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1.
Numerical experiments on the accuracy of ENO and modified ENO schemes   总被引:6,自引:0,他引:6  
In this paper we make further numerical experiments assessing an accuracy degeneracy phenomena reported by A. Rogerson and E. Meiburg (this issue, 1990). We also propose a modified ENO scheme, which recovers the correct order of accuracy for all the test problems with smooth initial conditions and gives results comparable to the original ENO schemes for discontinuous problems.Research supported by NSF grant No. DMS88-10150, NASA Langley contract No. NAS1-18605, and AFOSR grant No. 90-0093. Computation supported by NAS.  相似文献   

2.
In irregular scientific computational problems one is periodically forced to choosea delay point where some overhead cost is suffered to ensure correctness, or to improve subsequent performance. Examples of delay points are problem remappings, and global synchronizations. One sometimes has considerable latitude in choosing the placement and frequency of delay points; we consider the problem of scheduling delay points so as to minimize the overal execution time. We illustrate the problem with two examples, a regridding method which changes the problem discretization during the course of the computation, and a method for solving sparse triangular systems of linear equations. We show that one can optimally choose delay points in polynomial time using dynamic programming. However, the cost models underlying this approach are often unknown. We consequently examine a scheduling heuristic based on maximizing performance locally, and empirically show it to be nearly optimal on both problems. We explain this phenomenon analytically by identifying underlying assumptions which imply that overall performance is maximized asymptotically if local performance is maximized.This research was supported in part by the National Aeronautics and Space Administration under NASA contract NAS1-18107 while the author consulted at ICASE, Mail Stop 132C, NASA Langley Research Center, Hampton, Virginia 23665.Supported in part by NASA contract NAS1-18107, the Office of Naval Research under Contract No. N00014-86-K-0654, and NSF Grant DCR 8106181.  相似文献   

3.
Automatic process partitioning is the operation of automatically rewriting an algorithm as a collection of tasks, each operating primarily on its own portion of the data, to carry out the computation in parallel. Hybrid shared memory systems provide a hierarchy of globally accessible memories. To achieve high performance on such machines one must carefully distribute the work and the data so as to keep the workload balanced while optimizing the access to nonlocal data. In this paper we consider a semi-automatic approach to process partitioning in which the compiler, guided by advice from the user, automatically transforms programs into such an interacting set of tasks. This approach is illustrated with a picture processing example written in BLAZE, which is transformed by the compiler into a task system maximizing locality of memory reference.Research supported by an IBM Graduate Fellowship.Research supported under NASA Contract No. 520-1398-0356.Research supported by NASA Contract No. NAS1-18107 while the last two authors were in residence at ICASE, NASA, Langley Research Center.  相似文献   

4.
This paper presents an analytically robust, globally convergent approach to managing the use of approximation models of varying fidelity in optimization. By robust global behaviour we mean the mathematical assurance that the iterates produced by the optimization algorithm, started at an arbitrary initial iterate, will converge to a stationary point or local optimizer for the original problem. The approach presented is based on the trust region idea from nonlinear programming and is shown to be provably convergent to a solution of the original high-fidelity problem. The proposed method for managing approximations in engineering optimization suggests ways to decide when the fidelity, and thus the cost, of the approximations might be fruitfully increased or decreased in the course of the optimization iterations. The approach is quite general. We make no assumptions on the structure of the original problem, in particular, no assumptions of convexity and separability, and place only mild requirements on the approximations. The approximations used in the framework can be of any nature appropriate to an application; for instance, they can be represented by analyses, simulations, or simple algebraic models. This paper introduces the approach and outlines the convergence analysis.This research was supported by the Dept. of Energy grant DEFG03-95ER25257 and Air Force Office of Scientific Research grant F49620-95-1-0210This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681, USAThis research was supported by the Air Force Office of Scientific Research grant F49620-95-1-0210 and by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681, USA  相似文献   

