SEARCH · Engineering Papers
Results for “Mathematical Software”
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.
Problem Solving testbed for Uncertainty Analysis and Design Exploration
PSUADE (Problem Solving testbed for Uncertainty Analysis and Design Exploration) is a mathematical software useful for performing uncertainty quantification and sensitivity analysis.
Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205
Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.
Some mathematical tools for a modeller's workbench
The development of a mathematical software tools in workbench environment to model related objects more straightforward is outlined. A computer model from informal drawings and a plastic model of a helicopter is discussed. Lofting was the predominant, characteristic modelling technique. Ships and airplane designs use lofting as a technique because they have defined surfaces, (hulls and fuselages) from vertical station cuts perpendicular to the vertical center plane defining the major axis of reflective symmetry. A turbine blade from a jet engine was modelled in this way. The aerodynamic portion and the root comes from different paradigms. The union of these two parts into a coherent model is shown.
Experiments with conjugate gradient algorithms for homotopy curve tracking
There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.
Error Free Software
A mathematical theory for development of "higher order" software to catch computer mistakes resulted from a Johnson Space Center contract for Apollo spacecraft navigation. Two women who were involved in the project formed Higher Order Software, Inc. to develop and market the system of error analysis and correction. They designed software which is logically error-free, which, in one instance, was found to increase productivity by 600%. USE.IT defines its objectives using AXES -- a user can write in English and the system converts to computer languages. It is employed by several large corporations.
Expert system development for commonality analysis in space programs
This report is a combination of foundational mathematics and software design. A mathematical model of the Commonality Analysis problem was developed and some important properties discovered. The complexity of the problem is described herein and techniques, both deterministic and heuristic, for reducing that complexity are presented. Weaknesses are pointed out in the existing software (System Commonality Analysis Tool) and several improvements are recommended. It is recommended that: (1) an expert system for guiding the design of new databases be developed; (2) a distributed knowledge base be created and maintained for the purpose of encoding the commonality relationships between design items in commonality databases; (3) a software module be produced which automatically generates commonality alternative sets from commonality databases using the knowledge associated with those databases; and (4) a more complete commonality analysis module be written which is capable of generating any type of feasible solution.
Two new SciDAC institutes promote mathematical tools and software technology for high-performance computing
Bigger is often said to be better, and the newest extreme-scale computers certainly are bigger, with millions of processing units. Moreover, the breadth of science performed on the U.S. Department of Energy (DOE) computing facilities is expanding, with new technology such as artificial intelligence emerging. These advances are exciting, creating new opportunities for scientific discovery; however, they also raise new questions for scientists who want to exploit these advances for tackling more complex problems. Will my simulation code be able to utilize the accelerators in extreme-scale computing systems? Can I take advantage of the deepening memory hierarchy in heterogeneous processors? Is there a way around bottlenecks caused by the widening ratio of peak floating-point operations per second to I/0 bandwidth? How can I manage my huge amounts of data effectively? Can I analyze data in situ, or must I transfer it to offline storage for later analysis? To address such questions, DOE announced that it is providing $57.5 million over the next five years for two multidisciplinary teams — FASTMath and RAPIDS2 — to develop new tools and techniques to harness supercomputers for scientific discovery. The teams, called SciDAC Institutes, are part of the Scientific Discovery through Advanced Computing program.
Software Template for Instruction in Mathematics
Intelligent Math Tutor (IMT) is a software system that serves as a template for creating software for teaching mathematics. IMT can be easily connected to artificial-intelligence software and other analysis software through input and output of files. IMT provides an easy-to-use interface for generating courses that include tests that contain both multiple-choice and fill-in-the-blank questions, and enables tracking of test scores. IMT makes it easy to generate software for Web-based courses or to manufacture compact disks containing executable course software. IMT also can function as a Web-based application program, with features that run quickly on the Web, while retaining the intelligence of a high-level language application program with many graphics. IMT can be used to write application programs in text, graphics, and/or sound, so that the programs can be tailored to the needs of most handicapped persons. The course software generated by IMT follows a "back to basics" approach of teaching mathematics by inducing the student to apply creative mathematical techniques in the process of learning. Students are thereby made to discover mathematical fundamentals and thereby come to understand mathematics more deeply than they could through simple memorization.
AMTRAN system design and software description
Automatic Mathematical Translation language software for IBM 1130
A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation
The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world’s largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.
