Iterative saddle point techniques.
Iterative solution methods for minimizing convex, differentiable function in Euclidean space
DIFFERENTIAL EQUATION↗
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Results for “ITERATIVE SOLUTION”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Parabolized Navier-Stokes solutions of separation and trailing-edge flows
A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.
Brown, J. L.↗
Testing of FTS fingers and interface using a passive compliant robot manipulator
This report deals with testing of a pair of robot fingers designed for the Flight Telerobotic Servicer (FTS) to grasp a cylinder type of Orbital Replaceable Unit (ORU) interface. The report first describes the objectives of the study and then the testbed consisting of a Stewart Platform-based manipulator equipped with a passive compliant platform which also serves as a force/torque sensor. Kinematic analysis is then performed to provide a closed-form solution for the force inverse kinematics and iterative solution for the force forward kinematics using the Newton's Raphson Method. Mathematical expressions are then derived to compute force/torques applied to the FTS fingers during the mating/demating with the interface. The report then presents the three parts of the experimental study on the feasibility and characteristics of the fingers. The first part obtains data of forces applied by the fingers to the interface under various misalignments, the second part determines the maximum allowable capture angles for mating, and the third part processes and interprets the obtained force/torque data.
Nguyen, Charles C.↗
An iterative finite element-integral technique for predicting sound radiation from turbofan inlets
A new iterative solution technique for predicting the sound field radiated from a turbofan inlet is presented. The sound field is divided into two regions; the sound field within the inlet which is computed using the finite element method and the radiation field outside the inlet which is calculated using an integral solution technique. A 'unified' solution is obtained by matching the finite element and integral solutions at the interface between the interior and exterior regions. The applicability of the iterative technique is demonstrated by considering several simple cases for which exact or 'classical' solutions for the sound field are available. These examples show that the proper solution is obtained within five iterations. The overall accuracy of the method is demonstrated by comparison with experimental data.
Horowitz, S. J.↗
FORTRAN 4 program calculates velocities and streamlines in a tandem blade turbomachine
Computer program gives blade-to-blade solution of the two-dimensional, subsonic, compressible, nonviscous flow problem for a circular or straight infinite cascade of tandem or slotted turbomachine blades. The method of solution is based on the stream function using iterative solution of nonlinear finite-difference equations.
Katsanis, T.↗
Development of generalized block correction procedures for the solution of discretized Navier-Stokes equations
Effort is directed towards developing a solution method which combines advantages of both the iterative and the direct methods. It involves iterative solution on the fine grid, convergence of which is enhanced by a direct solution for correction quantities on a coarse grid. The proposed block correction procedure was applied to compute recirculating flow in a driven cavity.
Kelkar, Kanchan M.↗
Efficient Minimum-Polynomial And Reduced-Rank Extrapolation
MPERRE computer program accelerates convergence of sequence of vectors by use of minimum-polynomial extrapolation (MPE) and reduced-rank extrapolation (RRE). Effective in accelerating convergences of such sequences of vectors as those obtained from iterative solution of systems of linear and nonlinear equations. In conjunction with various iterative techniques, successfully employed in finite-difference solution of large-scale elliptic boundary-value problems and problems in computational-fluid-dynamics. Only input required is sequence of vectors, convergence of which is accelerated. Program economical and easy to use. Written in FORTRAN 77.
Sidi, Avram↗
Analysis and design of advanced composite bounded joints
Advances in the analysis of adhesive-bonded joints are presented with particular emphasis on advanced composite structures. The joints analyzed are of double-lap, single-lap, scarf, stepped-lap and tapered-lap configurations. Tensile, compressive, and in-plane shear loads are covered. In addition to the usual geometric variables, the theory accounts for the strength increases attributable to adhesive plasticity (in terms of the elastic-plastic adhesive model) and the joint strength reductions imposed by imbalances between the adherends. The solutions are largely closed-form analytical results, employing iterative solutions on a digital computer for the more complicated joint configurations. In assessing the joint efficiency, three potential failure modes are considered. These are adherend failure outside the joint, adhesive failure in shear, and adherend interlaminar tension failure (or adhesive failure in peel). Each mode is governed by a distinct mathematical analysis and each prevails throughout different ranges of geometric sizes and proportions.
