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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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12 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Efficient scalable algorithms for hierarchically semiseparable matrices

Hierarchically semiseparable (HSS) matrix algorithms are emerging techniques in constructing the superfast direct solvers for both dense and sparse linear systems. Here, we develope a set of novel parallel algorithms for the key HSS operations that are used for solving large linear systems. These include the parallel rank-revealing QR factorization, the HSS constructions with hierarchical compression, the ULV HSS factorization, and the HSS solutions. The HSS tree based parallelism is fully exploited at the coarse level. The BLACS and ScaLAPACK libraries are used to facilitate the parallel dense kernel operations at the ne-grained level. We have appplied our new parallel HSS-embedded multifrontal solver to the anisotropic Helmholtz equations for seismic imaging, and were able to solve a linear system with 6.4 billion unknowns using 4096 processors, in about 20 minutes. The classical multifrontal solver simply failed due to high demand of memory. To our knowledge, this is the first successful demonstration of employing the HSS algorithms in solving the truly large-scale real-world problems. Our parallel strategies can be easily adapted to the parallelization of the other rank structured methods.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2017

Efficient Scalable Parallel Higher Order Direct MoM-SIE Method With Hierarchically Semiseparable Structures for 3-D Scattering

A novel fast scalable parallel algorithm is proposed for the solution of large 3-D scattering problems based on: 1) the double (geometrical and current-approximation) higher order (DHO) method of moments (MoM) in the surface integral equation (SIE) formulation and 2) a direct solver for dense linear systems utilizing hierarchically semiseparable (HSS) structures. Namely, an HSS matrix representation is used for compression, factorization, and solution of the system matrix. In addition, a rank-revealing QR decomposition for memory compression is used, with a stopping criterion in terms of the relative rank tolerance value. One method for geometrical preprocessing of the scatterers based on the cobblestone distance sorting technique is employed in order to enhance the HSS algorithm accuracy and parallelization. Numerical examples show how the accuracy of the DHO HSS-MoM-SIE method is easily controllable by using the relative tolerance for the matrix compression. Furthermore, the examples demonstrate low memory consumption, as well as much faster simulation time, when compared to the direct LU decomposition. The method enables dramatically faster monostatic scattering computations than iterative solvers and reduced number of unknowns when compared to low-order discretizations. Finally, great scalability of the algorithm is demonstrated on more than one thousand processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

Here, we present a sparse linear system solver that is based on a multifrontal variant of Gaussian elimination and exploits low-rank approximation of the resulting dense frontal matrices. We use hierarchically semiseparable (HSS) matrices, which have low-rank off-diagonal blocks, to approximate the frontal matrices. For HSS matrix construction, a randomized sampling algorithm is used together with interpolative decompositions. The combination of the randomized compression with a fast ULV HSS factoriz ation leads to a solver with lower computational complexity than the standard multifrontal method for many applications, resulting in speedups up to 7 fold for problems in our test suite. The implementation targets many-core systems by using task parallelism with dynamic runtime scheduling. Numerical experiments show performance improvements over state-of-the-art sparse direct solvers. The implementation achieves high performance and good scalability on a range of modern shared memory parallel systems, including the Intel Xeon Phi (MIC). The code is part of a software package called STRUMPACK - STRUctured Matrices PACKage, which also has a distributed memory component for dense rank-structured matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

ButterflyPACK

ButterflyPACK is a mathematical software for rapidly solving large-scale dense linear systems that exhibit off-diagonal rank-deficiency properties. These targeted systems are either matrices arising from discretized boundary integral equations, or frontal matrices in multi-frontal solvers for differential equations. ButterflyPACK relies on low-rank and butterfly formats under Hierarchical matrix, HODLR or HSS frameworks to compress, factor/precondition and solve the linear system in quasi-linear time. ButterflyPACK is particularly useful for large-scale ill-conditioned matrices arising from high-frequency wave equations involving multiple right-hand-sides. ButterflyPACK is based on Fortran 2003, it also has interface written in C++. In addition, ButterflyPACK can be readily invoked from the software STRUMPACK. ButterflyPACK supports hybrid MPI/OpenMP programming models.

