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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Sparse Approximate Multifrontal Factorization with Composite Compression Methods

This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear computation and memory complexity when applied to sparse linear systems arising from spatial discretization of high-frequency wave equations. To further reduce the overall number of operations and especially the factorization memory usage to scale to larger problem sizes, in this article we develop a composite multifrontal solver that employs the HODBF format for large-sized fronts, a reduced-memory version of the nonhierarchical block low-rank format for medium-sized fronts, and a lossy compression format for small-sized fronts. This allows us to solve sparse linear systems of dimension up to 2.7 × larger than before and leads to a memory consumption that is reduced by 70% while ensuring the same execution time. The code is made publicly available in GitHub.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Scalable Matrix-Free Adaptive Product-Convolution Approximation for Locally Translation-Invariant Operators

We present an adaptive grid matrix-free operator approximation scheme based on a "product-convolution" interpolation of convolution operators. This scheme is appropriate for operators that are locally translation-invariant, even if these operators are high rank or full rank. Such operators arise in Schur complement methods for solving partial differential equations (PDEs), as Hessians in PDE-constrained optimization and inverse problems, as integral operators, as covariance operators, and as Dirichlet-to-Neumann maps. Constructing the approximation requires computing the impulse responses of the operator to point sources centered on nodes in an adaptively refined grid of sample points. A randomized a posteriori error estimator drives the adaptivity. Once constructed, the approximation can be efficiently applied to vectors using the fast Fourier transform. The approximation can be efficiently converted to hierarchical matrix (H-matrix) format, then inverted or factorized using scalable H-matrix arithmetic. The quality of the approximation degrades gracefully as fewer sample points are used, allowing cheap lower quality approximations to be used as preconditioners. Furthermore, this yields an automated method to construct preconditioners for locally translation-invariant Schur complements. We directly address issues related to boundaries and prove that our scheme eliminates boundary artifacts. We test the scheme on a spatially varying blurring kernel, on the nonlocal component of an interface Schur complement for the Poisson operator, and on the data misfit Hessian for an advection dominated advection-diffusion inverse problem. Numerical results show that the scheme outperforms existing methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Achieving strength-ductility synergy in hierarchical aluminum metal matrix composites via friction extrusion

We report the fabrication of aluminum metal matrix composites (Al-MMCs) with hierarchical architectures via friction extrusion (FE), a scalable, single-step, solid-phase processing technique. Precursor pucks containing 0–15 vol% Al₂O₃ particles were extruded into fully dense AA6061-based composite rods. The FE induced a tree-ring-like architecture of concentric particle-rich and particle-lean bands, yielding refined grains in particle-rich regions and coarser grains elsewhere. At the nanoscale, magnesium in AA6061 selectively reacted with Al₂O₃ particles to form virus-like nodes, improving particle–matrix bonding. This multi-scale design strategy, combining mesoscale architecture, microscale grain refinement, and nanoscale interface engineering overcome the conventional strength–ductility trade-off. Tensile testing showed substantial increases in yield and ultimate tensile strengths while retaining high ductility ( > 20%). Enhanced strain hardening, driven by the accumulation of geometrically necessary dislocations at interfaces, contributed to the performance. The hierarchical microstructure produced by FE demonstrates a promising pathway for scalable fabrication of lightweight MMCs for structural applications requiring a combined high strength and ductility.

