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All sources NASA NTRS DOE OSTI

DOE OSTI2018

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↗

DOE OSTI2018

Decrease time-to-solution through improved linear-system setup and solve (Milestone Report)

17 WIND ENERGY↗

DOE OSTI2015

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↗

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↗

NASA NTRS1989

Algebraic multigrid methods applied to problems in computational structural mechanics

The development of algebraic multigrid (AMG) methods and their application to certain problems in structural mechanics are described with emphasis on two- and three-dimensional linear elasticity equations and the 'jacket problems' (three-dimensional beam structures). Various possible extensions of AMG are also described. The basic idea of AMG is to develop the discretization sequence based on the target matrix and not the differential equation. Therefore, the matrix is analyzed for certain dependencies that permit the proper construction of coarser matrices and attendant transfer operators. In this manner, AMG appears to be adaptable to structural analysis applications.

Mccormick, Steve↗

NASA NTRS1993

Layout optimization with algebraic multigrid methods

Finding the optimal position for the individual cells (also called functional modules) on the chip surface is an important and difficult step in the design of integrated circuits. This paper deals with the problem of relative placement, that is the minimization of a quadratic functional with a large, sparse, positive definite system matrix. The basic optimization problem must be augmented by constraints to inhibit solutions where cells overlap. Besides classical iterative methods, based on conjugate gradients (CG), we show that algebraic multigrid methods (AMG) provide an interesting alternative. For moderately sized examples with about 10000 cells, AMG is already competitive with CG and is expected to be superior for larger problems. Besides the classical 'multiplicative' AMG algorithm where the levels are visited sequentially, we propose an 'additive' variant of AMG where levels may be treated in parallel and that is suitable as a preconditioner in the CG algorithm.

Regler, Hans↗

DOE OSTI2016

On the Degradation of the Effectiveness of Nonlinear Diffusion Acceleration with Parallel Block Jacobi Splitting

MOOSE's radiation transport module Rattlesnake comprises a first order S N solver that can be accelerated with a flexible Nonlinear Diffusion Acceleration. At each NDA iteration, the streaming and collision operator of the S{sub N} equations are (approximately) inverted using a transport sweep. When executed on multiple processors parallel block Jacobi (PBJ) splitting is utilized lagging the processor sub-domain's incoming angular fluxes making the implemented method asynchronous, i.e. the convergence properties of NDA become dependent on the number of concurrent tasks and details of the partitioning. Within this work, we study the NDA convergence properties for the two-dimensional C5G7 benchmark problem PBJ with p = 1, 2, 4, 8, 12, 16, 24, 32, 48, 60, 72, 96 and 144 concurrent tasks. Rosa studied the convergence properties of PBJ splitting methods with and without transport synthetic acceleration (TSA) in slab geometry and two-dimensional Cartesian geometry, respectively. Rosa's iteration scheme lags both the incoming angular fluxes and the scattering source making it very similar to the method described here. Rosa found by means of Fourier analysis that convergence of unaccelerated PBJ can degrade for optically thin subdomains, i.e. for a large number of processors given a fixed domain size. Depending on the choice of parameters application of TSA can lead to an effective algorithm. In contrast to Rosa's work, this work focuses on PBJ splitting for NDA accelerated solution of the multigroup eigenvalue problem. Later, Zerr and Anistratov used their integral transport matrix method in conjunction with PBJ. This iteration scheme is different as it does not lag the scattering source. Nevertheless, Fourier analysis with Diamond Difference spatial discretization showed that the method degrades with increasing the overall size of the spatial domain while keeping the sub-domain size constant. In the case of an infinite medium, the observed spectral radius becomes unity. These references establish the iterative performance of PBJ for one-group fixed source problems discretized on rectangular cells, but for the Rattlesnake first order NDA method, an emphasis lies on multigroup eigenvalue problems. In this setting, the additional complication arises that the low order equations are not exactly inverted, but only to some iterative criterion. Further, as the low order problem is solved using Jacobian-Free Newton Krylov methods, a suitable preconditioner for the GMRES iterations is required. As the effectiveness of the preconditioners may decrease when more concurrent processes are used, we expect the low order solve to impact the overall effectiveness of the NDA method in parallel execution as well. Therefore, this work focuses on the question of how detrimental the asynchronicity of the high and low order iterative solutions is for the effectiveness of NDA solutions of realistic, unstructured grid, multigroup eigenvalue problems. The iterative convergence properties of Rattlesnake's NDA method for multigroup eigenvalue problems are studied for varying number of concurrent processes. Rattlesnake's NDA method is asynchronous because the high order transport sweep uses PBJ splitting and because the low order solve's preconditioners, algebraic multigrid and additive Schwarz, are asynchronous. We found that up to 144 processes the number of Picard iterations increases by a factor of 2-3 affecting but not destroying NDA's parallel performance for the C5G7 benchmark problem, a representative LWR (light water reactor) configuration. The solution of the NDA low order eigenvalue problem posed greater problems than expected for the solvers currently available in Rattlesnake mainly because of problems to effectively precondition the modified low-order problem. As a matter of fact, the low order problem becomes an advection-diffusion problem. Non-robustness was observed for the AMG preconditioned coarse mesh acceleration for more than 60 concurrent processes, which was fixed by increasing the number of permissible V-cycles per AMG call. For fine mesh acceleration AMG proved to be ineffective and we resorted to ASM. For both AMG and ASM, increasing number of linear iterations per nonlinear are observed when increasing the number of processes, but for ASM this problem appears to be worse. The results from this work also indicate that initial development efforts should be diverted from implementation of a high-order parallel sweeping algorithm to the effective and robust iterative solution of the low order NDA multigroup eigenvalue problem. (authors)

97 MATHEMATICS AND COMPUTING↗

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 OSTI2010

Scaling Algebraic Multigrid Solvers: On the Road to Exascale

Algebraic Multigrid (AMG) solvers are an essential component of many large-scale scientific simulation codes. Their continued numerical scalability and efficient implementation is critical for preparing these codes for exascale. Our experiences on modern multi-core machines show that significant challenges must be addressed for AMG to perform well on such machines. We discuss our experiences and describe the techniques we have used to overcome scalability challenges for AMG on hybrid architectures in preparation for exascale.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

High resolution viscous fingering simulation in miscible displacement using a p-adaptive discontinuous Galerkin method with algebraic multigrid preconditioner

High resolution simulation of viscous fingering can offer an accurate and detailed prediction for subsurface engineering processes involving fingering phenomena. The fully implicit discontinuous Galerkin (DG) method has been shown to be an accurate and stable method to model viscous fingering with high Peclet number and mobility ratio. In this study, we present two techniques to speedup large scale simulations of this kind. The first technique relies on a simple p-adaptive scheme in which high order basis functions are employed only in elements near the finger fronts where the concentration has a sharp change. As a result, the number of degrees of freedom is significantly reduced and the simulation yields almost identical results to the more expensive simulation with uniform high order elements throughout the mesh. The second technique for speedup involves improving the solver efficiency. We present an algebraic multigrid (AMG) preconditioner which allows the DG matrix to leverage the robust AMG preconditioner designed for the continuous Galerkin (CG) finite element method. The resulting preconditioner works effectively for fixed order DG as well as p-adaptive DG problems. Finally, with the improvements provided by the p-adaptivity and AMG preconditioning, we can perform high resolution three-dimensional viscous fingering simulations required for miscible displacement with high Peclet number and mobility ratio in greater detail than before for well injection problems.

97 MATHEMATICS AND COMPUTING↗

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↗