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NASA NTRS2001

Efficiency Improvements to the Displacement Based Multilevel Structural Optimization Algorithm

Multilevel Structural Optimization (MSO) continues to be an area of research interest in engineering optimization. In the present project, the weight optimization of beams and trusses using Displacement based Multilevel Structural Optimization (DMSO), a member of the MSO set of methodologies, is investigated. In the DMSO approach, the optimization task is subdivided into a single system and multiple subsystems level optimizations. The system level optimization minimizes the load unbalance resulting from the use of displacement functions to approximate the structural displacements. The function coefficients are then the design variables. Alternately, the system level optimization can be solved using the displacements themselves as design variables, as was shown in previous research. Both approaches ensure that the calculated loads match the applied loads. In the subsystems level, the weight of the structure is minimized using the element dimensions as design variables. The approach is expected to be very efficient for large structures, since parallel computing can be utilized in the different levels of the problem. In this paper, the method is applied to a one-dimensional beam and a large three-dimensional truss. The beam was tested to study possible simplifications to the system level optimization. In previous research, polynomials were used to approximate the global nodal displacements. The number of coefficients of the polynomials equally matched the number of degrees of freedom of the problem. Here it was desired to see if it is possible to only match a subset of the degrees of freedom in the system level. This would lead to a simplification of the system level, with a resulting increase in overall efficiency. However, the methods tested for this type of system level simplification did not yield positive results. The large truss was utilized to test further improvements in the efficiency of DMSO. In previous work, parallel processing was applied to the subsystems level, where the derivative verification feature of the optimizer NPSOL had been utilized in the optimizations. This resulted in large runtimes. In this paper, the optimizations were repeated without using the derivative verification, and the results are compared to those from the previous work. Also, the optimizations were run on both, a network of SUN workstations using the MPICH implementation of the Message Passing Interface (MPI) and on the faster Beowulf cluster at ICASE, NASA Langley Research Center, using the LAM implementation of UP]. The results on both systems were consistent and showed that it is not necessary to verify the derivatives and that this gives a large increase in efficiency of the DMSO algorithm.

Plunkett, C. L.↗

NASA NTRS2003

Aerodynamic Shape Optimization Using Hybridized Differential Evolution

An aerodynamic shape optimization method that uses an evolutionary algorithm known at Differential Evolution (DE) in conjunction with various hybridization strategies is described. DE is a simple and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems. Various hybridization strategies for DE are explored, including the use of neural networks as well as traditional local search methods. A Navier-Stokes solver is used to evaluate the various intermediate designs and provide inputs to the hybrid DE optimizer. The method is implemented on distributed parallel computers so that new designs can be obtained within reasonable turnaround times. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. (The final paper will include at least one other aerodynamic design application). The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated.

Madavan, Nateri K.↗

NASA NTRS1990

Parallelized reliability estimation of reconfigurable computer networks

A parallelized system, ASSURE, for computing the reliability of embedded avionics flight control systems which are able to reconfigure themselves in the event of failure is described. ASSURE accepts a grammar that describes a reliability semi-Markov state-space. From this it creates a parallel program that simultaneously generates and analyzes the state-space, placing upper and lower bounds on the probability of system failure. ASSURE is implemented on a 32-node Intel iPSC/860, and has achieved high processor efficiencies on real problems. Through a combination of improved algorithms, exploitation of parallelism, and use of an advanced microprocessor architecture, ASSURE has reduced the execution time on substantial problems by a factor of one thousand over previous workstation implementations. Furthermore, ASSURE's parallel execution rate on the iPSC/860 is an order of magnitude faster than its serial execution rate on a Cray-2 supercomputer. While dynamic load balancing is necessary for ASSURE's good performance, it is needed only infrequently; the particular method of load balancing used does not substantially affect performance.

Nicol, David M.↗

NASA NTRS1993

Flexible language constructs for large parallel programs

The goal of the research described is to develop flexible language constructs for writing large data parallel numerical programs for distributed memory (MIMD) multiprocessors. Previously, several models have been developed to support synchronization and communication. Models for global synchronization include SIMD (Single Instruction Multiple Data), SPMD (Single Program Multiple Data), and sequential programs annotated with data distribution statements. The two primary models for communication include implicit communication based on shared memory and explicit communication based on messages. None of these models by themselves seem sufficient to permit the natural and efficient expression of the variety of algorithms that occur in large scientific computations. An overview of a new language that combines many of these programming models in a clean manner is given. This is done in a modular fashion such that different models can be combined to support large programs. Within a module, the selection of a model depends on the algorithm and its efficiency requirements. An overview of the language and discussion of some of the critical implementation details is given.

