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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Solving large sparse eigenvalue problems on supercomputers

An important problem in scientific computing consists in finding a few eigenvalues and corresponding eigenvectors of a very large and sparse matrix. The most popular methods to solve these problems are based on projection techniques on appropriate subspaces. The main attraction of these methods is that they only require the use of the matrix in the form of matrix by vector multiplications. The implementations on supercomputers of two such methods for symmetric matrices, namely Lanczos' method and Davidson's method are compared. Since one of the most important operations in these two methods is the multiplication of vectors by the sparse matrix, methods of performing this operation efficiently are discussed. The advantages and the disadvantages of each method are compared and implementation aspects are discussed. Numerical experiments on a one processor CRAY 2 and CRAY X-MP are reported. Possible parallel implementations are also discussed.

Philippe, Bernard↗
NASA NTRS1988

General linear codes for fault-tolerant matrix operations on processor arrays

Various checksum codes have been suggested for fault-tolerant matrix computations on processor arrays. Use of these codes is limited due to potential roundoff and overflow errors. Numerical errors may also be misconstrued as errors due to physical faults in the system. In this a set of linear codes is identified which can be used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU-decomposition, with minimum numerical error. Encoding schemes are given for some of the example codes which fall under the general set of codes. With the help of experiments, a rule of thumb for the selection of a particular code for a given application is derived.

Nair, V. S. S.↗
NASA NTRS1989

Satellite range delay simulator for a matrix-switched time division multiple-access network simulator

The Systems Integration, Test, and Evaluation (SITE) facility at NASA Lewis Research Center is presently configured as a satellite-switched time division multiple access (SS-TDMA) network simulator. The purpose of SITE is to demonstrate and evaluate advanced communication satellite technologies, presently embodied by POC components developed under NASA contracts in addition to other hardware, such as ground terminals, designed and built in-house at NASA Lewis. Each ground terminal in a satellite communications system will experience a different aspect of the satellite's motion due mainly to daily tidal effects and station keeping, hence a different duration and rate of variation in the range delay. As a result of this and other effects such as local oscillator instability, each ground terminal must constantly adjust its transmit burst timing so that data bursts from separate ground terminals arrive at the satellite in their assigned time slots, preventing overlap and keeping the system in synchronism. On the receiving end, ground terminals must synchronize their local clocks using reference transmissions received through the satellite link. A feature of the SITE facility is its capability to simulate the varying propagation delays and associated Doppler frequency shifts that the ground terminals in the network have to cope with. Delay is achieved by means of two NASA Lewis designed and built range delay simulator (RDS) systems, each independently controlled locally with front panel switches or remotely by an experiment control and monitor (EC/M) computer.

Nagy, Lawrence A.↗
NASA NTRS1990

Satellite range delay simulator for a matrix-switched time division multiple-access network simulation system

The Systems Integration, Test, and Evaluation (SITE) facility at NASA Lewis Research Center is presently configured as a satellite-switched time division multiple access (SS-TDMA) network simulator. The purpose of SITE is to demonstrate and evaluate advanced communication satellite technologies, presently embodied by POC components developed under NASA contracts in addition to other hardware, such as ground terminals, designed and built in-house at NASA Lewis. Each ground terminal in a satellite communications system will experience a different aspect of the satellite's motion due mainly to daily tidal effects and station keeping, hence a different duration and rate of variation in the range delay. As a result of this and other effects such as local oscillator instability, each ground terminal must constantly adjust its transmit burst timing so that data bursts from separate ground terminals arrive at the satellite in their assigned time slots, preventing overlap and keeping the system in synchronism. On the receiving end, ground terminals must synchronize their local clocks using reference transmissions received through the satellite link. A feature of the SITE facility is its capability to simulate the varying propagation delays and associated Doppler frequency shifts that the ground terminals in the network have to cope with. Delay is ahcieved by means of two NASA Lewis designed and built range delay simulator (RDS) systems, each independently controlled locally with front panel switches or remotely by an experiment control and monitor (EC/M) computer.