Liu, Yang↗
DOE OSTI2019

Microstructure and Mechanical Properties of B{sub 4}C-Blended M3:2 High-Speed Steel Powders Consolidated by Sintering and Heat Treatment

Water-atomized powders of M3:2 high-speed steel (HSS) were blended with B{sub 4}C and consolidated by cold press sintering. With the addition of B{sub 4}C (~ 0.2 vol.%), satisfactory mechanical properties were achieved for HSS by sintering at a temperature as low as 1190 °C [e.g., 53.2 ± 0.2 in the Rockwell hardness (HRC) and 3074 ± 56 MPa in bending strength]. High relative density (98.5%) and good strength were attributed to the mechanism described as follows: First, the atoms of boron and carbon escaped after the reaction between B{sub 4}C and iron matrix. Then, the sintered HSS was strengthened by boron atoms while they were distributed in M{sub 6}C or MC carbides and iron matrix. Second, a plenty of M{sub 6}C carbides were formed due to the release of carbon atoms. As a result, the value of solidus temperature was reduced. In addition, mechanical properties were greatly improved by heat treatment (quenching and tempering) (e.g., 61.2 ± 0.3 in HRC, 4356 ± 64 MPa in bending strength, and 42.3 ± 0.5 MPa m{sup 1/2} in fracture toughness, respectively).

36 MATERIALS SCIENCE↗
DOE OSTI2016

A Distributed-Memory Package for Dense Hierarchically Semi-Separable Matrix Computations Using Randomization

In this paper, we present a distributed-memory library for computations with dense structured matrices. A matrix is considered structured if its off-diagonal blocks can be approximated by a rank-deficient matrix with low numerical rank. Here, we use Hierarchically Semi-Separable (HSS) representations. Such matrices appear in many applications, for example, finite-element methods, boundary element methods, and so on. Exploiting this structure allows for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. The compression algorithm that we use, that computes the HSS form of an input dense matrix, relies on randomized sampling with a novel adaptive sampling mechanism. We discuss the parallelization of this algorithm and also present the parallelization of structured matrix-vector product, structured factorization, and solution routines. The efficiency of the approach is demonstrated on large problems from different academic and industrial applications, on up to 8,000 cores. Finally, this work is part of a more global effort, the STRUctured Matrices PACKage (STRUMPACK) software package for computations with sparse and dense structured matrices. Hence, although useful on their own right, the routines also represent a step in the direction of a distributed-memory sparse solver.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2018

A Study of Clustering Techniques and Hierarchical Matrix Formats for Kernel Ridge Regression

We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the execution time are drastically reduced compared to standard dense linear algebra routines. We consider both the general H matrix hierarchical format as well as Hierarchically Semi-Separable (HSS) matrices. Furthermore, we investigate the impact of several preprocessing and clustering techniques on the hierarchical matrix compression. Effective clustering of the input leads to a ten-fold increase in efficiency of the compression. The algorithms are implemented using the STRUMPACK solver library. These results confirm that - with correct tuning of the hyperparameters - classification using kernel ridge regression with the compressed matrix does not lose prediction accuracy compared to the exact - not compressed - kernel matrix and that our approach can be extended to O(1M) datasets, for which computation with the full kernel matrix becomes prohibitively expensive. We present numerical experiments in a distributed memory environment up to 1,024 processors of the NERSC's Cori supercomputer using well-known datasets to the machine learning community that range from dimension 8 up to 784.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

The Median Isn’t the Message: soil nutrient hot spots have a disproportionate influence on biogeochemical structure across years, seasons, and depths

Abstract Soil nutrient distribution is heterogeneous in space and time, potentially altering nutrient acquisition by trees and microorganisms. Ecologists have distinguished “hot spots” (HSs) as areas with enhanced and sustained rates of nutrient fluxes relative to the surrounding soil matrix. We evaluated the spatial and temporal patterns in nutrient flux HSs in two mixed-conifer forest soils by repeatedly sampling the soil solution at the same spatial locations (horizontally and vertically) over multiple seasons and years using ion exchange resins incubated in situ. The climate of these forests is Mediterranean, with intense fall rains occurring following summers with little precipitation, and highly variable winter snowfall. Hot spots formed most often for NO 3 − and Na + . Although nutrient HSs often occurred in the same spatial location multiple times, HSs persisted more often for PO 4 3− NH 4 + , and NO 3 − , and were more transient for Ca 2+ , Mg 2+ , and Na + . Sampling year (annual precipitation ranged from 558 to 1223 mm) impacted the occurrence of HSs for most nutrients, but season was only significant for PO 4 3− , NH 4 + , NO 3 − , and Na + , with HSs forming more often after fall rains than after spring snowmelt. The frequency of HSs significantly decreased with soil depth for all nutrients, forming most commonly immediately below the surficial organic horizon. Although HSs accounted for less than 17% of the sampling volume, they were responsible for 56–88% of PO 4 3− , NH 4 + , and NO 3 − resin fluxes. Our results suggest that macronutrient HSs have a disproportional contribution to soil biogeochemical structure, with implications for vegetation nutrient acquisition strategies and biogeochemical models. Graphical abstract

