Search NASA⌕ Search

SEARCH · Search NASA

Results for “iterative method”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

A boundary element alternating method for two-dimensional mixed-mode fracture problems

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

Raju, I. S.↗
NASA NTRS1987

Experience in grid optimization

Two optimization methods for solving a variational problem in grid generation are described and evaluated. The smoothness, cell volumes, and orthogonality of the variational integrals are examined. The Jacobi-Newton iterative method is compared to the Fletcher-Reeves conjugate gradient method. It is observed that a combination of the Jacobi-Newton iteration and the direct solution of the variational problem produces an algorithm which is easy to program and requires less storage and computer time/iteration than the conjugate gradient method.

Mastin, C. W.↗
NASA NTRS1992

Aerodynamic shape optimization via sensitivity analysis on decomposed computational domains

Direct and iterative method considered to be most applicable to large systems of linear equations arising in discrete sensitivity analysis are assessed. Based on a single-domain grid, computations are performed using a banded matrix solver and an iterative solver, the generalized minimum residual (GMRES) method. The banded matrix solver is found to be generally the most economical method for those applications where the number of right-hand sides is large (i.e., a large number of design variables or a large number of adjoint vectors). For systems of equations that are too large to be solved by direct methods, an approach is proposed whereby the computational domain is divided into small subdomains, and each subdomain is solved separately.

Eleshaky, Mohamed E.↗
NASA NTRS1978

Implementation of natural frequency analysis and optimality criterion design

A description is presented of an effective optimality criterion computer design approach for member size selection to improve frequency characteristics for moderately large structure models. It is shown that the implementation of the simultaneous iteration method within a natural frequency structural design optimization provides a method which is more efficient in isolating the lowest natural frequency modes than the frequently applied Stodola method. Additional computational advantages are derived by using previously converged eigenvectors at the start of the iterations during the second and the following design cycles. Vectors with random components can be used at the first design cycle, which, in relation to the entire computer time for the design program, results in only a moderate computational penalty.

Levy, R.↗
NASA NTRSDate not supplied

USM3D-ME Revised SA-neg Implementation and Assessment for Seventh Drag Prediction Workshop Solutions

Simulations performed by an unstructured-grid, cell-centered, finite-volume, mixed-element flow solver USM3D-MEwere presented at the Seventh Drag Prediction Workshop (DPW-7). Reynolds-averaged Navier-Stokes (RANS) solutions for the NASA high-speed common research model wing-body configuration were computed using a new implementation of the negative variant of the Spalart-Allmaras turbulence model (SA-neg) with hierarchical adaptive nonlinear iteration method (HANIM).ThisUSM3D-ME enhancement improved efficiency and robustness of RANS solutions resulting in fast iterative convergence to machine zero residuals on mixed-element unstructured grids provided by the DPW-7 organizing committee. This paper presents theoretical foundations for the new implementation of the SA-neg model and analyzesUSM3D-ME solutions for flow conditions corresponding to the required DPW-7 cases.

Boris Diskin↗
NASA NTRS1983

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problems preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
NASA NTRS1986

Preconditioners for the spectral multigrid method

The systems of algebraic equations which arise from spectral discretizations of elliptic equations are full and direct solutions of them are rarely feasible. Iterative methods are an attractive alternative because Fourier transform techniques enable the discrete matrix-vector products to be computed with nearly the same efficiency as is possible for corresponding but sparse finite difference discretizations. For realistic Dirichlet problem preconditioning is essential for acceptable convergence rates. A brief description of Chebyshev spectral approximations and spectral multigrid methods for elliptic problems is given. A survey of preconditioners for Dirichlet problems based on second-order finite difference methods is made. New preconditioning techniques based on higher order finite differences and on the spectral matrix itself are presented. The preconditioners are analyzed in terms of their spectra and numerical examples are presented.

Phillips, T. N.↗
NASA NTRS1994

CORSS: Cylinder Optimization of Rings, Skin, and Stringers

Launch vehicle designs typically make extensive use of cylindrical skin stringer construction. Structural analysis methods are well developed for preliminary design of this type of construction. This report describes an automated, iterative method to obtain a minimum weight preliminary design. Structural optimization has been researched extensively, and various programs have been written for this purpose. Their complexity and ease of use depends on their generality, the failure modes considered, the methodology used, and the rigor of the analysis performed. This computer program employs closed-form solutions from a variety of well-known structural analysis references and joins them with a commercially available numerical optimizer called the 'Design Optimization Tool' (DOT). Any ring and stringer stiffened shell structure of isotropic materials that has beam type loading can be analyzed. Plasticity effects are not included. It performs a more limited analysis than programs such as PANDA, but it provides an easy and useful preliminary design tool for a large class of structures. This report briefly describes the optimization theory, outlines the development and use of the program, and describes the analysis techniques that are used. Examples of program input and output, as well as the listing of the analysis routines, are included.

