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At least 361 records · Page 20

Galerkin/Runge-Kutta discretizations for parabolic equations with time dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗

Making Macroscopic Assemblies of Aligned Carbon Nanotubes

A method of aligning and assembling single-wall carbon nanotubes (SWNTs) to fabricate macroscopic structures has been invented. The method entails suspending SWNTs in a fluid, orienting the SWNTs by use of a magnetic and/or electric field, and then removing the aligned SWNTs from suspension in such a way as to assemble them while maintaining the alignment. SWNTs are essentially tubular extensions of fullerene molecules. It is desirable to assemble aligned SWNTs into macroscopic structures because the common alignment of the SWNTs in such a structure makes it possible to exploit, on a macroscopic scale, the unique mechanical, chemical, and electrical properties that individual oriented SWNTs exhibit at the molecular level. Because of their small size and high electrical conductivity, carbon nanotubes, and especially SWNTs, are useful for making electrical connectors in integrated circuits. Carbon nanotubes can be used as antennas at optical frequencies, and as probes in scanning tunneling microscopes, atomic-force microscopes, and the like. Carbon nanotubes can be used with or instead of carbon black in tires. Carbon nanotubes are useful as supports for catalysts. Ropes of SWNTs are metallic and, as such, are potentially useful in some applications in which electrical conductors are needed - for example, they could be used as additives in formulating electrically conductive paints. Finally, macroscopic assemblies of aligned SWNTs can serve as templates for the growth of more and larger structures of the same type. The great variety of tubular fullerene molecules and of the structures that could be formed by assembling them in various ways precludes a complete description of the present method within the limits of this article. It must suffice to present a typical example of the use of one of many possible variants of the method to form a membrane comprising SWNTs aligned substantially parallel to each other in the membrane plane. The apparatus used in this variant of the method (see figure) includes a reservoir containing SWNTs dispersed in a suspending agent (for example, dimethylformamide) and a reservoir containing a suitable solvent (for example, water mixed with a surfactant). By use of either pressurized gas supplied from upstream or suction from downstream, the suspension of SWNTs and the solvent are forced to mix and flow into a tank. A filter inside the tank contains pores small enough to prevent the passage of most SWNTs, but large enough to allow the passage of molecules of the solvent and suspending agent. The filter is oriented perpendicular to the flow path. A magnetic field parallel to the plane of the filter is applied. The success of the method is based on the tendency of SWNTs to become aligned with their longitudinal axes parallel to an applied magnetic field. The alignment energy of an SWNT increases with the length of the SWNT and the magnetic-field strength. In order to obtain an acceptably small degree of statistical deviation of SWNTs of a given length from alignment with a magnetic field, one must make the field strong enough so that the thermal energy associated with rotation of an SWNT away from alignment is less than the alignment energy.

Smalley, Richard E.↗

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↗

Dependability analysis of parallel systems using a simulation-based approach

The analysis of dependability in large, complex, parallel systems executing real applications or workloads is examined in this thesis. To effectively demonstrate the wide range of dependability problems that can be analyzed through simulation, the analysis of three case studies is presented. For each case, the organization of the simulation model used is outlined, and the results from simulated fault injection experiments are explained, showing the usefulness of this method in dependability modeling of large parallel systems. The simulation models are constructed using DEPEND and C++. Where possible, methods to increase dependability are derived from the experimental results. Another interesting facet of all three cases is the presence of some kind of workload of application executing in the simulation while faults are injected. This provides a completely new dimension to this type of study, not possible to model accurately with analytical approaches.

Sawyer, Darren Charles↗

Variance reduction in Monte Carlo analysis of rarefied gas diffusion.

The problem of rarefied diffusion between parallel walls is solved using the Monte Carlo method. The diffusing molecules are evaporated or emitted from one of the two parallel walls and diffuse through another molecular species. The Monte Carlo analysis treats the diffusing molecule as undergoing a Markov random walk, and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs, the expected Markov walk payoff is retained but its variance is reduced so that the Monte Carlo result has a much smaller error.

Perlmutter, M.↗

Collecting address traces from parallel computers

Trace driven simulation is a well-established method of performance analysis for single processor computer systems. However, efficient and accurate memory address tracing for parallel computer systems is not well understood. In this paper we present a critical survey of recently implemented approaches to address tracing and highlight the issues specific to collection of traces for both shared and distributed memory parallel computers. These issues include potential distortion of the relative ordering of events by the address tracing activity, realistic interleaving of addresses generated by multiple processors, and I/O and storage problems associated with collecting traces for large parallel systems. The strengths and weaknesses of the parallel tracing approaches are described.

Stunkel, Craig B.↗

Techniques for improving the Si-SiO2 interface characterization

The two techniques which have provided most of the information on interface states in MIS-C (metal-insulator-semiconductor-capacitor) structures are the 'quasi-static method' and the 'conductance method'. Sher et al. (1979) and Su et al. (1980) have suggested a number of improvements concerning these methods. The present investigation has the objective to extend the earlier results and to offer a new tentative interpretation of the data. A critical review is conducted of the data collection and reduction techniques for the quasi-static method, taking into account the sample, the quasi-static capacitance, and the surface potential. In connection with a discussion of the conductance method, attention is given to parallel conductance and capacitance measurements, interface-state densities, time constants, and measurements on a (110) surface orientation.

