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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Incomplete Sparse Approximate Inverses for Parallel Preconditioning

In this study, we propose a new preconditioning method that can be seen as a generalization of block-Jacobi methods, or as a simplification of the sparse approximate inverse (SAI) preconditioners. The “Incomplete Sparse Approximate Inverses” (ISAI) is in particular efficient in the solution of sparse triangular linear systems of equations. Those arise, for example, in the context of incomplete factorization preconditioning. ISAI preconditioners can be generated via an algorithm providing fine-grained parallelism, which makes them attractive for hardware with a high concurrency level. Finally, in a study covering a large number of matrices, we identify the ISAI preconditioner as an attractive alternative to exact triangular solves in the context of incomplete factorization preconditioning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Multifrontal Non-negative Matrix Factorization

Non-negative matrix factorization (Nmf) is an important tool in high-performance large scale data analytics with applications ranging from community detection, recommender system, feature detection and linear and non-linear unmixing. While traditional Nmf works well when the data set is relatively dense, however, it may not extract sufficient structure when the data is extremely sparse. Specifically, traditional Nmf fails to exploit the structured sparsity of the large and sparse data sets resulting in dense factors. We propose a new algorithm for performing Nmf on sparse data that we call multifrontal Nmf (Mf-Nmf) since it borrows several ideas from the multifrontal method for unconstrained factorization (e.g. LU and QR). We also present an efficient shared memory parallel implementation of Mf-Nmf and discuss its performance and scalability. We conduct several experiments on synthetic and realworld datasets and demonstrate the usefulness of the algorithm by comparing it against standard baselines. We obtain a speedup of 1.2x to 19.5x on 24 cores with an average speed up of 10.3x across all the real world datasets.

Sao, Piyush↗
DOE OSTI2017

Low-Rank Correction Methods for Algebraic Domain Decomposition Preconditioners

This study presents a parallel preconditioning method for distributed sparse linear systems, based on an approximate inverse of the original matrix, that adopts a general framework of distributed sparse matrices and exploits domain decomposition (DD) and low-rank corrections. The DD approach decouples the matrix and, once inverted, a low-rank approximation is applied by exploiting the Sherman--Morrison--Woodbury formula, which yields two variants of the preconditioning methods. The low-rank expansion is computed by the Lanczos procedure with reorthogonalizations. Numerical experiments indicate that, when combined with Krylov subspace accelerators, this preconditioner can be efficient and robust for solving symmetric sparse linear systems. Comparisons with pARMS, a DD-based parallel incomplete LU (ILU) preconditioning method, are presented for solving Poisson's equation and linear elasticity problems.

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 OSTI2016

Implementation and Tuning of Batched Cholesky Factorization and Solve for NVIDIA GPUs

Many problems in engineering and scientific computing require the solution of a large number of small systems of linear equations. Due to their high processing power, Graphics Processing Units became an attractive target for this class of problems, and routines based on the LU and the QR factorization have been provided by NVIDIA in the cuBLAS library. This work addresses the situation where the systems of equations are symmetric positive definite. The paper describes the implementation and tuning of the kernels for the Cholesky factorization and the forward and backward substitution. Targeted workloads involve the solution of thousands of linear systems of the same size, where the focus is on matrix dimensions from 5 by 5 to 100 by 100. Due to the lack of a cuBLAS Cholesky factorization, execution rates of cuBLAS LU and cuBLAS QR are used for comparison against the proposed Cholesky factorization in this work. Execution rates of forward and backward substitution routines are compared to equivalent cuBLAS routines. Comparisons against optimized multicore implementations are also presented. Superior performance is reached in all cases.

Computer Science↗
DOE OSTI2017

PSelInv—A Distributed Memory Parallel Algorithm for Selected Inversion: The Symmetric Case

We describe an efficient parallel implementation of the selected inversion algorithm for distributed memory computer systems, which we call PSelInv. The PSelInv method computes selected elements of a general sparse matrix Athat can be decomposed as A= LU, where L is lower triangular and U is upper triangular. The implementation described in this article focuses on the case of sparse symmetric matrices. It contains an interface that is compatible with the distributed memory parallel sparse direct factorization SuperLU-DIST. Yet, the underlying data structure and design of PSelInv allows it to be easily combined with other factorization routines, such as PARDISO. We discuss general parallelization strategies such as data and task distribution schemes. Specifically, we describe how to exploit the concurrency exposed by the elimination tree associated with the LU factorization of A. We demonstrate the efficiency and accuracy of PSelInv by presenting several numerical experiments. In particular, we show that PSelInv can run efficiently on more than 4,000 cores for a modestly sized matrix. We also show how PSelInv can be used to accelerate large-scale electronic structure calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

