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NASA NTRS1993

An object-oriented approach for parallel self adaptive mesh refinement on block structured grids

Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.

Lemke, Max↗
NASA NTRS1993

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Debussche, A.↗
NASA NTRS1993

Value added data archiving

Researchers in the Molecular Sciences Research Center (MSRC) of Pacific Northwest Laboratory (PNL) currently generate massive amounts of scientific data. The amount of data that will need to be managed by the turn of the century is expected to increase significantly. Automated tools that support the management, maintenance, and sharing of this data are minimal. Researchers typically manage their own data by physically moving datasets to and from long term storage devices and recording a dataset's historical information in a laboratory notebook. Even though it is not the most efficient use of resources, researchers have tolerated the process. The solution to this problem will evolve over the next three years in three phases. PNL plans to add sophistication to existing multilevel file system (MLFS) software by integrating it with an object database management system (ODBMS). The first phase in the evolution is currently underway. A prototype system of limited scale is being used to gather information that will feed into the next two phases. This paper describes the prototype system, identifies the successes and problems/complications experienced to date, and outlines PNL's long term goals and objectives in providing a permanent solution.

Berard, Peter R.↗
NASA NTRS1994

Hierarchically Parallelized Constrained Nonlinear Solvers with Automated Substructuring

This paper develops a parallelizable multilevel multiple constrained nonlinear equation solver. The substructuring process is automated to yield appropriately balanced partitioning of each succeeding level. Due to the generality of the procedure,_sequential, as well as partially and fully parallel environments can be handled. This includes both single and multiprocessor assignment per individual partition. Several benchmark examples are presented. These illustrate the robustness of the procedure as well as its capability to yield significant reductions in memory utilization and calculational effort due both to updating and inversion.

Padovan, Joe↗
NASA NTRS1993

An observing system simulation experiment for the Laser Atmospheric Wind Sounder (LAWS)

The present observing system-simulation experiments evaluate the potential of a Laser Atmospheric Wind Sounder (LAWS) instrument for 5-day forecasting, using a primitive-equation multilevel spectral global circulation model. A 55-deg-inclined and a 98-deg sun-synchronous orbit are examined, by adding LAWS wind profiles into a global 4D data-assimilation system, and comparing both the analyses and forecasts to a control experiment. The 4D data-assimilation system consists of a multivariate optimum interpolation analysis and a nonlinear, normal-mode intialization, using the aforementioned global circulation model.

Rohaly, G. D.↗
NASA NTRS1993

A fast algorithm for parallel computation of multibody dynamics on MIMD parallel architectures

In this paper the implementation of a parallel O(LogN) algorithm for computation of rigid multibody dynamics on a Hypercube MIMD parallel architecture is presented. To our knowledge, this is the first algorithm that achieves the time lower bound of O(LogN) by using an optimal number of O(N) processors. However, in addition to its theoretical significance, the algorithm is also highly efficient for practical implementation on commercially available MIMD parallel architectures due to its highly coarse grain size and simple communication and synchronization requirements. We present a multilevel parallel computation strategy for implementation of the algorithm on a Hypercube. This strategy allows the exploitation of parallelism at several computational levels as well as maximum overlapping of computation and communication to increase the performance of parallel computation.

Fijany, Amir↗
NASA NTRS1994

Evaluation of iconic versus F-map microburst displays

Previous studies have shown graphical presentation methods of hazardous wind shear to be superior to textual or audible warnings alone. Positional information and the strength of the hazard were observed to be and were cited by pilots as the most important factors in a display. In this experiment the use of the three different graphical presentations of hazardous wind shear are examined. Airborne predictive detectors of wind shear enable the dissemination of varying levels of information. The effectiveness of iconic and mapping display modes of different complexities are addressed through simulation and analysis. Different positional and time-varying situations are presented in a 'part-task' Boeing 767 simulator using data from actual microburst events. Experienced airline pilots fly approach profiles using both iconic and F-map wind shear alerting displays. Microburst accompanied each event is also shown to the pilot. Mapping display types are expected to be found exceptionally efficient at conveying location comparison information while iconic displays simplify the threat recognition process. Preliminary results from the simulator study are presented. Recommendations concerning the suitability of multilevel iconic and mapping displays are made. Situational problems with current display prototypes are also addressed.

