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Results for “sparse linear algebra”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

BiGlobal Secondary Instabilities of Roughness-Induced Transient Growth

Roughness-induced transient disturbances distort laminar boundary layers and can lead to premature transition if the roughness is of sufficient height and shape. If transition does occur, it does so through a high-frequency "secondary" instability of the roughness wake. A BiGlobal secondaryinstability code has been developed to solve the stability problem downstream of roughness. The code implements multiple solvers for incompressible/compressible, inviscid/viscous, and temporal/spatial stability. High-order finite differences, sparse matrix linear algebra, LU decomposition, and Arnoldi iterations are used to solve the resulting generalized eigenvalue problem. The code has been used to evaluate the stability properties of experimental roughness-induced transient growth on a flat-plate at low-speed and a slightly blunted cone at M∞= 6. The resulting mode shapes, growth rates, and spatial N-factors show excellent agreement with experimental data. The viscous mode shapes show the best agreement with the experimental disturbance profiles. Yet, execution time can be reduced by an order-of-magnitude by using the inviscid solvers with only modest differences in growth rates.

BiGlobal↗
DOE OSTI2015

Sparse linear systems: Theory of decomposition, methods, technology, applications and implementation in Wolfram Mathematica

In this paper we propose the theory of decomposition, methods, technologies, applications and implementation in Wol-fram Mathematica for the constructing the solutions of the sparse linear systems. One of the applications is the Sensor Location Problem for the symmetric graph in the case when split ratios of some arc flows can be zeros. The objective of that application is to minimize the number of sensors that are assigned to the nodes. We obtain a sparse system of linear algebraic equations and research its matrix rank. Sparse systems of these types appear in generalized network flow programming problems in the form of restrictions and can be characterized as systems with a large sparse sub-matrix representing the embedded network structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1972

Elimination on sparse symmetric systems of a special structure.

Consideration of the problem of finding a permutation of rows and columns and an algorithm for solving ordered systems of linear algebraic equations with sparse matrices having a certain regular structure. Two approaches to the solution of this problem, in which the sparsity is used to some extent, are outlined. One of them is a very general approach where optimal (or nearly optimal) ordering is sought and the algorithm for solving the ordered system treats the matrix element by element to perform only necessary operations. The other approach involves the use of band matrices. After comparing these two approaches, a third approach is then suggested which involves the use of pipe matrices, and a means of ordering the rows and columns to obtain this type of matrix is presented. Examples of matrices reordered by the proposed procedure are cited.

Segethova, J.↗
NASA NTRS1990

SPARSKIT: A basic tool kit for sparse matrix computations

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices.

Saad, Youcef↗
DOE OSTI2024

Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest A in a larger unitary transformation U that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such a gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of A, which is difficult in general, and not trivial even for well structured sparse matrices. Here, in this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well structured sparse matrices and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Two-Level Least Squares Methods in Krylov Subspaces

Two-level least squares acceleration approaches are applied to the Chebyshev acceleration method and the restarted conjugate residual method in solving systems of linear algebraic equations with sparse unsymmetric coefficient matrices arising from finite volume or finite element approximations of boundary-value problems on irregular grids. Application of the proposed idea to other iterative restarted processes also is considered. The efficiency of the algorithms suggested is investigated numerically on a set of model Dirichlet problems for the convection-diffusion equation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Numerical simulation of heat and mass transfer in unsteady nanofluid between two orthogonally moving porous coaxial disks

The paper deals with the study of heat and mass transfer in an unsteady viscous incompressible water-based nanofluid (containing Titanium dioxide nanoparticles) between two orthogonally moving porous coaxial disks with suction. A combination of iterative (successive over relaxation) and a direct method is employed for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar ODEs. It has been noticed that the rate of mass transfer at the disks decreases with the permeability Reynolds number whether the disks are approaching or receding. The findings of the present investigation may be beneficial for the electronic industry in maintaining the electronic components under effective and safe operational conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2019

SWinzip v. 2.0

SWinzip is a Matlab and C++ library for scientific lossy data compression and reconstruction using compressed sensing and tree-wavelets transforms. These methods are known for their large compression and usefulness in data analytics such as features extraction. Compressed sensing and wavelets methods rely heavily on sparse and dense linear algebra operations implemented through the Boost codes in our library. SWinzip accommodates data represented on both regular grids (e.g. image data) and point-clouds (e.g. unstructured meshes). In SWinzip v2.0, there is more focus on wavelet compression and the following features are added: - The matrix-free (direct) wavelet transform is implemented in both C++ and Matlab. A threshold-based compression can now be used. Examples for distributed compression are also added. - Python implementation of Alpert wavelet transforms - Field data comparison using wavelets in Matlab with global and local metrics

Solloum, Maher↗
NASA NTRS1985

Iterative solution of large, sparse linear systems on a static data flow architecture - Performance studies

The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.

Reed, D. A.↗
DOE OSTI2016

SWinzip v. 1.0

SWinzip is a Matlab and C++ library for scientific lossy data compression and reconstruction using compressed sensing and tree-wavelets transforms. These methods are known for their large compression and usefulness in data analytics such as features extraction. Compressed sensing and wavelets methods rely heavily on sparse and dense linear algebra operations implemented through the Boost codes in our library. SWinzip accommodates data represented on both regular grids (e.g. image data) and point-clouds (e.g. unstructured meshes).

