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At least 109 records · Page 6

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Nguyen, D. T.↗

Multiaxis Rainflow Fatigue Methods for Nonstationary Vibration

Mechanical structures and components may be subjected to cyclical loading conditions, including sine and random vibration. Such systems must be designed and tested accordingly. Rainflow cycle counting is the standard method for reducing a stress time history to a table of amplitude-cycle pairings prior to the Palmgren-Miner cumulative damage calculation. The damage calculation is straightforward for sinusoidal stress but very complicated for random stress, particularly for nonstationary vibration. This paper evaluates candidate methods and makes a recommendation for further study of a hybrid technique.

Irvine, T.↗

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

The use of hybrid integrated circuit techniques in biotelemetry applications

A review is presented of some features of hybrid integrated circuits that make their use advantageous in miniature biotelemetry applications. The various techniques for fabricating resistors, capacitors and interconnections by both thin film and thick film technology are discussed. The use of chip capacitors, resistors, and especially standard IC chips on substrates with fired-on interconnection patterns is emphasized. The review is designed primarily to acquaint biotelemetry users and designers with an overview of this fabrication technique so that they can better communicate their needs with an understanding of its limitations and advantages to facilities specializing in hybrid construction.

Fryer, T. B.↗

A hybrid perturbation Galerkin technique with applications to slender body theory

A two step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

A hybrid perturbation Galerkin technique with applications to slender body theory

A two-step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

A hybrid perturbation-Galerkin technique for partial differential equations

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Geer, James F.↗

A hybrid Pade-Galerkin technique for differential equations

A three-step hybrid analysis technique, which successively uses the regular perturbation expansion method, the Pade expansion method, and then a Galerkin approximation, is presented and applied to some model boundary value problems. In the first step of the method, the regular perturbation method is used to construct an approximation to the solution in the form of a finite power series in a small parameter epsilon associated with the problem. In the second step of the method, the series approximation obtained in step one is used to construct a Pade approximation in the form of a rational function in the parameter epsilon. In the third step, the various powers of epsilon which appear in the Pade approximation are replaced by new (unknown) parameters (delta(sub j)). These new parameters are determined by requiring that the residual formed by substituting the new approximation into the governing differential equation is orthogonal to each of the perturbation coordinate functions used in step one. The technique is applied to model problems involving ordinary or partial differential equations. In general, the technique appears to provide good approximations to the solution even when the perturbation and Pade approximations fail to do so. The method is discussed and topics for future investigations are indicated.

Geer, James F.↗

Coupling Turbulence in Hybrid LES-RANS Techniques

A formulation is proposed for hybrid LES-RANS computations that permits accurate computations during resolution changes, so that resolution may be changed at will in order to employ only as much resolution in each subdomain as is required by the physics. The two components of this formulation, establishing the accuracy of a hybrid model at constant resolutions throughout the RANS-to-LES range and maintaining that accuracy when resolution is varied, are demonstrated for decaying, homogeneous, isotropic turbulence.

Woodruff, Stephen L.↗

Locomotion training of legged robots using hybrid machine learning techniques

In this study artificial neural networks and fuzzy logic are used to control the jumping behavior of a three-link uniped robot. The biped locomotion control problem is an increment of the uniped locomotion control. Study of legged locomotion dynamics indicates that a hierarchical controller is required to control the behavior of a legged robot. A structured control strategy is suggested which includes navigator, motion planner, biped coordinator and uniped controllers. A three-link uniped robot simulation is developed to be used as the plant. Neurocontrollers were trained both online and offline. In the case of on-line training, a reinforcement learning technique was used to train the neurocontroller to make the robot jump to a specified height. After several hundred iterations of training, the plant output achieved an accuracy of 7.4%. However, when jump distance and body angular momentum were also included in the control objectives, training time became impractically long. In the case of off-line training, a three-layered backpropagation (BP) network was first used with three inputs, three outputs and 15 to 40 hidden nodes. Pre-generated data were presented to the network with a learning rate as low as 0.003 in order to reach convergence. The low learning rate required for convergence resulted in a very slow training process which took weeks to learn 460 examples. After training, performance of the neurocontroller was rather poor. Consequently, the BP network was replaced by a Cerebeller Model Articulation Controller (CMAC) network. Subsequent experiments described in this document show that the CMAC network is more suitable to the solution of uniped locomotion control problems in terms of both learning efficiency and performance. A new approach is introduced in this report, viz., a self-organizing multiagent cerebeller model for fuzzy-neural control of uniped locomotion is suggested to improve training efficiency. This is currently being evaluated for a possible patent by NASA, Johnson Space Center. An alternative modular approach is also developed which uses separate controllers for each stage of the running stride. A self-organizing fuzzy-neural controller controls the height, distance and angular momentum of the stride. A CMAC-based controller controls the movement of the leg from the time the foot leaves the ground to the time of landing. Because the leg joints are controlled at each time step during flight, movement is smooth and obstacles can be avoided. Initial results indicate that this approach can yield fast, accurate results.

Simon, William E.↗

Lorentz-Shaped Comet Dust Trail Cross Section from New Hybrid Visual and Video Meteor Counting Technique - Implications for Future Leonid Storm Encounters

A new hybrid technique of visual and video meteor observations was developed to provide high precision near real-time flux measurements for satellite operators from airborne platforms. A total of 33,000 Leonids. recorded on video during the 1999 Leonid storm, were watched by a team of visual observers using a video head display and an automatic counting tool. The counts reveal that the activity profile of the Leonid storm is a Lorentz profile. By assuming a radial profile for the dust trail that is also a Lorentzian, we make predictions for future encounters. If that assumption is correct, we passed 0.0003 AU deeper into the 1899 trailet than expected during the storm of 1999 and future encounters with the 1866 trailet will be less intense than. predicted elsewhere.

Jenniskens, Peter↗

Investigating a hybrid perturbation-Galerkin technique using computer algebra

A two-step hybrid perturbation-Galerkin method is presented for the solution of a variety of differential equations type problems which involve a scalar parameter. The resulting (approximate) solution has the form of a sum where each term consists of the product of two functions. The first function is a function of the independent field variable(s) x, and the second is a function of the parameter lambda. In step one the functions of x are determined by forming a perturbation expansion in lambda. In step two the functions of lambda are determined through the use of the classical Bubnov-Gelerkin method. The resulting hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Bubnov-Galerkin methods applied separately, while combining some of the good features of each. In particular, the results can be useful well beyond the radius of convergence associated with the perturbation expansion. The hybrid method is applied with the aid of computer algebra to a simple two-point boundary value problem where the radius of convergence is finite and to a quantum eigenvalue problem where the radius of convergence is zero. For both problems the hybrid method apparently converges for an infinite range of the parameter lambda. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Andersen, Carl M.↗