Nagy, Lawrence A.↗
NASA NTRS1990

Real-number codes for fault-tolerant matrix operations on processor arrays

A generalization of existing real number codes is proposed. It is proven that linearity is a necessary and sufficient condition for codes used for fault-tolerant matrix operations such as matrix addition, multiplication, transposition, and LU decomposition. It is also proven that for every linear code defined over a finite field, there exists a corresponding linear real-number code with similar error detecting capabilities. Encoding schemes are given for some of the example codes which fall under the general set of real-number codes. With the help of experiments, a rule is derived for the selection of a particular code for a given application. The performance overhead of fault tolerance schemes using the generalized encoding schemes is shown to be very low, and this is substantiated through simulation experiments.

Nair, V. S. S.↗
NASA NTRS1990

Effects of error sources on the parallelism of an optical matrix-vector processor

The error sources in a high accuracy optical matrix-vector processor are analyzed by numerical simulation in terms of their effects on the parallelism and speed of the processor. These effects are detailed for radices -2, -4 and -8. Radix -4 is shown to provide maximum parallel processing capabilities under the effects of the system's error sources. Processing speed is shown to be a function of matrix partitioning and the number of parallel processing channels. Consequently, radix -4 operation provides a higher processing speed than radix -2 and -8 for most matrix-vector multiplications when error source effects are considered.

Perlee, Caroline J.↗
NASA NTRS1991

Lanczos eigensolution method for high-performance computers

The theory, computational analysis, and applications are presented of a Lanczos algorithm on high performance computers. The computationally intensive steps of the algorithm are identified as: the matrix factorization, the forward/backward equation solution, and the matrix vector multiples. These computational steps are optimized to exploit the vector and parallel capabilities of high performance computers. The savings in computational time from applying optimization techniques such as: variable band and sparse data storage and access, loop unrolling, use of local memory, and compiler directives are presented. Two large scale structural analysis applications are described: the buckling of a composite blade stiffened panel with a cutout, and the vibration analysis of a high speed civil transport. The sequential computational time for the panel problem executed on a CONVEX computer of 181.6 seconds was decreased to 14.1 seconds with the optimized vector algorithm. The best computational time of 23 seconds for the transport problem with 17,000 degs of freedom was on the the Cray-YMP using an average of 3.63 processors.

Bostic, Susan W.↗
NASA NTRS1993

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Gedney, Stephen D.↗
NASA NTRS1995

CCD/CID Processors Would Offer Greater Precision

Charge-coupled-device/charge-injection-device (CCD/CID) data processors of proposed type offer advantages of massively parallel computational architecture and high computational speed typical of older CCD/CID data processors, but with increased precision. Useful in performing matrix vector multiplications in variety of applications, including solving partial differential equations, processing signal and image data, control computations, and neural-network simulations. Greater precision of proposed devices help to ensure accuracy in CCD/CID implementations of pseudospectral neural networks - particular class of artificial neural networks especially suited to solving nonlinear differential equations.

Barhen, Jacob↗
NASA NTRS1995

Development of Fast Algorithms Using Recursion, Nesting and Iterations for Computational Electromagnetics

In the first phase of our work, we have concentrated on laying the foundation to develop fast algorithms, including the use of recursive structure like the recursive aggregate interaction matrix algorithm (RAIMA), the nested equivalence principle algorithm (NEPAL), the ray-propagation fast multipole algorithm (RPFMA), and the multi-level fast multipole algorithm (MLFMA). We have also investigated the use of curvilinear patches to build a basic method of moments code where these acceleration techniques can be used later. In the second phase, which is mainly reported on here, we have concentrated on implementing three-dimensional NEPAL on a massively parallel machine, the Connection Machine CM-5, and have been able to obtain some 3D scattering results. In order to understand the parallelization of codes on the Connection Machine, we have also studied the parallelization of 3D finite-difference time-domain (FDTD) code with PML material absorbing boundary condition (ABC). We found that simple algorithms like the FDTD with material ABC can be parallelized very well allowing us to solve within a minute a problem of over a million nodes. In addition, we have studied the use of the fast multipole method and the ray-propagation fast multipole algorithm to expedite matrix-vector multiplication in a conjugate-gradient solution to integral equations of scattering. We find that these methods are faster than LU decomposition for one incident angle, but are slower than LU decomposition when many incident angles are needed as in the monostatic RCS calculations.