Hart-Smith, L. J.↗
Solution of viscous transonic flow over wings
Since the calculations of plane steady transonic flows conducted by Murman and Cole (1971), steady progress has been made with respect to the computation of inviscid transonic flows. It has been found that it is inadequate to consider practical wing design at transonic speeds without considering the effects of viscosity and turbulence. The present study has the objective to develop a zonal method for viscous transonic flow over three-dimensional (3-D) wings. The employed approach follows closely the viscous/inviscid interaction techniques discussed by Melnik et al. (1983) for viscous flow about airfoils. Attention is given to inviscid flow equations and boundary conditions, the solution of 3-D boundary layer and wake, an iterative solution to viscid-inviscid interaction analysis, and results obtained for a transonic cruise wing of transport type.
Chow, R. R.↗
Development of iterative techniques for the solution of unsteady compressible viscous flows
Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.
Sankar, Lakshmi N.↗
The Pekeris problem, and the interior of the pulsating sphere, first success of exact ray theory, and what rays?
This paper presents what is probably the first application of exact ray theory to provide nontrivial exact solutions of the Helmholtz equation. First, the Pekeris problem is considered. This is followed by consideration of the problem of the field maintained within a uniformly pulsating sphere. In the Pekeris problem, an iterative solution provides the exact solution on the second iteration. In the second problem, it is shown that the exact ray theory eliminates the focus of the geometric theory.
Mcaninch, Gerry L.↗
Solving Finite-Element Problems on a Concurrent Processor
By use of "conjugate gradients" technique, concurrent efficiency greater than 90 percent. Algorithm applies method of conjugate gradients to iterative solution of finite-element problems on concurrent processor. With algorithm, iteration rates nearly proportional to number of processors. For sufficiently large problems, fraction of proportional speedup achieved, called concurrent efficiency, exceeds 90 percent. Results indicate future application of this and related algorithms to large finite-element problems depend primarily upon applicability of iteratiave techniques, not upon issues of concurrency or efficiency.
Lyzenga, G. A.↗
A superlinear interior points algorithm for engineering design optimization
We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.
Herskovits, J.↗
Parallel Finite Element Solution of 3D Rayleigh-Benard-Marangoni Flows
A domain decomposition strategy and parallel gradient-type iterative solution scheme have been developed and implemented for computation of complex 3D viscous flow problems involving heat transfer and surface tension effects. Details of the implementation issues are described together with associated performance and scalability studies. Representative Rayleigh-Benard and microgravity Marangoni flow calculations and performance results on the Cray T3D and T3E are presented. The work is currently being extended to tightly-coupled parallel "Beowulf-type" PC clusters and we present some preliminary performance results on this platform. We also describe progress on related work on hierarchic data extraction for visualization.
Carey, G. F.↗
Finite-element analysis of nonlinear conduction problems subject to moving fields
Through the use of a space-time warp, specialized moving finite elements are developed that can be employed to generate a nonlinear heat conduction model for situations involving traveling boundary and heat generation fields superposed on an initial state. To facilitate the solution of the resulting nonlinear finite-element formulation, a multilevel heuristic iterative solution strategy is developed. In order to demonstrate the versatility and accuracy of the moving elements and their associated nonlinear solution strategy, the results of several numerical experiments are presented.
Padovan, J.↗
A finite element model with nonviscous damping
A constitutive law by which structural damping is modeled as a relationship between stress, strain, and strain rate in a material is used in conjunction with the finite element method to develop general integral expressions for viscous and nonviscous damping matrices. To solve the set of nonlinear equations resulting from the presence of nonviscous damping, a solution technique is developed by modifying the Newmark method to accommodate an iterative solution and treat the nonviscous damping as a pseudo-force. The technique is then checked for accuracy and convergence in single- and multi-degree-of-freedom problems, and is found to be accurate and efficient for initial-condition problems with small nonviscous damping.
Roussos, L. A.↗
An iterative finite element-integral technique for predicting sound radiation from turbofan inlets in steady flight
A new iterative solution technique for predicting the sound field radiated from a turbofan inlet in steady flight is presented. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. A continuous solution is obtained by matching the finite element and integral solutions at the interface between the two regions. The applicability of the iterative technique is demonstrated by comparison of experimental results with the theoretical results for several different inlet configurations with and without flow. These examples show that good agreement between experiment and theory is obtained within five iterations.
Horowitz, S. J.↗
Stability and dynamic analysis of a slender column with curved longitudinal stiffeners
The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.
Lake, Mark S.↗