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NASA NTRS1979

The simultaneous inference of stratospheric NO2-H2O and HNO3-CF2Cl2 using limb sounding radiometry

An inversion algorithm has been developed to simultaneously infer the concentrations of two gases with overlapping spectral signatures using limb emission measurements. The algorithm provides a solution in two or three iterations and has been tested in a simulation study for the inference of stratospheric NO2-H2O and HNO3-CF2Cl2. Existing satellite instrumentation was the basis for errors used in the calculations. These included noise, scale and bias errors, angular registration errors, spacecraft motion effects, and effects due to a finite instrument field of view. It is estimated that concentrations of all four gases can be measured globally from a satellite with errors of less than 20%.

Russell, J. M., III↗

NASA NTRS1986

A computer code for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

In this report, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BFC) systems has been developed. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme is used to approximate the convection terms in the governing equations. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm (SIMPLE-C). Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present computer code. The user's guide and computer program listing of the present code are also included.

Chen, Y. S.↗

NASA NTRS1986

A numerical method for three-dimensional incompressible flows using nonorthogonal body-fitted coordinate systems

In the present paper, a numerical method for solving the equations of motion of three-dimensional incompressible flows in nonorthogonal body-fitted coordinate (BEC) systems has been developed and evaluated. The equations of motion are transformed to a generalized curvilinear coordinate system from which the transformed equations are discretized using finite difference approximations in the transformed domain. The hybrid scheme and a central differencing plus artificial dissipation scheme are used to approximate the convection terms in the governing equations. Effects of these two schemes on the accuracy of numerical predictions are studied. Solutions of the finite difference equations are obtained iteratively by using a pressure-velocity correction algorithm, SIMPLE-C. Numerical examples of two- and three-dimensional, laminar and turbulent flow problems are employed to evaluate the accuracy and efficiency of the present numerical method.

Chen, Y. S.↗

NASA NTRS1986

Automatic decoupling of flexible spacecraft slewing maneuvers

The capability for large angle slewing maneuvers with very demanding pointing accuracy and tracking speed is increasingly required for space-based systems. This is particularly the case for space-based directed energy beam pointing. A method is thus proposed in this paper for commanding general pointing and tracking maneuvers with automatic correction for slew-excited structural deformations. All existing rigid body multiaxial slewing algorithms and flexible body vibration damping algorithms can then be used simultaneously, without design iterations. In particular, an example is given of a retargeting maneuver with specified line-of-sight settling time and no torque saturation.

Dwyer, T. A. W., III↗

NASA NTRS1988

Spectral element multigrid. Part 2: Theoretical justification

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from tha approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

Maday, Yvon↗

NASA NTRS1988

Spectral element miltigrid. II - Theoretical justification

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from the approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one-dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

Maday, Yvon↗

NASA NTRS1990

QMR: A Quasi-Minimal Residual method for non-Hermitian linear systems

The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. A novel BCG like approach is presented called the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.

Freund, Roland W.↗

NASA NTRS1990

An airfoil design method for viscous flows

An airfoil design procedure is described that has been incorporated into an existing two-dimensional Navier-Stokes airfoil analysis method. The resulting design method, an iterative procedure based on a residual-correction algorithm, permits the automated design of airfoil sections with prescribed surface pressure distributions. This paper describes the inverse design method and the technique used to specify target pressure distributions. An example airfoil design problem is described to demonstrate application of the inverse design procedure. It shows that this inverse design method develops useful airfoil configurations with a reasonable expenditure of computer resources.

Malone, J. B.↗

NASA NTRS1991

Airfoil design method using the Navier-Stokes equations

An airfoil design procedure is described that was incorporated into an existing 2-D Navier-Stokes airfoil analysis method. The resulting design method, an iterative procedure based on a residual-correction algorithm, permits the automated design of airfoil sections with prescribed surface pressure distributions. The inverse design method and the technique used to specify target pressure distributions are described. It presents several example problems to demonstrate application of the design procedure. It shows that this inverse design method develops useful airfoil configurations with a reasonable expenditure of computer resources.

Malone, J. B.↗

NASA NTRS1991

Iterative solution techniques in boundary element analysis

Iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single- and multizone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices, resulting in multizone BEA, is studied. Both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported. Included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods.

Kane, J. H.↗

NASA NTRS1993

A Lanczos algorithm for vibration, suckling and termal analysis

This paper reviews an eigensolver algorithm based on the Lanczos Method for vibration, buckling and thermal analysis. The original code was written for inclusion in the Computational Mechanics Testbed (COMET), a general purpose finite element code. A portable version of the Lanczos code that is optimized for high-performance supercomputers has been developed. Special features of the algorithm include the capability to compute rigid body modes, thermal modes and Lanczos vectors that are derived from the applied load vector. The latter is necessary when using the Lanczos vectors as reduced-basis vectors in transient structural response and transient heat conduction calculations. The modularity of the code allows the user the option of including the most up-to-date utilities, such as the equation solver best suited for the application. The algorithm is discussed in detail and results of several applications are presented. Timing results for a vibration application indicate that the Lanczos algorithm is twenty times faster than the subspace iteration method which has been extensively used in the past.

Bostic, Susan W.↗

NASA NTRS1996

Homotopy Solutions of Kepler's Equations

Kepler's Equation is solved using an integrative algorithm developed using homotropy theory. The solution approach is applicable to both elliptic and hyperbolic forms of Kepler's Equation. The results from the proposed algorithm compare quite favorably with those from existing iterative schemes.