Kalsar, Rajib [Pacific Northwest National Laborato↗
DOE OSTI2020

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

58 GEOSCIENCES↗
DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Distributed-memory lattice H-matrix factorization

We parallelize the LU factorization of a hierarchical low-rank matrix (H-matrix) on a distributed-memory computer. This is much more difficult than the H-matrix-vector multiplication due to the dataflow of the factorization, and it is much harder than the parallelization of a dense matrix factorization due to the irregular hierarchical block structure of the matrix. Block low-rank (BLR) format gets rid of the hierarchy and simplifies the parallelization, often increasing concurrency. However, this comes at a price of losing the near-linear complexity of the H-matrix factorization. In this work, we propose to factorize the matrix using a “lattice H-matrix” format that generalizes the BLR format by storing each of the blocks (both diagonals and off-diagonals) in the H-matrix format. These blocks stored in the H-matrix format are referred to as lattices. Thus, this lattice format aims to combine the parallel scalability of BLR factorization with the near-linear complexity of H-matrix factorization. We first compare factorization performances using the H-matrix, BLR, and lattice H-matrix formats under various conditions on a shared-memory computer. Our performance results show that the lattice format has storage and computational complexities similar to those of the H-matrix format, and hence a much lower cost of factorization than BLR. In conclusion, we then compare the BLR and lattice H-matrix factorization on distributed-memory computers. Our performance results demonstrate that compared with BLR, the lattice format with the lower cost of factorization may lead to faster factorization on the distributed-memory computer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations

Here, we propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Data-assimilated time-lapse visco-acoustic full-waveform inversion: Theory and application for injected CO 2 plume monitoring

Continuous seismic monitoring for quantifying CO 2 plume migration and detection of any potential leakages in the subsurface is essential for the security of long-term anthropogenic carbon dioxide geologic storage. Traditional time-lapse full-waveform inversion (TLFWI) methods aim to map the CO 2 distribution by estimating seismic velocity changes, but recent studies find that CO 2 -induced attenuation is an important complement to seismic velocity for tracking the CO 2 plumes and even quantifying the CO 2 saturation. We have developed a novel data-assimilated TLFWI method to construct high-resolution time-lapse velocity and attenuation changes from dense time-lapse monitoring data. This method consists of two theoretical developments: visco-acoustic full-waveform inversion (QFWI) and multiparameter hierarchical matrix-powered extended Kalman filter (mHiEKF). The method is capable of (1) posing temporal constraints to retrieve time-lapse information from dense monitoring data by using mHiEKF, (2) accurately recovering high-spatial-resolution velocity and attenuation perturbations using first-order equation system-based QFWI, and (3) providing the model uncertainty by estimating their model standard deviation. With numerical examples, we first find the effectiveness of the new QFWI on estimating accurate velocity and attenuation models simultaneously. Then, a CO 2 leakage case and a realistic Frio-II CO 2 monitoring case are presented to find the advantages and applicability of our data-assimilated QFWI method for estimating time-lapse changes using dense time-lapse monitoring surveys. Here, by assimilating time-lapse seismic monitoring data over time, our data-assimilated QFWI method can improve the resolution of velocity and attenuation changes and decrease their model uncertainties.

58 GEOSCIENCES↗
DOE OSTI2023

Leveraging peptide–cellulose interactions to tailor the hierarchy and mechanics of peptide–polymer hybrids

Inspired by spider silk's hierarchical diversity, we leveraged peptide motifs with the capability to tune structural arrangement for controlling the mechanical properties of a conventional polymer framework. The addition of nanofiller with hydrogen bonding sites was used as another pathway towards hierarchical tuning via matrix–filler interactions. Specifically, peptide–polyurea hybrids (PPUs) were combined with cellulose nanocrystals (CNCs) to develop mechanically-tunable nanocomposites via tailored matrix–filler interactions (or peptide–cellulose interactions). In this material platform, we explored the effect of these matrix–filler interactions on the secondary structure, hierarchical ordering, and mechanical properties of the peptide hybrid nanocomposites. Interactions between the peptide matrix and CNCs occur in all of the PPU/CNC nanocomposites, preventing α-helical ordering, but promoting inter-molecular hydrogen bonded β-sheet formation. Depending on peptide and CNC content, the Young's modulus varies from 10 to 150 MPa. Unlike conventional cellulose-reinforced polymer nanocomposites, the mechanical properties of these composite materials are dictated by a balance of CNC reinforcement, peptidic ordering, and microphase-separated morphology. This research highlights that leveraging peptide–cellulose interactions is a strategy to create materials with targeted mechanical properties for a specific application using a limited selection of building blocks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2022

Design of synthetic collagens that assemble into supramolecular banded fibers as a functional biomaterial testbed