Salzberger, Mark↗
NASA NTRS1994

The Design Manager's Aid for Intelligent Decomposition (DeMAID)

Before the design of new complex systems such as large space platforms can begin, the possible interactions among subsystems and their parts must be determined. Once this is completed, the proposed system can be decomposed to identify its hierarchical structure. The design manager's aid for intelligent decomposition (DeMAID) is a knowledge based system for ordering the sequence of modules and identifying a possible multilevel structure for design. Although DeMAID requires an investment of time to generate and refine the list of modules for input, it could save considerable money and time in the total design process, particularly in new design problems where the ordering of the modules has not been defined.

Rogers, James L.↗
NASA NTRS1994

On the application of under-decimated filter banks

Maximally decimated filter banks have been extensively studied in the past. A filter bank is said to be under-decimated if the number of channels is more than the decimation ratio in the subbands. A maximally decimated filter bank is well known for its application in subband coding. Another application of maximally decimated filter banks is in block filtering. Convolution through block filtering has the advantages that parallelism is increased and data are processed at a lower rate. However, the computational complexity is comparable to that of direct convolution. More recently, another type of filter bank convolver has been developed. In this scheme, the convolution is performed in the subbands. Quantization and bit allocation of subband signals are based on signal variance, as in subband coding. Consequently, for a fixed rate, the result of convolution is more accurate than is direct convolution. This type of filter bank convolver also enjoys the advantages of block filtering, parallelism, and a lower working rate. Nevertheless, like block filtering, there is no computational saving. In this article, under-decimated systems are introduced to solve the problem. The new system is decimated only by half the number of channels. Two types of filter banks can be used in the under-decimated system: the discrete Fourier transform (DFT) filter banks and the cosine modulated filter banks. They are well known for their low complexity. In both cases, the system is approximately alias free, and the overall response is equivalent to a tunable multilevel filter. Properties of the DFT filter banks and the cosine modulated filter banks can be exploited to simultaneously achieve parallelism, computational saving, and a lower working rate. Furthermore, for both systems, the implementation cost of the analysis or synthesis bank is comparable to that of one prototype filter plus some low-complexity modulation matrices. The individual analysis and synthesis filters have complex coefficients in the DFT filter banks but have real coefficients in the cosine modulated filter banks.

Lin, Y.-P.↗
NASA NTRS1995

Nonlinear structural analysis on distributed-memory computers

A computational strategy is presented for the nonlinear static and postbuckling analyses of large complex structures on massively parallel computers. The strategy is designed for distributed-memory, message-passing parallel computer systems. The key elements of the proposed strategy are: (1) a multiple-parameter reduced basis technique; (2) a nested dissection (or multilevel substructuring) ordering scheme; (3) parallel assembly of global matrices; and (4) a parallel sparse equation solver. The effectiveness of the strategy is assessed by applying it to thermo-mechanical postbuckling analyses of stiffened composite panels with cutouts, and nonlinear large-deflection analyses of HSCT models on Intel Paragon XP/S computers. The numerical studies presented demonstrate the advantages of nested dissection-based solvers over traditional skyline-based solvers on distributed memory machines.

Watson, Brian C.↗
NASA NTRS1995

Postbuckling and large-deflection nonlinear analyses on distributed-memory computers

A computational strategy is presented for postbuckling and nonlinear static analyses of large complex structures on distributed-memory parallel computers. The strategy is designed for message-passing parallel computer systems. The key elements of the proposed strategy are: (1) a multiple-parameter reduced basis technique; (2) a nested dissection (or multilevel substructuring) ordering scheme; (3) parallel assembly of global matrices; and (4) a parallel sparse equation solver. The effectiveness of the strategy is assessed by performing thermomechanical postbuckling analyses of stiffened composite panels with cutouts, and nonlinear large-deflection analyses of High Speed Civil Transport models on three distributed-memory computers. The numerical studies presented demonstrate the advantages of nested dissection-based solvers over traditional skyline-based solvers on distributed-memory machines.

