer architectures. For moving mesh problems that require linear-system reinitialization, the well-established strategy of amortizing preconditioner setup costs over a large number of time steps to reduce the solve time is no longer valid. Instead, results show that faster time to solution is achieved by reducing preconditioner setup costs at the expense of linear-system solve costs. Standard smoothed aggregation with Chebyshev relaxation was found to perform poorly when compared with classical AMG in terms of solve time and robustness. However, plain aggregation was comparable to classical AMG.
97 MATHEMATICS AND COMPUTING↗
Parallel performance of algebraic multigrid domain decomposition
Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication has become a significant bottleneck that limits its scalability as processor counts continue to grow on modern machines. This article examines the design, implementation, and parallel performance of a novel algorithm, algebraic multigrid domain decomposition (AMG-DD), designed specifically to limit communication. The goal of AMG-DD is to provide a low-communication alternative to standard AMG V-cycles by trading some additional computational overhead for a significant reduction in communication cost. Numerical results show that AMG-DD achieves superior accuracy per communication cost compared with AMG, and speedup over AMG is demonstrated on a large GPU cluster.
97 MATHEMATICS AND COMPUTING↗
Reducing communication in algebraic multigrid with multi-step node aware communication
Algebraic multigrid (AMG) is often viewed as a scalable [Formula: see text] solver for sparse linear systems. Yet, AMG lacks parallel scalability due to increasingly large costs associated with communication, both in the initial construction of a multigrid hierarchy and in the iterative solve phase. This work introduces a parallel implementation of AMG that reduces the cost of communication, yielding improved parallel scalability. It is common in Message Passing Interface (MPI), particularly in the MPI-everywhere approach, to arrange inter-process communication, so that communication is transported regardless of the location of the send and receive processes. Performance tests show notable differences in the cost of intra- and internode communication, motivating a restructuring of communication. In this case, the communication schedule takes advantage of the less costly intra-node communication, reducing both the number and the size of internode messages. Node-centric communication extends to the range of components in both the setup and solve phase of AMG, yielding an increase in the weak and strong scaling of the entire method.
Computer Science↗
Potential virus-mediated nitrogen cycling in oxygen-depleted oceanic waters
Viruses play an important role in the ecology and biogeochemistry of marine ecosystems. Beyond mortality and gene transfer, viruses can reprogram microbial metabolism during infection by expressing auxiliary metabolic genes (AMGs) involved in photosynthesis, central carbon metabolism, and nutrient cycling. While previous studies have focused on AMG diversity in the sunlit and dark ocean, less is known about the role of viruses in shaping metabolic networks along redox gradients associated with marine oxygen minimum zones (OMZs). Here, we analyzed relatively quantitative viral metagenomic datasets that profiled the oxygen gradient across Eastern Tropical South Pacific (ETSP) OMZ waters, assessing whether OMZ viruses might impact nitrogen (N) cycling via AMGs. Identified viral genomes encoded six N-cycle AMGs associated with denitrification, nitrification, assimilatory nitrate reduction, and nitrite transport. The majority of these AMGs (80%) were identified in T4-like Myoviridae phages, predicted to infect Cyanobacteria and Proteobacteria, or in unclassified archaeal viruses predicted to infect Thaumarchaeota. Four AMGs were exclusive to anoxic waters and had distributions that paralleled homologous microbial genes. Together, these findings suggest viruses modulate N-cycling processes within the ETSP OMZ and may contribute to nitrogen loss throughout the global oceans thus providing a baseline for their inclusion in the ecosystem and geochemical models.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Viral potential to modulate microbial methane metabolism varies by habitat
Methane is a potent greenhouse gas contributing to global warming. Microorganisms largely drive the biogeochemical cycling of methane, yet little is known about viral contributions to methane metabolism (MM). We analyzed 982 publicly available metagenomes from host-associated and environmental habitats containing microbial MM genes, expanding the known MM auxiliary metabolic genes (AMGs) from three to 24, including seven genes exclusive to MM pathways. These AMGs are recovered on 911 viral contigs predicted to infect 14 prokaryotic phyla including Halobacteriota, Methanobacteriota, and Thermoproteota. Of those 24, most were encoded by viruses from rumen (16/24), with substantially fewer by viruses from environmental habitats (0–7/24). To search for additional MM AMGs from an environmental habitat, we generate metagenomes from methane-rich sediments in Vrana Lake, Croatia. Therein, we find diverse viral communities, with most viruses predicted to infect methanogens and methanotrophs and some encoding 13 AMGs that can modulate host metabolisms. However, none of these AMGs directly participate in MM pathways. Together these findings suggest that the extent to which viruses use AMGs to modulate host metabolic processes (e.g., MM) varies depending on the ecological properties of the habitat in which they dwell and is not always predictable by habitat biogeochemical properties.