Finckenor, J.↗
NASA NTRS1994

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

The straightforward automatic-differentiation and the hand-differentiated incremental iterative methods are interwoven to produce a hybrid scheme that captures some of the strengths of each strategy. With this compromise, discrete aerodynamic sensitivity derivatives are calculated with the efficient incremental iterative solution algorithm of the original flow code. Moreover, the principal advantage of automatic differentiation is retained (i.e., all complicated source code for the derivative calculations is constructed quickly with accuracy). The basic equations for second-order sensitivity derivatives are presented; four methods are compared. Each scheme requires that large systems are solved first for the first-order derivatives and, in all but one method, for the first-order adjoint variables. Of these latter three schemes, two require no solutions of large systems thereafter. For the other two for which additional systems are solved, the equations and solution procedures are analogous to those for the first order derivatives. From a practical viewpoint, implementation of the second-order methods is feasible only with software tools such as automatic differentiation, because of the extreme complexity and large number of terms. First- and second-order sensitivities are calculated accurately for two airfoil problems, including a turbulent flow example; both geometric-shape and flow-condition design variables are considered. Several methods are tested; results are compared on the basis of accuracy, computational time, and computer memory. For first-order derivatives, the hybrid incremental iterative scheme obtained with automatic differentiation is competitive with the best hand-differentiated method; for six independent variables, it is at least two to four times faster than central finite differences and requires only 60 percent more memory than the original code; the performance is expected to improve further in the future.

Taylor, Arthur C., III↗
NASA NTRS1992

Finite element computation of incompressible flows

Among the solution techniques presented for FEM computation of incompressible flows are stabilized formulations designed to prevent the numerical oscillations that may be generated by (1) the presence of dominant advection terms in the governing equations, or (2) the failure to use an acceptable combination of interpolation functions to represent velocity and pressure fields. It is shown that the space-time formulation, in conjunction with the Galerkin-least squares methods, can be used to compute steady incompressible flows involving moving boundaries and interfaces; it is recommended that iteration methods be used to reduce the associated computational costs.

Tezduyar, T. E.↗
NASA NTRS1992

Examples Of Synthesis Of Dual-Shaped Reflectors

Report presents examples to demonstrate validity and utility of method of synthesis of offset dual-shape reflectors. Method of synthesis described by the authors in previous journal article. Current report reviews derivation of partial differential equations and iterative method of numerical solution. Discusses significance of starting point of numerical integration on each reflector surface; this point could be at center, on outer rim, or at interior point. Emphasizes that one of notable attributes of partial differential equations is speed with which they can be solved.

Galindo, Victor↗
NASA NTRS1990

A semiempirical method for obtaining fuselage normal areas from fuselage Mach sliced areas

An aircraft designed to meet low sonic boom or shaped ground overpressure signature requirements has a volume and lift equivalent area distribution which is in close agreement with the equivalent areas of a desired theoretical curve. Final-stage design modifications of the aircraft's geometry to meet this requirement are usually made through adjustments to the fuselage normal cross-section areas that are derived from the corresponding fuselage equivalent areas by iterative methods. The time required to obtain a good agreement between the desired low-boom area distribution and the conceptual aircraft total area distribution can be reduced by using a semi-empirical method which eliminates much of the final trial-and-error iteration previously employed. Fuselages from conceptual aircraft designed to generate low sonic boom ground overpressures at cruise Mach numbers of 2.0 and 3.0 were used as examples to examine the method's capabilities and limitations. Results indicated that the method has merit as a design tool consistent with other linear theory methods.

Mack, Robert J.↗
NASA NTRS1991

Implicit solvers for unstructured meshes

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.↗
NASA NTRS1983

Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms

The minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods for sequences of vectors. In a recent survey these methods were tested and compared with the scalar, vector, topological epsilon algorithms, and were observed to be more efficient than the latter. It was also observed that the two methods have similar convergence properties. The convergence and stability properties of these methods are analyzed and the performance of the acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods is discussed.

Sidi, A.↗
NASA NTRS1986

Preconditioned conjugate residual methods for the solution of spectral equations

Conjugate residual methods for the solution of spectral equations are described. An inexact finite-difference operator is introduced as a preconditioner in the iterative procedures. Application of these techniques is limited to problems for which the symmetric part of the coefficient matrix is positive definite. Although the spectral equation is a very ill-conditioned and full matrix problem, the computational effort of the present iterative methods for solving such a system is comparable to that for the sparse matrix equations obtained from the application of either finite-difference or finite-element methods to the same problems. Numerical experiments are shown for a self-adjoint elliptic partial differential equation with Dirichlet boundary conditions, and comparison with other solution procedures for spectral equations is presented.

Wong, Y. S.↗
NASA NTRS1993

Large-scale computation of incompressible viscous flow by least-squares finite element method

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Jiang, Bo-Nan↗
NASA NTRS1993

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, part 2

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallellize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet and perhaps will never be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient than explicit codes when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Farhat, Charbel↗