High-throughput characterization of Lu-doped zirconia

Lu-doped zirconia (LuDZ) was reported in the 1960s to be a poor oxygen ion conductor. However, we identified this system as worthy of reexamination based on the results of a machine learning-based screen for promising oxygen ion conductors, further supported by a physical argument: because Lu is the heaviest and smallest of the lanthanides, it should offer the possibility of high conductivity due to its high polarizability and size compatibility with the zirconia structure. Here the relationship between dopant concentration and conductivity in the LuDZ system was determined using a high throughput experimental methodology in which spatially resolved conductivity was measured across a compositionally graded film, spanning from Zr 0.93 Lu 0.07 O 1.965 to Zr 0.82 Lu 0.18 O 1.91 . The conductivity broadly peaks with composition at 15 cation % Lu, coinciding with the approximate phase boundary of the fully stabilized cubic phase. The composition-dependent conductivity measurements reveal a surprising increase in activation energy for ion transport with increasing Lu content with no change in this trend at the composition of the conductivity maximum. The pre-exponential factor increases sharply with Lu content, but displays a distinct plateau once the conductivity maximum composition is attained. At 500 °C, the conductivity of Zr 0.85 Lu 0.15 O 1.925 is 2 × 10 –3 S cm –1 , approaching that of optimally doped Sc-stabilized zirconia, which has the highest reported conductivity among zirconia compounds. In comparison to other oxide ion conductors, Lu-stabilized zirconia offers the advantage over ceria of negligible electronic conductivity and is easier to process than (La,Sr)(Ga,Mg)O 3-δ .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A continuous analogue of the tensor-train decomposition

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents functions using a tensor-train ansatz by replacing the three-dimensional TT cores with univariate matrix-valued functions. The main contribution of this paper is a framework to compute the FT that employs adaptive approximations of univariate fibers, and that is not connected to any tensorized discretization. The algorithm can be coupled with any univariate linear or nonlinear approximation procedure. We demonstrate that this approach can generate multivariate function approximations that are several orders of magnitude more accurate, for the same cost, than those based on the conventional approach of compressing the coefficient tensor of a tensor-product basis. Our approach is in the spirit of other continuous computation packages such as Chebfun, and yields an algorithm which requires the computation of “continuous” matrix factorizations such as the LU and QR decompositions of vector-valued functions. To support these developments, we describe continuous versions of an approximate maximum-volume cross approximation algorithm and of a rounding algorithm that re-approximates an FT by one of lower ranks. We demonstrate that our technique improves accuracy and robustness, compared to TT and quantics-TT approaches with fixed parameterizations, of high-dimensional integration, differentiation, and approximation of functions with local features such as discontinuities and other nonlinearities.

42 ENGINEERING↗
DOE OSTI2018

Lifetime-ever pneumonia among pre-school children across China – Associations with pre-natal and post-natal early life environmental factors

Highlights: • Childhood pneumonia can be influenced by prenatal and perinatal indoor exposure. • Mould and window condensation at birth is a risk factor for childhood pneumonia. • Prenatal exposure to redecoration and new furniture can increase the risk. • Cockroaches, mosquitos and flies are other risk factors in the home environment. • Farm exposure, breastfeeding and suburban or rural environment can be protective. Biomass burning is associated with childhood pneumonia but few studies exist on other indoor factors.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Achieving high-ZT in Te/Se-based thermoelectric materials via volume-constrained shear-induced plastic deformation

This study investigated the correlation between severe plastic deformation and microstructural evolution, along with the corresponding response in the thermoelectric performance. Specifically, severe plastic deformation introduced into intrinsically brittle thermoelectric materials like Bi 2 Te 3 - x Se x leads to microstructural changes ranging from nano- to micro- scales, including phase transformation, phase segregation, and stacking faults. The resultant residual strain and lattice defects in the Bi 2 Te 3-x Se x materials led to engineering of electronic bands, which increases the effective mass of electrons while controlling their concentration, thereby enhancing the power factor.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Efficiently enhanced photoluminescence in Eu3+-doped Lu2(MoO4)3 by Gd3+ substituting