Sher, A.↗

Mesh-matrix analysis method for electromagnetic launchers

The mesh-matrix method is a procedure for calculating the current distribution in the conductors of electromagnetic launchers with coil or flat-plate geometry. Once the current distribution is known the launcher performance can be calculated. The method divides the conductors into parallel current paths, or meshes, and finds the current in each mesh by matrix inversion. The author presents procedures for writing equations for the current and voltage relations for a few meshes to serve as a pattern for writing the computer code. An available subroutine package provides routines for field and flux coefficients and equation solution.

Elliott, David G.↗

Concurrent Finite-Element Analysis On Hypercube Computers

Improved approach to execution of finite-element codes on hypercube and similar concurrent data processors increases efficiency of computation for many different types of problems. Based on flexible general model of computation on, and communication among, large-node parallel processors. Hybrid combining direct methods within subdomains and preconditioned-conjugate-gradient (PCG) iteration on remaining boundary system to obtain method of solution both robust and efficient. Preserves general structure and function of conventional sequential finite-element-method software. Generalized to both distributed- and shared-memory multicomputers, eliminating degree of machine specificity restricting general usefulness.

Lyzenga, G. A.↗

On the parallel efficiency of the Frederickson-McBryan multigrid

To take full advantage of the parallelism in a standard multigrid algorithm requires as many processors as points. However, since coarse grids contain fewer points, most processors are idle during the coarse grid iterations. Frederickson and McBryan claim that retaining all points on all grid levels (using all processors) can lead to a superconvergent algorithm. The purpose of this work is to show that the parellel superconvergent multigrid (PSMG) algorithm of Frederickson and McBryan, though it achieves perfect processor utilization, is no more efficient than a parallel implementation of standard multigrid methods. PSMG is simply a new and perhaps simpler way of achieving the same results.

Decker, Naomi H.↗

Thomson scattering in magnetic fields

The equation of transfer in Thomson scattering atmospheres with magnetic fields is solved using Monte Carlo methods. Two cases, a plane parallel atmosphere with a magnetic field perpendicular to the atmosphere, and a dipole star, are investigated. The wavelength dependence of polarization from plane-parallel atmosphere is qualitatively similar to that observed in the magnetic white dwarf Grw+70 deg 8247, and the field strength determined by the calculation, 320 MG, is quantitatively similar to that determined from the line spectrum. The dipole model does not resemble the data as well as the single plane-parallel atmosphere.

Whitney, Barbara↗

Optical Backplane Interconnection

Optical backplane interconnection (OBIT), method of optically interconnecting many parallel outputs from data processor to many parallel inputs of other data processors by optically changing wavelength of output optical beam. Requires only one command: exact wavelength necessary to make connection between two desired processors. Many features, including smallness advantageous to incorporate OBIT into integrated optical device. Simplifies or eliminates wiring and speeds transfer of data over existing electrical or optical interconnections. Computer hookups and fiber-optical communication networks benefit from concept.

Hendricks, Herbert D.↗

Application of compiler-assisted multiple instruction rollback recovery to speculative execution

Speculative execution is a method to increase instruction level parallelism which can be exploited by both super-scalar and VLIW architectures. The key to a successful general speculation strategy is a repair mechanism to handle mispredicted branches and accurate reporting of exceptions for speculated instructions. Multiple instruction rollback is a technique developed for recovery from transient processor failure. Many of the difficulties encountered during recovery from branch misprediction or from instruction re-execution due to exception in a speculative execution architecture are similar to those encountered during multiple instruction rollback. The applicability of a recently developed compiler-assisted multiple instruction rollback scheme to aid in speculative execution repair is investigated. Extensions to the compiler-assisted scheme to support branch and exception repair are presented along with performance measurements across ten application programs.

Alewine, N. J.↗

The instant sequencing task: Toward constraint-checking a complex spacecraft command sequence interactively

Robotic spacecraft are controlled by sets of commands called 'sequences.' These sequences must be checked against mission constraints. Making our existing constraint checking program faster would enable new capabilities in our uplink process. Therefore, we are rewriting this program to run on a parallel computer. To do so, we had to determine how to run constraint-checking algorithms in parallel and create a new method of specifying spacecraft models and constraints. This new specification gives us a means of representing flight systems and their predicted response to commands which could be used in a variety of applications throughout the command process, particularly during anomaly or high-activity operations. This commonality could reduce operations cost and risk for future complex missions. Lessons learned in applying some parts of this system to the TOPEX/Poseidon mission will be described.

Horvath, Joan C.↗

Application of compiler-assisted multiple instruction rollback recovery to speculative execution

Speculative execution is a method to increase instruction level parallelism which can be exploited by both super-scalar and VLIW architectures. The key to a successful general speculation strategy is a repair mechanism to handle mispredicted branches and accurate reporting of exceptions for speculated instructions. Multiple instruction rollback is a technique developed for recovery from transient processor failure. Many of the difficulties encountered during recovery from branch misprediction or from instruction re-execution due to exception in a speculative execution architecture are similar to those encountered during multiple instruction rollback. The applicability of a recently developed compiler-assisted multiple instruction rollback scheme to aid in speculative execution repair is investigated. Extensions to the compiler-assisted scheme to support branch and exception repair are presented along with performance measurements across ten application programs.

Alewine, N. J.↗

Algorithms for parallel and vector computations

This is a final report on work performed under NASA grant NAG-1-1112-FOP during the period March, 1990 through February 1995. Four major topics are covered: (1) solution of nonlinear poisson-type equations; (2) parallel reduced system conjugate gradient method; (3) orderings for conjugate gradient preconditioners, and (4) SOR as a preconditioner.

Ortega, James M.↗