Chew, W. C.↗
NASA NTRS1998

Performance of an Axisymmetric Rocket Based Combined Cycle Engine During Rocket Only Operation Using Linear Regression Analysis

The all rocket mode of operation is shown to be a critical factor in the overall performance of a rocket based combined cycle (RBCC) vehicle. An axisymmetric RBCC engine was used to determine specific impulse efficiency values based upon both full flow and gas generator configurations. Design of experiments methodology was used to construct a test matrix and multiple linear regression analysis was used to build parametric models. The main parameters investigated in this study were: rocket chamber pressure, rocket exit area ratio, injected secondary flow, mixer-ejector inlet area, mixer-ejector area ratio, and mixer-ejector length-to-inlet diameter ratio. A perfect gas computational fluid dynamics analysis, using both the Spalart-Allmaras and k-omega turbulence models, was performed with the NPARC code to obtain values of vacuum specific impulse. Results from the multiple linear regression analysis showed that for both the full flow and gas generator configurations increasing mixer-ejector area ratio and rocket area ratio increase performance, while increasing mixer-ejector inlet area ratio and mixer-ejector length-to-diameter ratio decrease performance. Increasing injected secondary flow increased performance for the gas generator analysis, but was not statistically significant for the full flow analysis. Chamber pressure was found to be not statistically significant.

Smith, Timothy D.↗
NASA NTRS1971

A New All Solid State Approach to Gaseous Pollutant Detection

Recent efforts in our laboratories have concentrated on the development of an all solid state gas sensor, by combining solid electrolyte (ion exchange membrane) technology with advanced thin film deposition processes. With the proper bias magnitude and polarity these miniature electro-chemical,cells show remarkable current responses for many common pollution gases. Current activity is now focused on complementing a multiple array (matrix) of these solid state sensors, with a digital electronic scanner device possessing "scan-compare-identify-alarm: capability. This innovative approach to multi-component pollutant gas analysis may indeed be the advanced prototype for the "third generation" class of pollution analysis instrumentation so urgently needed in the decade ahead.

Brown, V.↗
NASA NTRS2000

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗
NASA NTRS1999

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Lockard, David P.↗
NASA NTRS2004

Open-Source Software for Modeling of Nanoelectronic Devices

The Nanoelectronic Modeling 3-D (NEMO 3-D) computer program has been upgraded to open-source status through elimination of license-restricted components. The present version functions equivalently to the version reported in "Software for Numerical Modeling of Nanoelectronic Devices" (NPO-30520), NASA Tech Briefs, Vol. 27, No. 11 (November 2003), page 37. To recapitulate: NEMO 3-D performs numerical modeling of the electronic transport and structural properties of a semiconductor device that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantum-mechanical behavior of the device resolved to the atomistic level of granularity. NEMO 3-D solves the applicable quantum matrix equation on a Beowulf-class cluster computer by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. A prior upgrade of NEMO 3-D incorporated a capability for a strain treatment, parameterized for bulk material properties of GaAs and InAs, for two tight-binding submodels. NEMO 3-D has been demonstrated in atomistic analyses of effects of disorder in alloys and, in particular, in bulk In(x)Ga(1-x)As and in In(0.6)Ga(0.4)As quantum dots.