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

STRUMPACK -- STRUctured Matrices PACKage

STRUMPACK - STRUctured Matrices PACKage - is a package for computations with sparse and dense structured matrix, i.e., matrices that exhibit some kind of low-rank property, in particular Hierarchically Semi Separable structure (HSS). Such matrices appear in many applications, e.g., FEM, BEM, Integral equations. etc. Exploiting this structure using certain compression algorithms allow for fast solution of linear systems and/or fast computation of matrix-vector products, which are the two main building blocks of matrix computations. STRUMPACK has presently two main components: a distributed-memory dense matrix computations package and a shared-memory sparse direct solver.

Source record↗
DOE OSTI2015

Process depending morphology and resulting physical properties of TPU

Thermoplastic polyurethane (TPU) is a rubber like material with outstanding properties, e.g. for seal applications. TPU basically provides high strength, low frictional behavior and excellent wear resistance. Though, due to segmented structure of TPU, which is composed of hard segments (HSs) and soft segments (SSs), physical properties depend strongly on the morphological arrangement of the phase separated HSs at a certain ratio of HSs to SSs. It is obvious that the TPU deforms differently depending on its bulk morphology. Basically, the morphology can either consist of HSs segregated into small domains, which are well dispersed in the SS matrix or of few strongly phase separated large size HS domains embedded in the SS matrix. The morphology development is hardly ruled by the melt processing conditions of the TPU. Depending on the morphology, TPU provides quite different physical properties with respect to strength, deformation behavior, thermal stability, creep resistance and tribological performance. The paper deals with the influence of important melt processing parameters, such as temperature, pressure and shear conditions, on the resulting physical properties tested by tensile and relaxation experiments. Furthermore the morphology is studied employing differential scanning calorimeter (DSC), transmission light microscopy (TLM), scanning electron beam microscopy (SEM) and transmission electron beam microscopy (TEM) investigations. Correlations between processing conditions and resulting TPU material properties are elaborated. Flow and shear simulations contribute to the understanding of thermal and flow induced morphology development.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A special generalized HSS method for discrete ill-posed problems

In this paper, we use a new special generalized Hermitian and skew-Hermitian splitting (SGHSS) method for solving ill-posed inverse problems. Based on an augmented system formulation, we apply a new splitting for the Hermitian part of the coefficient matrix and discuss on the convergence of this iterative method. Moreover, the optimal parameter minimizing the spectral radius of iteration matrix is derived. Finally, we present some numerical examples to demonstrate the performance of the presented method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

The generalized Uzawa-SHSS method for non-Hermitian saddle-point problems

Recently, Li and Wu (2015) proposed the single-step Hermitian and skew-Hermitian splitting (SHSS) method for solving the non-Hermitian positive definite linear systems. Based on the single-step Hermitian and skew-Hermitian splitting of the (1,1) part of the saddle-point coefficient matrix, a new Uzawa-type method is proposed for solving a class of saddle-point problems with non-Hermitian positive definite (1,1) parts. Convergence (Semi-convergence) properties of this new method for nonsingular (singular) are derived under suitable conditions. Numerical examples are implemented to confirm the theoretical results and verify that this new method is more feasibility and robustness than the new HSS-like (NHSS-like), the Uzawa-HSS and the parameterized Uzawa-skew-Hermitian triangular splitting (PU-STS) methods for solving both the nonsingular and the singular saddle-point problems with non-Hermitian positive definite and Hermitian dominant (1,1) parts.

97 MATHEMATICS AND COMPUTING↗