Collagens are the most abundant proteins of the extracellular matrix, and the hierarchical folding and supramolecular assembly of collagens into banded fibers is essential for mediating cell-matrix interactions and tissue mechanics. Collagen extracted from animal tissues is a valuable commodity, but suffers from safety and purity issues, limiting its biomaterials applications. Synthetic collagen biomaterials could address these issues, but their construction requires molecular-level control of folding and supramolecular assembly into ordered banded fibers, comparable to those of natural collagens. Here, we show an innovative class of banded fiber-forming synthetic collagens that recapitulate the morphology and some biological properties of natural collagens. The synthetic collagens comprise a functional-driver module that is flanked by adhesive modules that effectively promote their supramolecular assembly. Multiscale simulations support a plausible molecular-level mechanism of supramolecular assembly, allowing precise design of banded fiber morphology. We also experimentally demonstrate that synthetic fibers stimulate osteoblast differentiation at levels comparable to natural collagen. This work thus deepens understanding of collagen biology and disease by providing a ready source of safe, functional biomaterials that bridge the current gap between the simplicity of peptide biophysical models and the complexity of in vivo animal systems.

Jinyuan Hu↗
DOE OSTI2020

Hierarchical Membrane Dynamics in Phase-Separated Model Membranes

Lipid membranes, the primary matrix of cell membranes, exhibit a hierarchy of dynamics from molecular motions to collective undulations, which control spatiotemporal membrane phenomena and regulate various cellular functions. Thus, understanding how various dynamic modes influence membrane behavior is crucial to uncovering the design rules of cell membranes and implementing them in future technologies. Previous membrane dynamics studies using neutron spin-echo spectroscopy (NSE) have shed light on the dependence of collective membrane fluctuations on viscoelastic membrane properties, demonstrating that thickness fluctuation modes (100ns) are dictated by membrane viscosity, which directly governs fast (ps) molecular diffusive motions. Here, we focus on phase-separating lipid membranes, composed of DMPC:DSPC mixtures, to understand the effect of domain formation/growth on hierarchical matrix dynamics using selective lipid deuteration and different neutron spectroscopy techniques. NSE measurements on DMPC:DSPC-d83 (70:30 mol%) show that bending rigidity of the DMPC-rich matrix graduallyincreases with decreasing temperature - as the fully-fluid membrane approaches the upper phase transition (i.e. with the formation of transient DSPC clusters) - and increases further in the phase coexistence region with the growth of DSPC domains. Comparatively, NSE measurements on DMPC-d54:DSPC-d83 vesicles show pronounced matrix thickness fluctuations in the fully-fluid phase and drastic suppression of this fluctuation mode in the gel-fluid coexistence phase, even when the DMPC-rich matrix is still in its fluid phase. This suppression in fluctuations suggests an increase in the matrix viscosity with the growth of gel DSPC domains, which is further investigated by selectively measuring lipid diffusion in the DMPC-rich matrix using neutron backscattering spectroscopy. Comparisons of the experimental results with coarse-grained MD simulationsillustrate the underlying coupling mechanisms. Overall, these observations indicate a clear mechanical and viscoelastic coupling betweenlipid domains and their host matrix, suggesting that domain formation influences membrane properties beyond local effects.

Carrillo, Jan Michael↗
DOE OSTI2022

Hierarchical microstructures: a potential route to enhanced stability in structural materials for advanced nuclear reactors

The drive to increase efficiency in nuclear energy systems is leading to the need for materials that operate at higher temperatures and stress levels for extended periods, while maintaining stable microstructures to ensure their performance is not compromised. A novel route to producing materials that can perform well in such environments is the creation of hierarchical microstructures. A hierarchical microstructure is a microstructure in which features are present at multiple length scales simultaneously. In this work, a hierarchical microstructure is fabricated in a nickel-base superalloy, featuring nanometer-size gamma precipitates inside larger gamma-prime particles, which are in turn embedded in the gamma matrix phase. The hierarchical features of the microstructure lead to enhanced stability of the gamma-prime precipitates during annealing; the particle size does not follow the expected t^(1/3) growth law predicted by the classic LSW theory. Phase-field simulations are used to understand the unexpected stability of the gamma-prime precipitates.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Hierarchical microstructures: a potential route to enhanced stability in structural materials for advanced nuclear reactors

