ALBERT

Description: MATH77 is a high quality library of ANSI FORTRAN 77 subprograms implementing contemporary algorithms for the basic computational processes of science and engineering. The portability of MATH77 meets the needs of present-day scientists and engineers who typically use a variety of computing environments. Release 4.0 of MATH77 contains 454 user-callable and 136 lower-level subprograms. Usage of the user-callable subprograms is described in 69 sections of the 416 page users' manual. The topics covered by MATH77 are indicated by the following list of chapter titles in the users' manual: Mathematical Functions, Pseudo-random Number Generation, Linear Systems of Equations and Linear Least Squares, Matrix Eigenvalues and Eigenvectors, Matrix Vector Utilities, Nonlinear Equation Solving, Curve Fitting, Table Look-Up and Interpolation, Definite Integrals (Quadrature), Ordinary Differential Equations, Minimization, Polynomial Rootfinding, Finite Fourier Transforms, Special Arithmetic , Sorting, Library Utilities, Character-based Graphics, and Statistics. Besides subprograms that are adaptations of public domain software, MATH77 contains a number of unique packages developed by the authors of MATH77. Instances of the latter type include (1) adaptive quadrature, allowing for exceptional generality in multidimensional cases, (2) the ordinary differential equations solver used in spacecraft trajectory computation for JPL missions, (3) univariate and multivariate table look-up and interpolation, allowing for "ragged" tables, and providing error estimates, and (4) univariate and multivariate derivative-propagation arithmetic. MATH77 release 4.0 is a subroutine library which has been carefully designed to be usable on any computer system that supports the full ANSI standard FORTRAN 77 language. It has been successfully implemented on a CRAY Y/MP computer running UNICOS, a UNISYS 1100 computer running EXEC 8, a DEC VAX series computer running VMS, a Sun4 series computer running SunOS, a Hewlett-Packard 720 computer running HP-UX, a Macintosh computer running MacOS, and an IBM PC compatible computer running MS-DOS. Accompanying the library is a set of 196 "demo" drivers that exercise all of the user-callable subprograms. The FORTRAN source code for MATH77 comprises 109K lines of code in 375 files with a total size of 4.5Mb. The demo drivers comprise 11K lines of code and 418K. Forty-four percent of the lines of the library code and 29% of those in the demo code are comment lines. The standard distribution medium for MATH77 is a .25 inch streaming magnetic tape cartridge in UNIX tar format. It is also available on a 9~track 1600 BPI magnetic tape in VAX BACKUP format and a TK50 tape cartridge in VAX BACKUP format. An electronic copy of the documentation is included on the distribution media. Previous releases of MATH77 have been used over a number of years in a variety of JPL applications. MATH77 Release 4.0 was completed in 1992. MATH77 is a copyrighted work with all copyright vested in NASA.

Description: The paper first presents the details of the development of a new six-noded plane triangular finite dynamic element. A block Lanczos algorithm is developed next for the accurate and efficient solution of the quadratic matrix eigenvalue problem associated with the finite dynamic element formulation. The resulting computer program fully exploits matrix sparsity inherent in such a discretization and proves to be most efficient for the extraction of the usually required first few roots and vectors, including repeated ones. Most importantly, the present eigenproblem solution is shown to be comparable to that of the corresponding finite element analysis, thereby rendering the associated dynamic element method rather attractive owing to superior convergence characteristics of such elements, presented herein.

Description: The modeling and simulation of hypersonic vehicles which involve the interaction of a number of major technical disciplines including aerodynamics, structures, heat transfer, propulsion, and control engineering are described. Finite element numerical formulations of individual disciplines including their appropriate integration for multidisciplinary simulation are presented. An efficient unstructured grid generation strategy, evolved by modifying an existing code, is developed.

Description: Data from radar range and Doppler observations of Venus at inferior conjunction

Description: Mathematical and numerical least squares solution of linear equations, using Householder algorithm

Description: This paper presents pertinent details of the development and application of an integrated, multidisciplinary finite element analysis tool for the effective modeling and simulation of aerospace vehicles including hypersonic ones. Recent advances in this connection include more efficient CFD solution techniques and also aeroservoelastic stability analysis methods that employ unsteady aerodynamic forces for computation of flutter and divergence speeds. An accelerated Euler solution procedure based on the Aitken acceleration technique has recently been implemented that effects considerable improvement in solution efficiency for the same level of solution accuracy, as evidenced by example problems presented in the paper. A summary of finite element numerical formulations for the various individual disciplines as well as for the unified aeroservoelastic analysis and some relevant numerical examples are also presented in the paper.