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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Multigrid with Overlapping Patches

Solving boundary value problems with optimal efficiency requires adaptivity and multilevel techniques. Previously, an implementation of the AFACx algorithm is presented that is based on rectangular Cartesian grids. This implementation does not allow for the over]ap of grids that lie on the same level of refinement. We investigate the case in which these grids overlap. A standard technique for overlapping grids is the Schwarz algorithm. Some ways of using the Schwarz algorithm in a standard multigrid scheme are presented. Also, a problem that arises in some situations with non-aligned, overlapping grids is described. This situation comes up in a natural way when the Schwarz algorithm is used as a relaxation scheme within a multilevel algorithm. We identify the reason for the bad convergence and show that by more sophisticated interpolation the difficulties can be overcome. Then we present a multiplicative Schwarz algorithm for a large number of grids that has a high potential for parallelization. Finally we give some numerical results for the FACx algorithm with overlapping grids on each refinement level. The implementation of the described codes uses C++ and the array class libraries A++ and P++. Using the A++/P++ programming environment, it was possible to move from a serial code to a parallel code within a few days.

Berndt, Markus↗
NASA NTRS2001

Tools and Techniques for Measuring and Improving Grid Performance

This viewgraph presentation provides information on NASA's geographically dispersed computing resources, and the various methods by which the disparate technologies are integrated within a nationwide computational grid. Many large-scale science and engineering projects are accomplished through the interaction of people, heterogeneous computing resources, information systems and instruments at different locations. The overall goal is to facilitate the routine interactions of these resources to reduce the time spent in design cycles, particularly for NASA's mission critical projects. The IPG (Information Power Grid) seeks to implement NASA's diverse computing resources in a fashion similar to the way in which electric power is made available.

Biswas, Rupak↗
NASA NTRS2004

Complexity Computational Environment: Data Assimilation SERVOGrid

We are using Web (Grid) service technology to demonstrate the assimilation of multiple distributed data sources (a typical data grid problem) into a major parallel high-performance computing earthquake forecasting code. Such a linkage of Geoinformatics with Geocomplexity demonstrates the value of the Solid Earth Research Virtual Observatory (SERVO) Grid concept, and advance Grid technology by building the first real-time large-scale data assimilation grid Here we develop the next steps for both the SERVO concept and the identified need for a Solid Earth problem-solving environment. We use a challenging motivating problem of importance to NASA namely integrating NASA space geodetic observations with numerical simulations of a changing earth.

data assimiliation↗
NASA NTRS2004

QuakeSim and the Solid Earth Research Virtual Observatory

We are developing simulation and analysis tools in order to develop a solid Earth science framework for understanding and studying active tectonic and earthquake processes. The goal of QuakeSim and its extension, the Solid Earth Research Virtual Observatory (SERVO), is to study the physics of earthquakes using state-of-the-art modeling, data manipulation, and pattern recognition technologies. We are developing clearly defined accessible data formats and code protocols as inputs to simulations, which are adapted to high-performance computers. The solid Earth system is extremely complex and nonlinear resulting in computationally intensive problems with millions of unknowns. With these tools it will be possible to construct the more complex models and simulations necessary to develop hazard assessment systems critical for reducing future losses from major earthquakes. We are using Web (Grid) service technology to demonstrate the assimilation of multiple distributed data sources (a typical data grid problem) into a major parallel high-performance computing earthquake forecasting code. Such a linkage of Geoinformatics with Geocomplexity demonstrates the value of the Solid Earth Research Virtual Observatory (SERVO) Grid concept, and advances Grid technology by building the first real-time large-scale data assimilation grid.

virtual observatory↗
NASA NTRS1998

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required a fine initial mesh. Results indicate that our parallel load balancing strategy will remain viable on large numbers of processors.

Oliker, Leonid↗
NASA NTRS1994

Design and implementation of a parallel unstructured Euler solver using software primitives

This paper is concerned with the implementation of a three-dimensional unstructured-grid Euler solver on massively parallel distributed-memory computer architectures. The goal is to minimize solution time by achieving high computational rates with a numerically efficient algorithm. An unstructured multigrid algorithm with an edge-based data structure has been adopted, and a number of optimizations have been devised and implemented to accelerate the parallel computational rates. The implementation is carried out by creating a set of software tools, which provide an interface between the parallelization issues and the sequential code, while providing a basis for future automatic run-time compilation support. Large practical unstructured grid problems are solved on the Intel iPSC/860 hypercube and Intel Touchstone Delta machine. The quantitative effects of the various optimizations are demonstrated, and we show that the combined effect of these optimizations leads to roughly a factor of 3 performance improvement. The overall solution efficiency is compared with that obtained on the Cray Y-MP vector supercomputer.