5.
An efficient three-dimensional unstructured Euler solver is parallelized on a CRAY Y-MP C90 shared-memory computer and on an Intel Touchstone Delta distributed-memory computer. This paper relates the experiences gained and describes the software tools and hardware used in this study. Performance comparisons between the two differing architectures are made.This work was sponsored in part by ARPA (NAG-1-1485) and by NASA Contract No. NAS1-19480 while authors Mavriplis, Saltz and Das were in residence at ICASE, NASA Langley Research Center, Hampton, Virginia. This research was performed in part using the Intel Touchstone Delta System operated by Caltech on behalf of the Concurrent Supercomputing Consortium. Access to this fecility was provided by NASA Langley Research Center and the Center for Research in Parallel Processing. The content of the information does not necessarily reflect the position or the policy of the Government and no official endorsement should be inferred.  相似文献   

6.
We develop a topology optimization approach to design two- and three-dimensional phononic (elastic) materials, focusing primarily on surface wave filters and waveguides. These utilize propagation modes that transmit elastic waves where the energy is contained near a free surface of a material. The design of surface wave devices is particularly attractive given recent advances in nano- and micromanufacturing processes, such as thin-film deposition, etching, and lithography, which make it possible to precisely place thin film materials on a substrate with submicron feature resolution. We apply our topology optimization approach to a series of three problems where the layout of two materials (silicon and aluminum) is sought to achieve a prescribed objective: (1) a grating to filter bulk waves of a prescribed frequency in two and three dimensions, (2) a surface wave device that uses a patterned thin film to filter waves of a single or range of frequencies, and (3) a fully three-dimensional structure to guide a wave generated by a harmonic input on a free surface to a specified output port on the surface. From the first to the third example, the resulting topologies increase in sophistication. The results demonstrate the power and promise of our computational framework to design sophisticated surface wave devices.  相似文献   

7.
Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear PDE with discontinuous solutions, Fourier spectral method will produce poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We have found out that the moments against analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a Gegenbauer polynomial based post-processing.Research supported by ARO Grant DAAL03-91-G-0123 and DAAH04-94-G-0205, NSF Grant DMS-9211820, NASA Grant NAG1-1145 and contract NAS1-19480 while the first author was in residence at ICASE, NASA Langley Research Center, Hampton, Virginia 23681-0001, and AFOSR Grant 93-0090.  相似文献   

8.
Important insights into program operation can be gained by observing dynamic execution behavior. Unfortunately, many high-performance machines provide execution profile summaries as the only tool for performance investigation. We have developed a tracing library for the CRAY X-MP and CRAY-2 supercomputers that supports the low-overhead capture of execution events for sequential and multitasked programs. This library has been extended to use the automatic instrumentation facilities on these machines, allowing trace data from routine entry and exit, and other program segments, to be captured. To assess the utility of the trace-based tools, three of the Perfect Benchmark codes have been tested in scalar and vector modes with the tracing instrumentation. In addition to computing summary execution statistics from the traces, interesting execution dynamics appear when studying the trace histories. It is also possible to model application performance based on properties identified from traces. Our conclusion is that adding tracing support in Cray supercomputers can have significant returns in improved performance characterization and evaluation.An earlier version of this paper was presented at Supercomputing '90.Supported in part by the National Science Foundation under Grants No. NSF MIP-88-07775 and No. NSF ASC-84-04556, and the NASA Ames Research Center Grant No. NCC-2-559.Supported in part by the National Science Foundation under grant NSF ASC-84-04556.Supported in part by the National Science Foundation under grants NSF CCR-86-57696, NSF CCR-87-06653 and NSF CDA-87-22836 and by the National Aeronautics and Space Administration under NASA Contract Number NAG-1-613.  相似文献   

9.
Domain decomposition for wave propagation problems   总被引:5,自引:0,他引:5  
The problem posed by domain decomposition methods is to find the correct modeling of physical phenomena across the interfaces separating the subdomains. The technique described here for wave propagation problems is based on physical grounds since it relies on the fact that the wave equation can be decomposed into incoming and outgoing wave modes at the boundaries of the subdomains. The inward propagating waves depend on the solution exterior to the subdomains and therefore are computed from the appropriate boundary conditions, while the behavior of the outward propagating waves is determined by the solution inside the subdomains. The technique is applied to the anisotropic-viscoelastic wave equation, which practically includes all the possible rheologies of one-phase media.  相似文献   

10.
There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green's function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green's function. The numerical results demonstrated the accuracy and efficiency of the proposed method.  相似文献   

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