Highlights: • The Gd{sup 3+} doped samples had been discovered to show much better luminescent properties than Lu{sub 2}(MoO{sub 4}){sub 3}:0.02Eu{sup 3+}. • The influence of Gd{sup 3+} ions on luminescence behavior was discussed. • The DFT calculation indicates that the structure of Gd{sub 2}(MoO{sub 4}){sub 3} is more propitious for luminescence than that of Lu{sub 2}(MoO{sub 4}){sub 3}. - Abstract: A series of Lu{sub 2-x}Gd{sub x}(MoO{sub 4}){sub 3}:0.02Eu{sup 3+} (x = 0–2) red-emitting phosphors have been synthesized by the standard solid-state reaction method. Interestingly, the Gd concentration plays a profound role to influence the luminescence property. A conspicuous monotonic increase could be found in the influence of Gd{sup 3+} concentration to the emission intensity, and finally Gd{sub 2}(MoO{sub 4}){sub 3}:0.02Eu{sup 3+} exhibits the strongest red light emission with the intensifying factor even reaching 3.04-fold compared to Lu{sub 2}(MoO{sub 4}){sub 3}:0.02Eu{sup 3+}. Careful structural analysis suggested that up to about 80% (x = 1.6) Lu can be substituted by Gd with the same crystal structure of Lu{sub 2}(MoO{sub 4}){sub 3} being retained, while a higher Gd concentration would lead to it crystallizing in the Gd{sub 2}(MoO{sub 4}){sub 3} structure. We believe that the variation of crystal structure is responsible for the photoluminescence enhancing process.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Lu-Hf and Sm-Nd geochronological constraints on the influence of subduction metamorphism in controlling the Hf-Nd terrestrial array: Evidence from the world’s orogenic belts

To create a better understanding of the influence of subduction metamorphism on the Hf-Nd terrestrial array, this study examines all of the available Lu-Hf and Sm-Nd garnet isochron ages from the world’s orogenic eclogites and amphi bolites. The garnet isochron y-intercept values provide a record of each sample’s epsilon Hf ( ε Hf) and Nd ( ε Nd) at the age recorded by the isochron, which in the case of most orogenic eclogites and amphibolites is the time of prograde metamorphism during subduction. It is further possible to assess the extent to which each sample’s Lu-Hf and Sm-Nd isotope systematics have remained undisturbed since the date recorded by the isochron by comparison of the bulk-rock isotope systematics with the isochron initial value. This approach provides a means of understanding the Lu-Hf and Sm-Nd systematics of post-subduction metamorphic oceanic crust. On a global scale, the coupled Lu-Hf and Sm-Nd isotope systematics of this crust closely align with the Hf-Nd terrestrial array and have average 176 Lu/ 177 Hf and 147 Sm/ 144 Nd ratios within error of the chondritic uniform reservoir values. This is an important finding because it suggests that a reservoir of deeply subducted oceanic crust, possibly residing at the core-mantle boundary, is unlikely to be significantly fractionated from the Hf-Nd terrestrial array. In contrast to the samples of subduction-metamorphosed oceanic crust, metamorphic rocks with a continental crustal protolith demonstrate garnet isochron initial values and bulk-rock Lu-Hf and Sm-Nd isotope systematics indicating significant decoupling from the Hf-Nd terrestrial array. However, because this material is not readily subducted, this strongly decoupled signature is unlikely to be transferred into deep Earth. Mixing calculations aimed at developing a clearer understanding of what factors control decoupling of a sample’s Lu-Hf and Sm-Nd systematics from the Hf-Nd terrestrial array highlight the complexity of mass-transfer regimes operating in the subduction environment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Measurements and computational analysis of the natural decay of 176 Lu

Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of 176 Lu forbidden β decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments. Purpose: Perform the first precision measurements of 176 Lu β-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the 176 Lu β-decay Q value. Compare the shape of the precisely determined experimental β spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement. Method: Here, the 176 Lu β-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The β decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The β-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach. Results: Both β transitions of 176 Lu were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of 6.3×10 –6 relative to its β decays. The 176 Lu β-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise β end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary β decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The β-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant gA, which was extracted according to different assumptions. Conclusion: The implemented self-scintillation method has provided unmatched observations of 176 Lu, independently validated by the first direct measurements of its β-decay Q value by Penning trap mass spectrometry. Theoretical study of the main β transition led to the extraction of very different effective gA and log10f values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

Neutral carbon emission in luminous infrared galaxies: the [C i] lines as total molecular gas tracers