59 BASIC BIOLOGICAL SCIENCES↗
Synergy and antagonism in a genome-scale model of metabolic hijacking by bacteriophages
Bacteriophage auxiliary metabolic genes (AMGs) alter host metabolism by hijacking reactions, but previous studies mostly inferred their roles from annotations, ignoring system-wide impacts and phage production. Here we integrate AMGs and phage assembly into a genome-scale metabolic model of Prochloroccocus marinus MED4 infected by P-HM2. We show that 17 directly hijacked reactions substantially affect more than 30% of the reactions in MED4 metabolism, including carbon fixation, photosynthesis, and nucleotide synthesis, distinguishing these AMGs as either phage aligned—shifting feasible reaction velocities in accordance with maximal phage production—or phage antialigned. Pareto optimization reveals that phage-aligned reactions alter phage-host growth trade-offs, while phage-antialigned reactions do not. We experimentally validate our predictions of system-level AMG impacts by measuring the N-dependent effect of P-HM2 cp12 expression on growth in a model relative of the genetically intractable MED4, Synechococcus elongatus. We also show that AMGs’ indirect impacts are synergistically and antagonistically coupled, providing systems-level insight into AMG perturbations and highlighting how nontrivial cascading effects shape host metabolism.
Rozum, Jordan C. [Pacific Northwest National Labor↗
Diffusion Synthetic Acceleration for Heterogeneous Domains, Compatible with Voids
A standard approach to solving the S N transport equations is to use source iteration with diffusion synthetic acceleration (DSA). Although this approach is widely used and effective on many problems, there remain some practical issues with DSA preconditioning, particularly on highly heterogeneous domains. For large-scale parallel simulation, it is critical that both (a) preconditioned source iteration converges rapidly and (b) the action of the DSA preconditioner can be applied using fast, scalable solvers, such as algebraic multigrid (AMG). For heterogeneous domains, these two interests can be at odds. In particular, there exist DSA diffusion discretizations that can be solved rapidly using AMG, but they do not always yield robust/fast convergence of the larger source iteration. Conversely, there exist robust DSA discretizations where source iteration converges rapidly on difficult heterogeneous problems, but fast parallel solvers like AMG tend to struggle applying the action of such operators. Moreover, very few current methods for the solution of deterministic transport are compatible with voids. This paper develops a new heterogeneous DSA preconditioner based on only preconditioning the optically thick subdomains. The resulting method proves robust on a variety of heterogeneous transport problems, including a linearized hohlraum mesh related to inertial confinement fusion. Moreover, the action of the preconditioner is easily computed using O(1) AMG iterations, convergence of the transport iteration typically requires 2 to 5× fewer iterations than current state-of-the-art “full” DSA, and the proposed method is trivially compatible with voids. On the hohlraum problem, rapid convergence is obtained by preconditioning less than 3% of the mesh elements with five to ten AMG iterations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Non-Galerkin Coarse Grids for Algebraic Multigrid
Algebraic multigrid (AMG) is a popular and effective solver for systems of linear equations that arise from discretized partial differential equations. And while AMG has been effectively implemented on large scale parallel machines, challenges remain, especially when moving to exascale. Particularly, stencil sizes (the number of nonzeros in a row) tend to increase further down in the coarse grid hierarchy, and this growth leads to more communication. Therefore, as problem size increases and the number of levels in the hierarchy grows, the overall efficiency of the parallel AMG method decreases, sometimes dramatically. This growth in stencil size is due to the standard Galerkin coarse grid operator, $P^T A P$, where $P$ is the prolongation (i.e., interpolation) operator. For example, the coarse grid stencil size for a simple three-dimensional (3D) seven-point finite differencing approximation to diffusion can increase into the thousands on present day machines, causing an associated increase in communication costs. We therefore consider algebraically truncating coarse grid stencils to obtain a non-Galerkin coarse grid. First, the sparsity pattern of the non-Galerkin coarse grid is determined by employing a heuristic minimal “safe” pattern together with strength-of-connection ideas. Second, the nonzero entries are determined by collapsing the stencils in the Galerkin operator using traditional AMG techniques. The result is a reduction in coarse grid stencil size, overall operator complexity, and parallel AMG solve phase times.