Fitz-Coy, Norman↗

NASA NTRS1996

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Pavarino, Luca F.↗

NASA NTRS1975

Advances in Application of Fast Semidirect Computational Methods in Transonic Flow

This paper is intended as a review and summary of the advances made in a recently developed approach for rapid numerical solution of the equations of inviscid transonic aerodynamics. The investigation has been limited to two-dimensional, steady, inviscid flow over airfoils in a subsonic free stream, with emphasis on development of a rapid computational technique, rather than on generality of application. The approach uses finite-difference algorithms called "fast direct elliptic solvers" within an iteration scheme. "Direct" means that the entire computation field is solved at once, rather than in successive traverses over the field as in a point- or line-relaxation method. Such an iterative method is referred to as "semidirect." The iterative convergence can be faster than in other relaxation methods because changes are felt simultaneously at all points in each succeeding iteration. Direct elliptic solvers and semidirect methods have restrictions, but these are gradually being removed. Direct solvers were first developed for solving Poisson's equation on a rectangle without interior boundaries. A method to treat first-order systems, a direct Cauchy-Riemann solver has also been developed. Numerical treatment of part of a system of nonlinear equations by a Poisson solver has been reported. Also Poisson solvers in semidirect methods were used for nonseparable elliptic equations. The semidirect method was extended to the solution of a problem of mixed type, where the improved Murman-Cole transonic small-disturbance difference equations were solved. A slightly supercritical flow over a biconvex airfoil was treated successfully, but the iterations did not converge for more strongly supercritical conditions In another work the addition of terms ot both sides of the difference equations stabilized the iteration for supercritical conditions with large supersonic zones. For this, the Cauchy-Riemann solver was revised to incl,ude the needed terms. Most recently, the evaluation of parameters for rapid convergence and comparisons, with Murman's line-relaxation method was described. The method was extended to full second order accuracy in a fully conservative formulation in another work.

Martin, E. Dale↗

NASA NTRS2001

Automatic Synthesis of UML Designs from Requirements in an Iterative Process

The Unified Modeling Language (UML) is gaining wide popularity for the design of object-oriented systems. UML combines various object-oriented graphical design notations under one common framework. A major factor for the broad acceptance of UML is that it can be conveniently used in a highly iterative, Use Case (or scenario-based) process (although the process is not a part of UML). Here, the (pre-) requirements for the software are specified rather informally as Use Cases and a set of scenarios. A scenario can be seen as an individual trace of a software artifact. Besides first sketches of a class diagram to illustrate the static system breakdown, scenarios are a favorite way of communication with the customer, because scenarios describe concrete interactions between entities and are thus easy to understand. Scenarios with a high level of detail are often expressed as sequence diagrams. Later in the design and implementation stage (elaboration and implementation phases), a design of the system's behavior is often developed as a set of statecharts. From there (and the full-fledged class diagram), actual code development is started. Current commercial UML tools support this phase by providing code generators for class diagrams and statecharts. In practice, it can be observed that the transition from requirements to design to code is a highly iterative process. In this talk, a set of algorithms is presented which perform reasonable synthesis and transformations between different UML notations (sequence diagrams, Object Constraint Language (OCL) constraints, statecharts). More specifically, we will discuss the following transformations: Statechart synthesis, introduction of hierarchy, consistency of modifications, and "design-debugging".

Schumann, Johann↗

NASA NTRS1996

Methanococcus jannaschii genome: revisited

Analysis of genomic sequences is necessarily an ongoing process. Initial gene assignments tend (wisely) to be on the conservative side (Venter, 1996). The analysis of the genome then grows in an iterative fashion as additional data and more sophisticated algorithms are brought to bear on the data. The present report is an emendation of the original gene list of Methanococcus jannaschii (Bult et al., 1996). By using a somewhat more updated database and more relaxed (and operator-intensive) pattern matching methods, we were able to add significantly to, and in a few cases amend, the gene identification table originally published by Bult et al. (1996).

Non-NASA Center↗

NASA NTRS2005

Encoders for block-circulant LDPC codes

In this paper, we present two encoding methods for block-circulant LDPC codes. The first is an iterative encoding method based on the erasure decoding algorithm, and the computations required are well organized due to the block-circulant structure of the parity check matrix. The second method uses block-circulant generator matrices, and the encoders are very similar to those for recursive convolutional codes. Some encoders of the second type have been implemented in a small Field Programmable Gate Array (FPGA) and operate at 100 Msymbols/second.

encoders↗

NASA NTRS2014

Optimal Design of Calibration Signals in Space Borne Gravitational Wave Detectors

Future space borne gravitational wave detectors will require a precise definition of calibration signals to ensure the achievement of their design sensitivity. The careful design of the test signals plays a key role in the correct understanding and characterization of these instruments. In that sense, methods achieving optimal experiment designs must be considered as complementary to the parameter estimation methods being used to determine the parameters describing the system. The relevance of experiment design is particularly significant for the LISA Pathfinder mission, which will spend most of its operation time performing experiments to characterize key technologies for future space borne gravitational wave observatories. Here we propose a framework to derive the optimal signals in terms of minimum parameter uncertainty to be injected to these instruments during its calibration phase. We compare our results with an alternative numerical algorithm which achieves an optimal input signal by iteratively improving an initial guess. We show agreement of both approaches when applied to the LISA Pathfinder case.

LISA Path_nder mission↗