Development of a methodology for classifying software errors
A mathematical formalization of the intuition behind classification of software errors is devised and then extended to a classification discipline: Every classification scheme should have an easily discernible mathematical structure and certain properties of the scheme should be decidable (although whether or not these properties hold is relative to the intended use of the scheme). Classification of errors then becomes an iterative process of generalization from actual errors to terms defining the errors together with adjustment of definitions according to the classification discipline. Alternatively, whenever possible, small scale models may be built to give more substance to the definitions. The classification discipline and the difficulties of definition are illustrated by examples of classification schemes from the literature and a new study of observed errors in published papers of programming methodologies.
A Study of Visualization for Mathematics Education
Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.
Towards a Theory for Integration of Mathematical Verification and Empirical Testing
From the viewpoint of a project manager responsible for the V&V (verification and validation) of a software system, mathematical verification techniques provide a possibly useful orthogonal dimension to otherwise standard empirical testing. However, the value they add to an empirical testing regime both in terms of coverage and in fault detection has been difficult to quantify. Furthermore, potential cost savings from replacing testing with mathematical verification techniques cannot be realized until the tradeoffs and synergies can be formulated. Integration of formal verification with empirical testing is also difficult because the idealized view of mathematical verification providing a correctness proof with total coverage is unrealistic and does not reflect the limitations imposed by computational complexity of mathematical techniques. This paper first describes a framework based on software reliability and formalized fault models for a theory of software design fault detection - and hence the utility of various tools for debugging. It then describes a utility model for integrating mathematical and empirical techniques with respect to fault detection and coverage analysis. It then considers the optimal combination of black-box testing, white-box (structural) testing, and formal methods in V&V of a software system. Using case studies from NASA software systems, it then demonstrates how this utility model can be used in practice.
The Laboratory for Oceans Computing Facility
The first VAX computer in the Laboratory for Oceans Computing Facility (LOCF) was installed and the facility was largely expanded. The growth is not only in hardware and software, but also in the number of users and in supporting research and development projects. The LOCF serves as a general purpose computing facility for: ocean color research projects, sea ice research projects, processing of the Nimbus-7 Coastal Zone Color Scanner data set, real time ingest and analysis of TIROS-N satellite data, study of the Synthetic Aperture Radar data, study of LANDSAT data, and many others. The physical space and the electrical power layout of the computing room were modified to accommodate all the equipment. The LOCF has several image processing stations which include two International Imaging Systems (IIS) model 75 processors and one Adage processor. The facility has the capability of ingesting the TIROS-N HRPT satellite data on a real time basis. More than 30 software packages were installed on the systems. System software packages, network software, FORTRAN and C compilers, database management software, image processing software, graphics, mathematics and statistics packages, TAE, Catalog Manager, GEMPAK, LAS and many other software developed on the LOCF computers such as SEAPAK have greatly advanced the capability of the LOCF.
Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring H 1 , H (curl), or H (div)-conforming elements on meshes of squares or cubes. To test how well trimmed serendipity elements perform in comparison to traditional tensor product elements, we perform a sequence of numerical experiments including the primal Poisson, mixed Poisson, and Maxwell cavity eigenvalue problems. Overall, we find that the trimmed serendipity elements converge, as expected, at the same rate as the respective tensor product elements, while being able to offer significant savings in the time or memory required to solve certain problems.
Bound Constrained Partial DifferentialEquation Inverse Problem Solution by theSemi-Smooth Newton Method
We present the mathematical derivation, software implementation details, and computational results for a semi-smooth Newton method applied to two inverse problems governed by partial differential equations with bound constraints. The two problems share mathematical structural similarities to density-based topology optimization problems. The semi-smooth Newton method provides a mesh independent solution computation for the two test problems. A key step is that the complementarity part of the necessary optimality conditions are reformulated with the use of a complementarity functionφsuch that the complementarity conditions are satisfied if and only if a zero of a nonsmooth function has been obtained. The modular finite element package MFEM is utilized for the software implementation. In addition we constructed a matrix-free Operator to enable the use of efficient Krylov subspace IterativeSolver of MFEM for the solution of our two target problems.
Mathematical specifications of the Onboard Navigation Package (ONPAC) simulator (revision 1)
The mathematical theory of the computational algorithms employed in the onboard navigation package system is described. This system, which simulates an onboard navigation processor, was developed to aid in the design and evaluation of onboard navigation software. The mathematical formulations presented include the factorized UDU(T) form of the extended Kalman filter, the equations of motion of the user satellite, the user clock equations, the observation equations and their partial derivatives, the coodinate transformations, and the matrix decomposition algorithms.