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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Marching methods for elliptic problems. II, III

Higher-order operators for marching methods for elliptic equations are considered. Higher-order is understood in the sense of higher-order accuracy solutions to second-order Poisson equations, and in the sense of higher-order elliptic equations such as the biharmonic equation. The use of deferred corrections for overcoming stability problems is illustrated. Direct and iterative methods of extending the mesh size are considered. Multiple marching, patching, and influence extending techniques are described.

Roache, P. J.↗
NASA NTRS1983

Programming substructure computations for elliptic problems on the CHiP system

A number of studies have been conducted with the aim to apply parallel computation to problems associated with solving finite element equations arising in structural mechanics and fluid dynamics. These studies have provided many important results. The present investigation is concerned with a set of experiments designed to test two ideas, including configurability and substructuring. The considered algorithms and tests are intended for implementation on the Configurable, Highly Parallel (CHiP) family of architecture described by Snyder (1982). The ChiP computer is composed of homogeneous processing elements (PEs) placed at regular intervals in a lattice of programmable switches. Two examples of the role of configurability and substructuring for simple iterative algorithms are considered, giving attention to conjugate gradient iterations, and tridiagonal systems of equations.

Gannon, D.↗
NASA NTRS1982

Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

A systematic approach to generate periodic orbits in the elliptic restricted problem of three bodies is introduced. The approach is based on (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to periodic orbits in the elliptic restricted problem. Two families of periodic orbits of the elliptic restricted problem are found by this approach. The mass ratio of the primaries of these orbits is equal to that of the Sun-Jupiter system. The sidereal mean motions between the infinitesimal body and the smaller primary are in a 2:5 resonance, so as to approximate the Sun-Jupiter-Saturn system. The lineaar stabilities of these periodic orbits are studied as functions of the eccentricities of the primaries and of the infinitesimal body. The results show that both stable and unstable periodic orbits exist in the elliptic restricted problem that are close to the actual Sun-Jupiter-Saturn system. However, the periodic orbit closest to the actual Sun-Jupiter-Saturn system is (linearly) stable.

Kwok, J. H.↗
NASA NTRS1975

A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem

Bounded motion about Lagrange collinear libration points is considered for a perturbed elliptic-restricted problem. A practical application is the motion of a satellite near a libration point collinear with the sun and the earth-moon barycenter. Such a system is treated here as an earth-sun-satellite elliptic restricted problem with lunar perturbations. The method of dual time scales is utilized to develop a uniformly valid three-dimensional analytical solution to the satellite's equations of motion. The analytical development applies somewhat generally to that class of four-body problems where the second primary mass is much greater than the first, and the third primary mass is much greater than the second.

Richardson, D. L.↗
NASA NTRS1983

Chaotic behavior and the origin of the 3/1 Kirkwood gap

The sudden eccentricity increases discovered by Wisdom (1982) are reproduced in numerical integrations of the planar ecliptic restricted three-body problem, verifying that this phenomenon is real. Mapping derivations are qualitatively reviewed and the maximum Liapunov characteristic exponent and its importance for determining the character of a trajectory are explained. The results of a number of calculations of this exponent using the differential equations for the unaveraged three-body problem are shown and compared to equivalent calculations using a mapping. In all cases the two approaches agree whether the orbits are chaotic or quasiperiodic. The mappings are used to trace out the chaotic zone near the 3/1 commensurability, both in the planar-ecliptic problem and in the three-dimensional elliptic problem. The outer boundary of the chaotic zone coincides with the boundary of the 3/1 Kirkwood gap in the actual distribution of asteroids within the errors of the asteroid orbital elements.

Wisdom, J.↗
NASA NTRS1971

Calculation of trajectories using constant and slowly varying functions

A method is presented for calculating trajectories for the restricted problem of three bodies which utilizes conic propagation of the state vector with frequency correction of position and velocity by means of a constant or slowly varying function. This method of calculating trajectories was applied to the planar circular restricted three body problem, the planar elliptic restricted problem, and the ephemeral restricted problem. Two methods (the refined method and the straight forward method) of determining the direction of the position correction are presented for the circular restricted problem and the elliptic restricted problem of three bodies. Only the straight forward method was used with the ephemeral restricted problem. The earth, the moon, and a space vehicle comprise the restricted three body model that is used.

Culpepper, B. K.↗
NASA NTRS1981

An adaptive, multi-level method for elliptic boundary value problems

Subroutine PLTMG is a FORTRAN program for solving self-adjoint elliptic boundary value problems in general regions of R-squared. It is based on a piecewise linear triangle finite element method, an adaptive grid refinement procedure, and a multi-level iterative method to solve the resulting sets of linear equations. This paper describes the method and presents some numerical results and comparisons.

Bank, R. E.↗
NASA NTRS1981

Numerical algorithms for finite element computations on arrays of microprocessors

The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.

Ortega, J. M.↗