The drive to increase efficiency in nuclear energy systems is leading to the need for materials that operate at higher temperatures and stress levels for extended periods, while maintaining stable microstructures to ensure their performance is not compromised. A novel route to producing materials that can perform well in such environments is the creation of hierarchical microstructures. A hierarchical microstructure is a microstructure in which features are present at multiple length scales simultaneously. In this work, a hierarchical microstructure is fabricated in a nickel-base superalloy, featuring nanometer-size gamma precipitates inside larger gamma-prime particles, which are in turn embedded in the gamma matrix phase. The hierarchical features of the microstructure lead to enhanced stability of the gamma-prime precipitates during annealing; the particle size does not follow the expected t^(1/3) growth law predicted by the classic LSW theory. Phase-field simulations are used to understand the unexpected stability of the gamma-prime precipitates.

36 - MATERIALS SCIENCE↗
NASA NTRS1997

Dynamic Reconstruction and Multivariable Control for Force-Actuated, Thin Facesheet Adaptive Optics

The Multiple Mirror Telescope (MMT) under development at the University of Arizona takes a new approach in adaptive optics placing a large (0.65 m) force-actuated, thin facesheet deformable mirror at the secondary of an astronomical telescope, thus reducing the effects of emissivity which are important in IR astronomy. However, The large size of the mirror and low stiffness actuators used drive the natural frequencies of the mirror down into the bandwidth of the atmospheric distortion. Conventional adaptive optics takes a quasi-static approach to controlling the, deformable mirror. However, flexibility within the control bandwidth calls for a new approach to adaptive optics. Dynamic influence functions are used to characterize the influence of each actuator on the surface of the deformable mirror. A linearized model of atmospheric distortion is combined with dynamic influence functions to produce a dynamic reconstructor. This dynamic reconstructor is recognized as an optimal control problem. Solving the optimal control problem for a system with hundreds of actuators and sensors is formidable. Exploiting the circularly symmetric geometry of the mirror, and a suitable model of atmospheric distortion, the control problem is divided into a number of smaller decoupled control problems using circulant matrix theory. A hierarchic control scheme which seeks to emulate the quasi-static control approach that is generally used in adaptive optics is compared to the proposed dynamic reconstruction technique. Although dynamic reconstruction requires somewhat more computational power to implement, it achieves better performance with less power usage, and is less sensitive than the hierarchic technique.

Grocott, Simon C. O.↗
DOE OSTI2023

Enhancing Composite Toughness Through Hierarchical Interphase Formation

High strength and ductility are highly desired in fiber-reinforced composites, yet achieving both simultaneously remains elusive. A hierarchical architecture is developed utilizing high aspect ratio chemically transformable thermoplastic nanofibers that form covalent bonding with the matrix to toughen the fiber-matrix interphase. The nanoscale fibers are electrospun on the micrometer-scale reinforcing carbon fiber, creating a physically intertwined, randomly oriented scaffold. Unlike conventional covalent bonding of matrix molecules with reinforcing fibers, here, the nanofiber scaffold is utilized - interacting non-covalently with core fiber but bridging covalently with polymer matrix - to create a high volume fraction of immobilized matrix or interphase around core reinforcing elements. This mechanism enables efficient fiber-matrix stress transfer and enhances composite toughness. Molecular dynamics simulation reveals enhancement of the fiber-matrix adhesion facilitated by nanofiber-aided hierarchical bonding with the matrix. The elastic modulus contours of interphase regions obtained from atomic force microscopy clearly indicate the formation of stiffer interphase. These nanoengineered composites exhibit a ≈60% and ≈100% improved in-plane shear strength and toughness, respectively. This approach opens a new avenue for manufacturing toughened high-performance composites.

36 MATERIALS SCIENCE↗