Oyafuso, Fabiano↗
NASA NTRS2003

Numerical Modeling of Nanoelectronic Devices

Nanoelectronic Modeling 3-D (NEMO 3-D) is a computer program for numerical modeling of the electronic structure properties of a semiconductor device that is embodied in a crystal containing as many as 16 million atoms in an arbitrary configuration and that has overall dimensions of the order of tens of nanometers. The underlying mathematical model represents the quantummechanical behavior of the device resolved to the atomistic level of granularity. The system of electrons in the device is represented by a sparse Hamiltonian matrix that contains hundreds of millions of terms. NEMO 3-D solves the matrix equation on a Beowulf-class cluster computer, by use of a parallel-processing matrix vector multiplication algorithm coupled to a Lanczos and/or Rayleigh-Ritz algorithm that solves for eigenvalues. In a recent update of NEMO 3-D, a new strain treatment, parameterized for bulk material properties of GaAs and InAs, was developed for two tight-binding submodels. The utility of the NEMO 3-D was demonstrated in an atomistic analysis of the effects of disorder in alloys and, in particular, in bulk In(x)Ga(l-x)As and in In0.6Ga0.4As quantum dots.

Klimeck, Gerhard↗
NASA NTRS2013

Nondestructive Analysis of Astromaterials by Micro-CT and Micro-XRF Analysis for PET Examination

An integral part of any sample return mission is the initial description and classification of returned samples by the preliminary examination team (PET). The goal of the PET is to characterize and classify returned samples and make this information available to the larger research community who then conduct more in-depth studies on the samples. The PET tries to minimize the impact their work has on the sample suite, which has in the past limited the PET work to largely visual, nonquantitative measurements (e.g., optical microscopy). More modern techniques can also be utilized by a PET to nondestructively characterize astromaterials in much more rigorous way. Here we discuss our recent investigations into the applications of micro-CT and micro-XRF analyses with Apollo samples and ANSMET meteorites and assess the usefulness of these techniques in future PET. Results: The application of micro computerized tomography (micro-CT) to astromaterials is not a new concept. The technique involves scanning samples with high-energy x-rays and constructing 3-dimensional images of the density of materials within the sample. The technique can routinely measure large samples (up to approx. 2700 cu cm) with a small individual voxel size (approx. 30 cu m), and has the sensitivity to distinguish the major rock forming minerals and identify clast populations within brecciated samples. We have recently run a test sample of a terrestrial breccia with a carbonate matrix and multiple igneous clast lithologies. The test results are promising and we will soon analyze a approx. 600 g piece of Apollo sample 14321 to map out the clast population within the sample. Benchtop micro x-ray fluorescence (micro-XRF) instruments can rapidly scan large areas (approx. 100 sq cm) with a small pixel size (approx. 25 microns) and measure the (semi) quantitative composition of largely unprepared surfaces for all elements between Be and U, often with sensitivity on the order of a approx. 100 ppm. Our recent testing of meteorite and Apollo samples on micro-XRF instruments has shown that they can easily detect small zircons and phosphates (approx. 10 m), distinguish different clast lithologies within breccias, and identify different lithologies within small rock fragments (2-4 mm soil Apollo soil fragments).

Zeigler, R. A.↗
NASA NTRSDate not supplied

Performance Optimization Methods for a Memory-Bound, Unstructured-Grid CFD Application on Massively Parallel GPU Platforms

Computational performance of the FUN3D unstructured-grid computational fluid dynamics (CFD) application on massively parallel GPU environments is memory-bound and highly dependent upon efficient reads from and atomic updates to the irregular cell-, edge-, and node-based data structures. In this talk, we present recent efforts into optimizing select performance-critical kernels on NVIDIA Tesla V100 and A100 GPUs and AMD CDNA MI100 GPUs. A novel use of L2 cache residency controls and asynchronous loads into on-chip shared memory are explored on the A100 GPU for the sparse iterative solver, which is dominated by mixed-precision, sparse matrix vector multiplication. Demonstrations show that these methods improve global memory bandwidth utilization by 13.5% on the A100 GPU. Several techniques are also presented that use registers and/or shared memory to facilitate array transposition and aggregation which combine to reduce the frequency and increase the cache efficiency of floating-point atomic updates to the irregular data structures. These methods are demonstrated to improve the kernel throughput by nearly 500% on select kernels on the AMD MI100 over atomic updates directly to global memory. Overall, both V100 and A100 GPUs outperformed the MI100 GPU on kernels dominated by double-precision atomic updates; however, the techniques demonstrated here reduced the performance gap and improved the MI100 performance.

GPU CPU unstructured CFD memory↗