Rosing, Matthew↗

NASA NTRS1987

Mapping a battlefield simulation onto message-passing parallel architectures

Perhaps the most critical problem in distributed simulation is that of mapping: without an effective mapping of workload to processors the speedup potential of parallel processing cannot be realized. Mapping a simulation onto a message-passing architecture is especially difficult when the computational workload dynamically changes as a function of time and space; this is exactly the situation faced by battlefield simulations. This paper studies an approach where the simulated battlefield domain is first partitioned into many regions of equal size; typically there are more regions than processors. The regions are then assigned to processors; a processor is responsible for performing all simulation activity associated with the regions. The assignment algorithm is quite simple and attempts to balance load by exploiting locality of workload intensity. The performance of this technique is studied on a simple battlefield simulation implemented on the Flex/32 multiprocessor. Measurements show that the proposed method achieves reasonable processor efficiencies. Furthermore, the method shows promise for use in dynamic remapping of the simulation.

Nicol, David M.↗

NASA NTRS1993

Performance analysis of a large-grain dataflow scheduling paradigm

A paradigm for scheduling computations on a network of multiprocessors using large-grain data flow scheduling at run time is described and analyzed. The computations to be scheduled must follow a static flow graph, while the schedule itself will be dynamic (i.e., determined at run time). Many applications characterized by static flow exist, and they include real-time control and digital signal processing. With the advent of computer-aided software engineering (CASE) tools for capturing software designs in dataflow-like structures, macro-dataflow scheduling becomes increasingly attractive, if not necessary. For parallel implementations, using the macro-dataflow method allows the scheduling to be insulated from the application designer and enables the maximum utilization of available resources. Further, by allowing multitasking, processor utilizations can approach 100 percent while they maintain maximum speedup. Extensive simulation studies are performed on 4-, 8-, and 16-processor architectures that reflect the effects of communication delays, scheduling delays, algorithm class, and multitasking on performance and speedup gains.

Young, Steven D.↗

NASA NTRS2003

The Electric Propulsion Interactions Code (EPIC): A Member of the NASA Space Environment and Effects Program (SEE) Toolset

Science Applications International Corporation is currently developing the Electric Propulsion Interactions Code, EPIC, as part of a project sponsored by the Space Environments and Effects Program at NASA Marshall Space Flight Center. Now in its second year of development, EPIC is an interactive computer toolset that allows the construction of a 3-D spacecraft model, and the assessment of a variety of interactions between its subsystems and the plume from an electric thruster. This paper reports on the progress of EPZC including the recently added ability to exchange results the NASA Charging Analyzer Program, Nascap-2k. The capability greatly enhances EPIC's range of applicability. Expansion of the toolset's various physics models proceeds in parallel with the overall development of the software. Also presented are recent upgrades of the elastic scattering algorithm in the electric propulsion Plume Tool. These upgrades are motivated by the need to assess the effects of elastically scattered ions on the SIC for ion beam energies that exceed loo0 eV. Such energy levels are expected in future high-power (>10 kW) ion propulsion systems empowered by nuclear sources.

Mikellides, Ioannis G.↗

NASA NTRS1987

Optimal mapping of irregular finite element domains to parallel processors

Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.

Flower, J.↗

NASA NTRS1999

On the Fast Evaluation Method of Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Planetary Atmospheres in Thermal IR and Microwave

Evaluation of weighting functions in the atmospheric remote sensing is usually the most computer-intensive part of the inversion algorithms. We present an analytic approach to computations of temperature and mixing ratio weighting functions that is based on our previous results but the resulting expressions use the intermediate variables that are generated in computations of observable radiances themselves. Upwelling radiances at the given level in the atmosphere and atmospheric transmittances from space to the given level are combined with local values of the total absorption coefficient and its components due to absorption of atmospheric constituents under study. This makes it possible to evaluate the temperature and mixing ratio weighting functions in parallel with evaluation of radiances. This substantially decreases the computer time required for evaluation of weighting functions. Implications for the nadir and limb viewing geometries are discussed.

Ustinov, E. A.↗

NASA NTRS2004

Fast-Acquisition/Weak-Signal-Tracking GPS Receiver for HEO

A report discusses the technical background and design of the Navigator Global Positioning System (GPS) receiver -- . a radiation-hardened receiver intended for use aboard spacecraft. Navigator is capable of weak signal acquisition and tracking as well as much faster acquisition of strong or weak signals with no a priori knowledge or external aiding. Weak-signal acquisition and tracking enables GPS use in high Earth orbits (HEO), and fast acquisition allows for the receiver to remain without power until needed in any orbit. Signal acquisition and signal tracking are, respectively, the processes of finding and demodulating a signal. Acquisition is the more computationally difficult process. Previous GPS receivers employ the method of sequentially searching the two-dimensional signal parameter space (code phase and Doppler). Navigator exploits properties of the Fourier transform in a massively parallel search for the GPS signal. This method results in far faster acquisition times [in the lab, 12 GPS satellites have been acquired with no a priori knowledge in a Low-Earth-Orbit (LEO) scenario in less than one second]. Modeling has shown that Navigator will be capable of acquiring signals down to 25 dB-Hz, appropriate for HEO missions. Navigator is built using the radiation-hardened ColdFire microprocessor and housing the most computationally intense functions in dedicated field-programmable gate arrays. The high performance of the algorithm and of the receiver as a whole are made possible by optimizing computational efficiency and carefully weighing tradeoffs among the sampling rate, data format, and data-path bit width.