97 MATHEMATICS AND COMPUTING↗
Isolation and characterization of 24 phages infecting the plant growth-promoting rhizobacterium Klebsiella sp. M5al
Bacteriophages largely impact bacterial communities via lysis, gene transfer, and metabolic reprogramming and thus are increasingly thought to alter nutrient and energy cycling across many of Earth’s ecosystems. However, there are few model systems to mechanistically and quantitatively study phage-bacteria interactions, especially in soil systems. Here, we isolated, sequenced, and genomically characterized 24 novel phages infectingKlebsiellasp. M5al, a plant growth-promoting, nonencapsulated rhizosphere-associated bacterium, and compared many of their features against all 565 sequenced, dsDNAKlebsiellaphage genomes. Taxonomic analyses revealed that theseKlebsiellaphages belong to three known phage families (Autographiviridae,Drexlerviridae, andStraboviridae) and two newly proposed phage families (CandidatusMavericviridaeand Ca.Rivulusviridae). At the phage family level, we found that core genes were often phage-centric proteins, such as structural proteins for the phage head and tail and DNA packaging proteins. In contrast, genes involved in transcription, translation, or hypothetical proteins were commonly not shared or flexible genes. Ecologically, we assessed the phages’ ubiquity in recent large-scale metagenomic datasets, which revealed they were not widespread, as well as a possible direct role in reprogramming specific metabolisms during infection by screening their genomes for phage-encoded auxiliary metabolic genes (AMGs). Even though AMGs are common in the environmental literature, only one of our phage families,Straboviridae, contained AMGs, and the types of AMGs were correlated at the genus level. Host range phenotyping revealed the phages had a wide range of infectivity, infecting between 1–14 of our 22 bacterial strain panel that included pathogenicKlebsiellaandRaoultellastrains. This indicates that not all capsule-independent Klebsiella phages have broad host ranges. Together, these isolates, with corresponding genome, AMG, and host range analyses, help build theKlebsiellamodel system for studying phage-host interactions of rhizosphere-associated bacteria.
Science & Technology - Other Topics↗
Decrease time-to-solution through improved linear-system setup and solve
The goal of the ExaWind project is to enable predictive simulations of wind farms composed of many MW-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 code in the ExaWind project is Nalu, which is an unstructured-grid solver for the acoustically-incompressible Navier-Stokes equations, and mass continuity is maintained through pressure projection. The 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 re-initialization of matrices and re-computation of preconditioners is required at every time step We describe in this report our efforts to decrease the setup and solution time for the mass-continuity Poisson system with respect to the benchmark timing results reported in FY18 Q1. In particular, we investigate improving and evaluating two types of algebraic multigrid (AMG) preconditioners: Classical Ruge-Stfiben AMG (C-AMG) and smoothed-aggregation AMG (SA-AMG), which are implemented in the Hypre and Trilinos/MueLu software stacks, respectively. Preconditioner performance was optimized through existing capabilities and settings.
17 WIND ENERGY↗
Decrease time-to-solution through improved linear-system setup and solve (Milestone Report)
The goal of the ExaWind project is to enable predictive simulations of wind farms composed of many MW-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. We describe in this report our efforts to decrease the setup and solution time for the mass-continuity Poisson system with respect to the benchmark timing results reported in FY18 Q1. In particular, we investigate improving and evaluating two types of algebraic multigrid (AMG) preconditioners: Classical Ruge-Stfiben AMG (C-AMG) and smoothed-aggregation AMG (SA-AMG), which are implemented in the Hypre and Trilinos/MueLu software stacks, respectively.
17 WIND ENERGY↗
On the scalability of the Albany/FELIX first-order Stokes approximation ice sheet solver for large-scale simulations of the Greenland and Antarctic ice sheets
We examine the scalability of the recently developed Albany/FELIX finite-element based code for the first-order Stokes momentum balance equations for ice flow. We focus our analysis on the performance of two possible preconditioners for the iterative solution of the sparse linear systems that arise from the discretization of the governing equations: (1) a preconditioner based on the incomplete LU (ILU) factorization, and (2) a recently-developed algebraic multigrid (AMG) preconditioner, constructed using the idea of semi-coarsening. A strong scalability study on a realistic, high resolution Greenland ice sheet problem reveals that, for a given number of processor cores, the AMG preconditioner results in faster linear solve times but the ILU preconditioner exhibits better scalability. A weak scalability study is performed on a realistic, moderate resolution Antarctic ice sheet problem, a substantial fraction of which contains floating ice shelves, making it fundamentally different from the Greenland ice sheet problem. Here, we show that as the problem size increases, the performance of the ILU preconditioner deteriorates whereas the AMG preconditioner maintains scalability. This is because the linear systems are extremely ill-conditioned in the presence of floating ice shelves, and the ill-conditioning has a greater negative effect on the ILU preconditioner than on the AMG preconditioner.
54 ENVIRONMENTAL SCIENCES↗
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.↗
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↗
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↗