Das, R.↗
NASA NTRS1992

The design and implementation of a parallel unstructured Euler solver using software primitives

This paper is concerned with the implementation of a three-dimensional unstructured grid Euler-solver on massively parallel distributed-memory computer architectures. The goal is to minimize solution time by achieving high computational rates with a numerically efficient algorithm. An unstructured multigrid algorithm with an edge-based data structure has been adopted, and a number of optimizations have been devised and implemented in order to accelerate the parallel communication rates. The implementation is carried out by creating a set of software tools, which provide an interface between the parallelization issues and the sequential code, while providing a basis for future automatic run-time compilation support. Large practical unstructured grid problems are solved on the Intel iPSC/860 hypercube and Intel Touchstone Delta machine. The quantitative effect of the various optimizations are demonstrated, and we show that the combined effect of these optimizations leads to roughly a factor of three performance improvement. The overall solution efficiency is compared with that obtained on the CRAY-YMP vector supercomputer.

Das, R.↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Inviscid Fluxes

Cell-centered and node-centered approaches have been compared for unstructured finite-volume discretization of inviscid fluxes. The grids range from regular grids to irregular grids, including mixed-element grids and grids with random perturbations of nodes. Accuracy, complexity, and convergence rates of defect-correction iterations are studied for eight nominally second-order accurate schemes: two node-centered schemes with weighted and unweighted least-squares (LSQ) methods for gradient reconstruction and six cell-centered schemes two node-averaging with and without clipping and four schemes that employ different stencils for LSQ gradient reconstruction. The cell-centered nearest-neighbor (CC-NN) scheme has the lowest complexity; a version of the scheme that involves smart augmentation of the LSQ stencil (CC-SA) has only marginal complexity increase. All other schemes have larger complexity; complexity of node-centered (NC) schemes are somewhat lower than complexity of cell-centered node-averaging (CC-NA) and full-augmentation (CC-FA) schemes. On highly anisotropic grids typical of those encountered in grid adaptation, discretization errors of five of the six cell-centered schemes converge with second order on all tested grids; the CC-NA scheme with clipping degrades solution accuracy to first order. The NC schemes converge with second order on regular and/or triangular grids and with first order on perturbed quadrilaterals and mixed-element grids. All schemes may produce large relative errors in gradient reconstruction on grids with perturbed nodes. Defect-correction iterations for schemes employing weighted least-square gradient reconstruction diverge on perturbed stretched grids. Overall, the CC-NN and CC-SA schemes offer the best options of the lowest complexity and secondorder discretization errors. On anisotropic grids over a curved body typical of turbulent flow simulations, the discretization errors converge with second order and are small for the CC-NN, CC-SA, and CC-FA schemes on all grids and for NC schemes on triangular grids; the discretization errors of the CC-NA scheme without clipping do not converge on irregular grids. Accurate gradient reconstruction can be achieved by introducing a local approximate mapping; without approximate mapping, only the NC scheme with weighted LSQ method provides accurate gradients. Defect correction iterations for the CC-NA scheme without clipping diverge; for the NC scheme with weighted LSQ method, the iterations either diverge or converge very slowly. The best option in curved geometries is the CC-SA scheme that offers low complexity, second-order discretization errors, and fast convergence.

Diskin, Boris↗
NASA NTRS1989

A numerically exact full wave packet approach to molecule-surface scattering

A numerically exact spectral method for solving the time-dependent Schroedinger equation in spherical coordinates is described. The angular dependence of the wave function is represented on a two-dimensional grid of evenly spaced points. The fast Fourier transform algorithm is used to transform between the angle space representation of the wave function and its conjugate representation in momentum space. The time propagation of the wave function is evaluated using an expansion of the time evolution operator as a series of Chebyshev polynomials. Calculations performed for a model system representing H2 scattering from a rectangular corrugated surface yield transition probabilities that are in excellent agreement with those obtained using the close-coupling wave packet (CCWP) method. However, the new method is found to require substantially more computation time than the CCWP method because of the large number of grid points needed to represent the angular dependence of the wave function and the variation in the number of terms required in the Chebyshev representation of the time evolution operator.

Mowrey, R. C.↗
NASA NTRS1998

MOLA Topography of Impact Basins in the Northern Hemisphere of Mars

Coverage of the northern hemisphere of Mars by the Mars Orbiter Laser Altimeter (MOLA) during the aerobraking hiatus and the two Science Phasing Operation periods provides improved definition and characterization of large impact basins. Gridded MOLA data show the Utopia Basin has a pronounced bowl-like structure, as opposed to the interior rises suggested by the earlier USGS DEM. The elevation structure is concentric about the basin center as mapped by McGill. In particular, the proposed inner ring closely follows the -4 km contour over much of the southern, western and northwestern sides. Higher topography along portions of the dichotomy boundary aligns with the basin's outer ring. High topography in the polar region also occurs where the outer ring should lie, raising the possibility that perhaps some of the polar topography is due to basin structure as well as ice. Two MOLA passes near Phison Rupes provide evidence for a large "stealth" hole where Viking imagery show little evidence of any major structure. The 2 km deep, 600 km wide depression at 31OW, 3ON is as large as the Cassini impact basin 1000 km to the SW. While Cassini is easily recognized in image data, the "MOLA Hole" is not. If this depression is a deeply eroded and buried impact basin (as perhaps suggested by a decrease in the crater density and somewhat smoother terrain than in adjacent areas), it is not clear why it has managed to maintain its great depth. In Tempe at the dichotomy boundary a 300 km wide impact basin is revealed by pronounced bowl-like topography centered at 87W, 47N, even though only about 1/3 of the basin rim structure is obvious. The basin lies on a sloping boundary zone, with the more buried N rim up to 2 km below the rugged S rim. A similar N-S asymmetry in basin ring structure occurs for the much larger Isidis Basin, where the S rim rises 6 km but the subdued N rim rises barely 2 km above the floor. There is essentially no topographic expression of the main ring in the NE quadrant of Isidis where, if it exists, it lies below Hesperian-age plains.