Wintemitz, Luke↗

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 NTRS1980

Asynchronous interactive control systems

A class of interactive control systems is derived by generalizing interactive manipulator control systems. The general structural properties of such systems are discussed and an appropriate general software implementation is proposed. This is based on the fact that tasks of interactive control systems can be represented as a network of a finite set of actions which have specific operational characteristics and specific resource requirements, and which are of limited duration. This has enabled the decomposition of the overall control algorithm into a set of subalgorithms, called subcontrollers, which can operate simultaneously and asynchronously. Coordinate transformations of sensor feedback data and actuator set-points have enabled the further simplification of the subcontrollers and have reduced their conflicting resource requirements. The modules of the decomposed control system are implemented as parallel processes with disjoint memory space communicating only by I/O. The synchronization mechanisms for dynamic resource allocation among subcontrollers and other synchronization mechanisms are also discussed in this paper. Such a software organization is suitable for the general form of multiprocessing using computer networks with distributed storage.

Vuskovic, M. I.↗

NASA NTRS1984

Numerical simulation of the interaction of a vortex with stationary airfoil in transonic flow

A perturbation form of an implicit conservative, noniterative numerical algorithm for the two-dimensional thin layer Navier-Stokes and Euler equations is used to compute the interaction flow-field of a vortex with stationary airfoil. A Lamb-like analytical vortex having a finite core is chosen to interact with a thick (NACA 0012) and a thin (NACA 64A006) airfoil independently in transonic flow. Two different configurations of vortex interaction are studied, viz., (1) when the vortex is fixed at one location in the flowfield, and (2) when the vortex is convecting past the airfoil at freestream velocity. Parallel computations of this interacting flowfield are also done using a version of the Transonic Small Disturbance Code (ATRAN2). A special treatment of the leading edge region for thin airfoils is included in this code. With this, the three methods gave qualitatively similar results for the weaker interactions considered in this study. However, the strongest interactions considered proved to be beyond the capabilities of the small disturbance code. The results also show a far greater influence of the vortex on the airfoil flowfield when the vortex is stationary than when it is convecting with the flow.

Srinivasan, G. R.↗

NASA NTRS2000

A Parallel Approach To Optimum Actuator Selection With a Genetic Algorithm

Recent discoveries in smart technologies have created a variety of aerodynamic actuators which have great potential to enable entirely new approaches to aerospace vehicle flight control. For a revolutionary concept such as a seamless aircraft with no moving control surfaces, there is a large set of candidate locations for placing actuators, resulting in a substantially larger number of combinations to examine in order to find an optimum placement satisfying the mission requirements. The placement of actuators on a wing determines the control effectiveness of the airplane. One approach to placement Maximizes the moments about the pitch, roll, and yaw axes, while minimizing the coupling. Genetic algorithms have been instrumental in achieving good solutions to discrete optimization problems, such as the actuator placement problem. As a proof of concept, a genetic has been developed to find the minimum number of actuators required to provide uncoupled pitch, roll, and yaw control for a simplified, untapered, unswept wing model. To find the optimum placement by searching all possible combinations would require 1,100 hours. Formulating the problem and as a multi-objective problem and modifying it to take advantage of the parallel processing capabilities of a multi-processor computer, reduces the optimization time to 22 hours.

Rogers, James L.↗

NASA NTRS1992

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗

NASA NTRS1995

Newton-Krylov-Schwarz: An implicit solver for CFD

Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

Cai, Xiao-Chuan↗

NASA NTRS2018

The Convergence of Analysis Produced by Overlapping Assimilation Streams

When conducting a reanalysis for a long period, it is common to do so using multiple, parallel computational schemes. A period of overlap is included to foster continuity between successive streams. At the GMAO, the overlap period is one year. By the end of that period, the time mean anlysis for corresponding overlapped months are almost identical, as desired. The variances of differences at corresponding analysis times within each month, however, do not converge to zero. Instead their monthly variances converge to values that are a significant fraction of the the estimated variances of analysis errors. This occurs although the overlapping streams use the same observations, assimilation model, and assimilation algorithm, differing only in the background applied information applied at the beginning of the overlap period.

Errico, Ronald M.↗

NASA NTRS1982

Profiles of electrified drops and bubbles

Axisymmetric equilibrium shapes of conducting drops and bubbles, (1) pendant or sessile on one face of a circular parallel-plate capacitor or (2) free and surface-charged, are found by solving simultaneously the free boundary problem consisting of the augmented Young-Laplace equation for surface shape and the Laplace equation for electrostatic field, given the surface potential. The problem is nonlinear and the method is a finite element algorithm employing Newton iteration, a modified frontal solver, and triangular as well as quadrilateral tessellations of the domain exterior to the drop in order to facilitate refined analysis of sharply curved drop tips seen in experiments. The stability limit predicted by this computer-aided theoretical analysis agrees well with experiments.

Basaran, O. A.↗