Salloum, Maher↗
DOE OSTI2015

Threaded Operations on Sparse Matrices

We investigate the use of sparse matrices and OpenMP multi-threading on linear algebra operations involving them. Several sparse matrix data structures are presented. Implementation of the multi- threading primarily occurs in the level one and two BLAS functions used within the four algorithms investigated{the Power Method, Conjugate Gradient, Biconjugate Gradient, and Jacobi's Method. The bene ts of launching threads once per high level algorithm are explored.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

High performance sparse multifrontal solvers on modern GPUs

Here, we have ported the numerical factorization and triangular solve phases of the sparse direct solver STRUMPACK to GPU. STRUMPACK implements sparse LU factorization using the multifrontal algorithm, which performs most of its operations in dense linear algebra operations on so-called frontal matrices of various sizes. Our GPU implementation off-loads these dense linear algebra operations, as well as the sparse scatter–gather operations between frontal matrices. For the larger frontal matrices, our GPU implementation relies on vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs and rocBLAS and rocSOLVER for AMD GPUs. For the smaller frontal matrices we developed custom CUDA and HIP kernels to reduce kernel launch overhead. Overall, high performance is achieved by identifying submatrix factorizations corresponding to sub-trees of the multifrontal assembly tree which fit entirely in GPU memory. The multi-GPU setting uses SLATE (Software for Linear Algebra Targeting Exascale) as a modern GPU-aware replacement for ScaLAPACK. On 4 nodes of SUMMIT the code runs ~10X faster when using all 24 V100 GPUs compared to when it only uses the 168 POWER9 cores. On 8 SUMMIT nodes, using 48 V100 GPUs, the sparse solver reaches over 50TFlop/s. Compared to SuperLU, on a single V100, for a set of 17 matrices our implementation is faster for all but one matrix, and is on average 5X (median 4X) faster

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A framework for solving atomistic phonon-structure scattering problems in the frequency domain using perfectly matched layer boundaries

We present a numerical approach to the solution of elastic phonon-interface and phonon-nanostructure scattering problems based on a frequency-domain decomposition of the atomistic equations of motion and the use of perfectly matched layer (PML) boundaries. Unlike molecular dynamic wavepacket analysis, the current approach provides the ability to simulate scattering from individual phonon modes, including wavevectors in highly dispersive regimes. Like the atomistic Green's function method, the technique reduces scattering problems to a system of linear algebraic equations via a sparse, tightly banded matrix regardless of dimensionality. However, the use of PML boundaries enables rapid absorption of scattered wave energies at the boundaries and provides a simple and inexpensive interpretation of the scattered phonon energy flux calculated from the energy dissipation rate in the PML. The accuracy of the method is demonstrated on connected monoatomic chains, for which an analytic solution is known. The parameters defining the PML are found to affect the performance and guidelines for selecting optimal parameters are given. The method is used to study the energy transmission coefficient for connected diatomic chains over all available wavevectors for both optical and longitudinal phonons; it is found that when there is discontinuity between sublattices, even connected chains of equivalent acoustic impedance have near-zero transmission coefficient for short wavelengths. The phonon scattering cross section of an embedded nanocylinder is calculated in 2D for a wide range of frequencies to demonstrate the extension of the method to high dimensions. The calculations match continuum theory for long-wavelength phonons and large cylinder radii, but otherwise show complex physics associated with discreteness of the lattice. Examples include Mie oscillations which terminate when incident phonon frequencies exceed the maximum available frequency in the embedded nanocylinder, and scattering efficiencies larger than two near the Brillouin zone edge.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

PAPI software-defined events for in-depth performance analysis

The methodology and standardization layer provided by the Performance Application Programming Interface (PAPI) has played a vital role in application profiling for almost two decades. It has enabled sophisticated performance analysis tool designers and performance-conscious scientists to gain insights into their applications by simply instrumenting their code using a handful of PAPI functions that “just work” across different hardware components. In the past, PAPI development had focused primarily on hardware-specific performance metrics. However, the rapidly increasing complexity of software infrastructure poses new measurement and analysis challenges for the developers of large-scale applications. In particular, acquiring information regarding the behavior of libraries and runtimes—used by scientific applications—requires low-level binary instrumentation, or APIs specific to each library and runtime. No uniform API for monitoring events that originate from inside the software stack has emerged. In this article, we present our efforts to extend PAPI’s role so that it becomes the de facto standard for exposing performance-critical events, which we refer to as software-defined events (SDEs), from different software layers. Upgrading PAPI with SDEs enables monitoring of both types of performance events—hardware- and software-related events—in a uniform way, through the same consistent PAPI. The goal of this article is threefold. First, we motivate the need for SDEs and describe our design decisions regarding the functionality we offer through PAPI’s new SDE interface. Second, we illustrate how SDEs can be utilized by different software packages, specifically, by showcasing their use in the numerical linear algebra library MAGMA-Sparse, the tensor algebra library TAMM that is part of the NWChem suite, and the compiler-based performance analysis tool Byfl. Third, we provide a performance analysis of the overhead that results from monitoring SDEs and discuss the trade-offs between overhead and functionality.

Jagode, Heike↗
NASA NTRS2016

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

Zubair, Mohammad↗
DOE OSTI2023

Fast truncated SVD of sparse and dense matrices on graphics processors

We investigate the solution of low-rank matrix approximation problems using the truncated singular value decomposition (SVD). For this purpose, we develop and optimize graphics processing unit (GPU) implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work takes advantage of the fact that the two methods are composed of very similar linear algebra building blocks, which can be assembled using numerical kernels from existing high-performance linear algebra libraries. Furthermore, the experiments with several sparse matrices arising in representative real-world applications and synthetic dense test matrices reveal a performance advantage of the block Lanczos algorithm when targeting the same approximation accuracy.

Computer Science↗