We present a statistical study of the [C i] ({sup 3}P{sub 1} → {sup 3}P{sub 0}), [C i] ({sup 3}P{sub 2} → {sup 3}P{sub 1}) lines (hereafter [C i] (1–0) and [C i] (2–1), respectively) and the CO(1–0) line for a sample of (ultra-)luminous infrared galaxies ((U)LIRGs). We explore the correlations between the luminosities of CO(1–0) and [C i] lines, and find that L{sub CO(1−0)}{sup ′} correlates almost linearly with both L{sub [C I](1−0)}{sup ′} and L{sub [C I](2−1)}{sup ′}, suggesting that [C i] lines can trace total molecular gas mass, at least for (U)LIRGs. We also investigate the dependence of L{sub [C I](1−0)}{sup ′}/L{sub CO(1−0)}{sup ′}, L{sub [C I](2−1)}{sup ′}/L{sub CO(1−0)}{sup ′}, and L{sub [C I](2−1)}{sup ′}/L{sub [C I](1−0)}{sup ′} on the far-infrared color of 60-to-100 μm, and find non-correlation, a weak correlation, and a modest correlation, respectively. Under the assumption that these two carbon transitions are optically thin, we further calculate the [C i] line excitation temperatures, atomic carbon masses, and mean [C i] line flux-to-H{sub 2} mass conversion factors for our sample. The resulting H{sub 2} masses using these [C i]-based conversion factors roughly agree with those derived from L{sub CO(1−0)}{sup ′} and CO-to-H{sub 2} conversion factor.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Understanding the Adsorption of Rare-Earth Elements in Oligo-Grafted Mesoporous Carbon

Rare-earth elements (REEs) are 17 elements of the periodic table primarily consisting of lanthanides. In modern society, the usage of REEs is ubiquitous in almost all modern gadgets and therefore efficient recovery and separation of REEs are of high importance. Selective adsorption and chelation of REEs in solid sorbents is a unique and sustainable process for their recovery. In this work, single-stranded oligos with 100 units of thymine were grafted onto carboxylated mesoporous carbon to synthesize a sorbent with phosphorus and oxygen functionalities. Additionally, the sorbent was characterized by X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy, and scanning electron microscopy-energy-dispersive X-ray spectroscopy. Three different REEs with varying atomic radii and densities, Lu, Dy, and La, were adsorbed onto the carbon from aqueous solutions. It was observed that the adsorbed amounts increased with the increase in the atomic radius or decrease in the atomic density. Calculation of the distribution coefficients for all the equilibrium adsorption amounts suggested that adsorption is more effective in the lower concentration region. The L 3 -edge X-ray absorption near-edge structure confirmed a 3+ oxidation state of REEs in the adsorbed phase. Extended X-ray absorption fine structure (EXAFS) confirmed the binding of REEs with oxygen functionalities in the adsorbed phase. The radial distribution functions calculated from the EXAFS data suggest a longer RE–O distance for La compared to those for Lu and Dy. The coordination numbers and Debye–Waller factors have typical values of about 8–9 atoms and 0.01–0.02 Å 2 , respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Nanomolar Copper Enhances Mercury Methylation by Desulfovibrio desulfuricans ND132

Methylmercury (MeHg) is produced by certain anaerobic microorganisms, such as the sulfate-reducing bacterium Desulfovibrio desulfuricans ND132, but environmental factors affecting inorganic mercury [Hg(II)] uptake and methylation remain unclear. We report that the presence of a small amount of copper ions [Cu(II), <100 nM] enhances Hg(II) uptake and methylation by washed cells of ND132, while Hg(II) methylation is inhibited at higher Cu(II) concentrations because of the toxicity of copper to the microorganism. The enhancement or inhibitory effect of Cu(II) is dependent on both time and concentration. The presence of nanomolar concentrations of Cu(II) facilitates rapid uptake of Hg(II) (within minutes) and doubles MeHg production within a 24 h period, but micromolar concentrations of Cu(II) completely inhibit Hg(II) methylation. Metal ions such as zinc [Zn(II)] and nickel [Ni(II)] also inhibit but do not enhance Hg(II) methylation under the same experimental conditions. Furthermore, these observations suggest a synergistic effect of Cu(II) on Hg(II) uptake and methylation, possibly facilitated by copper transporters or metallochaperones in this organism, and highlight the fact that complex environmental factors affect MeHg production in the environment.

59 BASIC BIOLOGICAL SCIENCES↗