Watson, Brian C.↗
NASA NTRS1992

Towards a fast implementation of spectral nested dissection

We describe the spectral nested dissection (SND) algorithm, a new algorithm for computing orderings appropriate for parallel factorization of sparse, symmetric matrices. The algorithm makes use of spectral properties of the Laplacian matrix associated with the given matrix to compute separators. We evaluate the quality of the spectral orderings with respect to several measures: fill, elimination tree height, height and weight balances of elimination trees, and clique tree heights. We use some very large structural analysis problems as test cases and demonstrate on these real applications (such as the Space Shuttle Solid Rocket Booster) that spectral orderings compare quite favorably with commonly used orderings, outperforming them by a wide margin for some of these measures. The only disadvantage of SND is its relatively long execution time. We will present some recent efforts to improve the execution time using both a multilevel and a hybrid approach. We use SND in computing a multifrontal numerical factorization with the different orderings on an eight processor Cray Y-MP and show its effectiveness. We believe that spectral nested dissection is a major breakthrough in terms of generating efficient sparse orderings for parallel machines.

Pothen, Alex↗
NASA NTRS1994

Emission-line studies of young stars. 4: The optical forbidden lines

Optical forbidden line strengths and profiles are discussed for a sample of 30 T Tauri stars and 12 Herbig Ae-Be stars. Transitions of (C I), (N II), (O I), (O II), (S II), (Ca II), (Cr II), (Fe II), and (Ni II) are detected. Profile variability occurred in DG Tau and probably other sources. The ensemble profiles can be divided into four generic components that may represent distinct emitting regions; (1) narrow rest-velocity lines, (2) 'low'-velocity lines (peaking at less than or approximately +/- 50 km s(exp -1)), (3) 'high'-velocity (usually greater than or approximately +/- 100 km s(exp -1)) blueshifted peaks or wings, and (4) high-velocity redshifted peaks. Among T Tauri stars, the rest-velocity lines appear most often in sources with weak and narrow permitted lines, such as the Ca II triplet. The low- and high-velocity blueshifted components usually appear together in sources with strong and broad Ca II triplet lines. If the velocity-shifted lines form in jets, the smallest (full) opening angles required by the profiles are less than or approximately 20 deg for the narrow, blueshifted (Ca II) lines of DG Tau and HL Tau. Other lines in DG Tau are much broader, implying larger opening angles or greater velocity dispersions. The variability in DG Tau also implies significant changes in the collimation or velocity coherence on timescales of a few years. RW Aur and AS 353A have blue- and redshifted line peaks that could form in oppositely directed jets. The strong (S II) lambda 6716 and lambda 6731 lines in RW Aur are exclusively redshifted and require opening angles less than or approximately 60 deg. Measurements of different profiles in the same spectrum show that the physical conditions change with the line-of-sight velocities. The most persistent trends are for more (N II) and (O II) and less (O I) lambda 5577 flux at high velocities. Constraints on the physical conditions are derived by modeling the emission lines via multilevel ions in 'coronal ionization equilibrium.' A single temperature and density cannot fully describe the line spectra in any velocity interval. Temperatures in the (O I) region are 9000 less than or approximately T(sub e) less than 14,000 K, and the ionization fraction (of H) is less than 35%. The densities derived from (O I) include n(sub e) less than or approximately 5 x 10(exp 5) to approximately 10(exp 7) cm(exp -3), but n(sub e) greater than or approximately 10(exp 6) cm(exp -3) obtains only at low velocities. In the (S II) regions the densities are lower, 10(exp 3) less than or approximately n(sub e) less than or approximately 7 x 10(exp 4) cm(exp -3), and the temperatures are probably higher, T(sub e) greater than or approximately 13,000 K. At high velocities (only) there is additional hot gas that produces (N II) and (O II), possibly most of the (S II), and little (O I). This region is characterized by T(sub e) greater than or approximately 15,000 K, n(sub e) less than or approximately 10(exp 5) cm(exp -3), and an ionization fraction greater than or approximately 50%. When combined with the spatially segregated emitting regions observed by others by spectral imaging, these results suggest decreasing n(sub e) and increasing T(sub e) away from the star in at least the high velocity gas.