Frey, Herbert↗
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 NTRS1994

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Tam, Christopher K. W.↗
NASA NTRS1981

Comparison of the Nimbus-4 BUV ozone data with the Ames two-dimensional model

Predictions by the Ames two-dimensional model of altitude, latitude and seasonal variations in ozone distribution are compared with the first two years of Nimbus 4 backscattered ultraviolet (BUV) measurements in a preliminary attempt at model verification. The ozone observations consist of mixing ratios on the 1-, 2-, 5-, and 10-mbar pressure surfaces zonally and time averaged to obtain seasonal means for 1970 and 1971. The model is based on chemical reaction and photolysis rate constants recommended by the NASA Panel for Data Evaluation (1979), diurnally averaged for latitudes from 80 deg N to 80 deg S and altitudes from 0 to 60 km with 5 deg horizontal and 2.5 km vertical grid spacings. The large altitude, latitude and seasonal variations observed in the data are found to agree well with model predictions. Examination of the sensitivity of the model predictions to various assumed parameters indicates that improvements in agreement may be obtained by variations of the odd chlorine mixing ratio, odd-nitrogen level and transport parameters.

Borucki, W. J.↗
NASA NTRS1983

Theoretical investigations of high lift aerodynamics

A program which generates a coordinate system for a two element airfoil with the mesh points concentrated in areas of significant vorticity, i.e., boundary layer and wake is operational. The 'imbedded' grid method developed allows a transition from the scale of the main airfoil to the scale of the flap. This requirement is essential for the modeling of viscous flows over the flap and slat of a multielement airfoil. An airfoil mounted in a 2-D wind tunnel was formulated. The program is ready for a fine grid and a large number of planes to explore the characteristics of a Navier-Stokes solver in a quasi-3D case. The program was converted to a form suitable for the STAR computer. Runs were made to map a three dimensional flow field for a wall airfoil intersection with and without lift.

Bennett, G.↗
NASA NTRS1983

Interplanetary magnetic field and tropospheric circulation

The relation between interplanetary magnetic sector boundary crossings and areas of high vorticity in the troposphere that was reported during 1963-1973 cannot be investigated in the years after 1973 because of changes in the processing of the 500 mb height grids prepared by the National Meteorological Center. In particular, we cannot say that the effect disappeared. The same applies to vorticity computed from NMC winds grids. The Limited Area Fine Mesh grid has a large noise in computed vorticity after December 3, 1974. Therefore the interesting analysis of Larsen and Kelley cannot be extended. They had found that forecasts of Vorticity Area Index were significantly poorer after a sector boundary. Previously announced in STAR as N83-25251

Wilcox, J. M.↗
NASA NTRS1989

Use of GEMPAK at NMC

This paper considers the use of the General Meteorological Package (GEMPAK) system developed by the NASA Goddard Space Flight Center. The interactive capabilites included in the GEMPAK are examined, and the changes of GEMPACK necessary for the accommodation of the large volume of gridded NMC data are discussed. Some preliminary results are presented.

Petersen, Ralph A.↗
NASA NTRS1992

Numerical solutions for heat flow in adhesive lap joints

The present formulation for the modeling of heat transfer in thin, adhesively bonded lap joints precludes difficulties associated with large aspect ratio grids required by standard FEM formulations. This quasi-static formulation also reduces the problem dimensionality (by one), thereby minimizing computational requirements. The solutions obtained are found to be in good agreement with both analytical solutions and solutions from standard FEM programs. The approach is noted to yield a more accurate representation of heat-flux changes between layers due to a disbond.

Howell, P. A.↗
NASA NTRS1993

Energy considerations in computational aeroacoustics

A finite-volume multistage time-stepping Euler code is used to investigate the use of CFD algorithms for the direct calculation of acoustics. The 2D compressible inviscid flow about an accelerating or decelerating circular cylinder is used as a model problem. The time evolution of the energy transfer from the cylinder to the fluid, as the cylinder is moved from rest to some nonnegligible velocity, is clearly seen. By examining the temporal and spatial characteristics of the numerical solution, a distinction can be made between the propagating acoustic energy, the convecting energy associated with the entropy change in the fluid, and the energy contained in the local aerodynamic field. Systematic variation of the cylinder acceleration shows that the radiated acoustic energy depends strongly upon the rate of acceleration or deceleration. The computational grid has a large effect on the ratio of acoustic energy to nonphysical entropy associated energy, while the role of the explicit artificial viscosity seems to be of second order. The entropy term was nearly negligible in all cases the cylinder was started slowly.

Brentner, Kenneth S.↗