Hamann, Fred↗
NASA NTRS1994

Evidence for Ni-56 yields Co-56 yields Fe-56 decay in type Ia supernovae

In the prevailing picture of Type Ia supernovae (SN Ia), their explosive burning produces Ni-56, and the radioactive decay chain Ni-56 yields Co-56 yields Fe-56 powers the subsequent emission. We test a central feature of this theory by measuring the relative strengths of a (Co III) emission feature near 5900 A and a (Fe III) emission feature near 4700 A. We measure 38 spectra from 13 SN Ia ranging from 48 to 310 days after maximum light. When we compare the observations with a simple multilevel calculation, we find that the observed Fe/Co flux ratio evolves as expected when the Fe-56/Co-56 abundance ratio follows from Ni-56 yields Co-56 yields Fe-56 decay. From this agreement, we conclude that the cobalt and iron atoms we observe through SN Ia emission lines are produced by the radioactive decay of Ni-56, just as predicted by a wide range of models for SN Ia explosions.

Kuchner, Marc J.↗
NASA NTRS1994

Modeling radiative transfer in molecular clouds. 1: HCO(+) in the star-forming region W49A North

A new general multilevel, non-Local Thermodynamic Equilibrium (LTE) radiative transfer code, valid for any velocity field, is applied to HCO(+) observations of W49A North. Three classes of collapse models are considered: free-fall collapse (v proportional to 1/sq. root of r), rho proportional to r(exp -3/2) throughout the molecular cloud, successfully reproduces the features of the observations and gives the best fit to the J = 1-0 and J = 3-2 profiles both toward the prominent H II component G of W49A North and off the center. In addition to a slow radial fall-off of density, the theoretical modeling implies the following for the molecular cloud: the large line widths result from motions occurring within the inner 1 pc, and there are probably one or more fragments with peculiar velocities within this same region.

Dickel, Helene R.↗
NASA NTRS1994

Buckling and vibration analysis of laminated panels using VICONOPT

The analysis aspects of the 23,000-line FORTRAN program VIPASA with constraints and optimization (VICONOPT) are described. Overall stiffness matrices assembled from the earlier exact vibration and instability of plate assemblies including shear and anisotropy (VIPASA) flat plate stiffnesses are optionally coupled by Langrangian multipliers to find critical buckling loads, or natural frequencies of undamped vibration, of prismatic assemblies of anisotropic flat plates with arbitrarily located point supports or simple transverse supporting frames. The longitudunal continuity of typical wing and fuselage panels is closely approximated because the solutions are for the infinitely long structure obtained by repeating a bay and its supports longitudinally. Any longitudinally invariant in-plane plate stresses are permitted, and very rapid solutions are guaranteed by numerous refinements, including multilevel substructuring and a method for repetitive cross sections that is exact for regular polygons used to represent cylinders. Modal displacements and stresses in or between plies of laminated plates are calculated and plotted, with values being recovered at all nodes of substructures. Comparison with usual approximate finite-element methods confirms that, for comparably converged solutions, VICONOPT is typically between 100 and 10(exp 4) times faster.

Kennedy, David↗
NASA NTRS1995

Program Helps Decompose Complex Design Systems

DeMAID (Design Manager's Aid for Intelligent Decomposition) computer program is knowledge-based software system for ordering sequence of modules and identifying possible multilevel structure for design problems such as large platforms in outer space. Groups modular subsystems on basis of interactions among them. Saves considerable amount of money and time in total design process, particularly in new design problem in which order of modules has not been defined. Originally written for design problems, also applicable to problems containing modules (processes) that take inputs and generate outputs. Available in three machine versions: Macintosh written in Symantec's Think C 3.01, Sun, and SGI IRIS in C language.

Rogers, James L., Jr.↗
NASA NTRS1995

Multidisciplinary design optimization using multiobjective formulation techniques

This report addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for calculating computational grid sensitivities and aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The developed sensitivity analysis technique are then used within a multidisciplinary optimization procedure for designing aerospace vehicles. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The proceduredeveloped is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the aircraft aerodynamic and structural performance when compared to a reference or baseline configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

Chattopadhyay, Aditi↗