SEARCH · Engineering Papers

Results for “matrix product operators”

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.

SourceResearch connectionFrom yearThrough year

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

At least 19 records

All sources NASA NTRS DOE OSTI

NASA NTRS2001

Automatic Overset Grid Generation with Heuristic Feedback Control

An advancing front grid generation system for structured Overset grids is presented which automatically modifies Overset structured surface grids and control lines until user-specified grid qualities are achieved. The system is demonstrated on two examples: the first refines a space shuttle fuselage control line until global truncation error is achieved; the second advances, from control lines, the space shuttle orbiter fuselage top and fuselage side surface grids until proper overlap is achieved. Surface grids are generated in minutes for complex geometries. The system is implemented as a heuristic feedback control (HFC) expert system which iteratively modifies the input specifications for Overset control line and surface grids. It is developed as an extension of modern control theory, production rules systems and subsumption architectures. The methodology provides benefits over the full knowledge lifecycle of an expert system for knowledge acquisition, knowledge representation, and knowledge execution. The vector/matrix framework of modern control theory systematically acquires and represents expert system knowledge. Missing matrix elements imply missing expert knowledge. The execution of the expert system knowledge is performed through symbolic execution of the matrix algebra equations of modern control theory. The dot product operation of matrix algebra is generalized for heuristic symbolic terms. Constant time execution is guaranteed.

Robinson, Peter I.↗

NASA NTRS1992

Comparison of optics and electronics for the calculation of matrix-vector products

Optical processors are attractive because of their ability to perform massively parallel operations such as matrix vector products. The inherently analog nature of optical calculations requires that optical processors be based on analog computations. While the speed at which such analog operations can be performed as well as the natural parallelism of optical systems are great advantages of optical processors, the analog representation of values severely limits the achievable accuracy. Furthermore, optical processors are limited by the need to convert information to and from the intensity of light. Digitization can be used to increase the accuracy of optical matrix-vector processors, but causes a severe reduction in speed. This paper compares the throughput and power requirements of optical and electronic processors, showing that optical matrix-vector processors can provide a greater number of operations/Watt than conventional electronics.

Gary, C. K.↗

NASA NTRS1999

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗

NASA NTRS2006

UID.. .Now That's Gonna Leave A Mark

Since 1975 bar codes on products at the retail counter have been accepted as the standard for entering product identity for price determination. Since the beginning of the 21st century, the Data Matrix symbol has become accepted as the bar code format that is marked directly on a part, assembly or product that is durable enough to identify that item for its lifetime. NASA began the studies for direct part marking Data Matrix symbols on parts during the Return to Flight activities after the Challenger Accident. Over the 20 year period that has elapsed since Challenger, a mountain of studies, analyses and focused problem solutions developed by and for NASA have brought about world changing results. NASA Technical Standard 6002 and NASA Handbook 6003 for Direct Part Marking Data Matrix Symbols on Aerospace Parts have formed the basis for most other standards on part marking internationally. NASA and its commercial partners have developed numerous products and methods that addressed the difficulties of collecting part identification in aerospace operations. These products enabled the marking of Data Matrix symbols in virtually every situation and the reading of symbols at great distances, severe angles, under paint and in the dark without a light. Even unmarkable delicate parts now have a process to apply a chemical mixture, recently trademarked as Nanocodes, that can be converted to Data Matrix information through software. The accompanying intellectual property is protected by ten patents, several of which are licensed. Direct marking Data Matrix on NASA parts dramatically decreases data entry errors and the number of parts that go through their life cycle marked, two major threats to sound configuration management and flight safety. NASA is said to only have people and stuff with information connecting them. Data Matrix is one of the most significant improvements since Challenger to the safety and reliability of that connection.

Schramm, Fred↗

NASA NTRS2006

NASA Technologies for Product Identification

Since 1975 bar codes on products at the retail counter have been accepted as the standard for entering product identity for price determination. Since the beginning of the 21st century, the Data Matrix symbol has become accepted as the bar code format that is marked directly on a part, assembly or product that is durable enough to identify that item for its lifetime. NASA began the studies for direct part marking Data Matrix symbols on parts during the Return to Flight activities after the Challenger Accident. Over the 20 year period that has elapsed since Challenger, a mountain of studies, analyses and focused problem solutions developed by and for NASA have brought about world changing results. NASA Technical Standard 6002 and NASA Handbook 6003 for Direct Part Marking Data Matrix Symbols on Aerospace Parts have formed the basis for most other standards on part marking internationally. NASA and its commercial partners have developed numerous products and methods that addressed the difficulties of collecting part identification in aerospace operations. These products enabled the marking of Data Matrix symbols in virtually every situation and the reading of symbols at great distances, severe angles, under paint and in the dark without a light. Even unmarkable delicate parts now have a process to apply a chemical mixture called NanocodesTM that can be converted to a Data Matrix. The accompanying intellectual property is protected by 10 patents, several of which are licensed. Direct marking Data Matrix on NASA parts virtually eliminates data entry errors and the number of parts that go through their life cycle unmarked, two major threats to sound configuration management and flight safety. NASA is said to only have people and stuff with information connecting them. Data Matrix is one of the most significant improvements since Challenger to the safety and reliability of that connection. This presentation highlights the accomplishments of NASA in its efforts to develop technologies for automatic identification, its efforts to implement them and its vision on their role in space.

Schramm, Fred, Jr.↗

NASA NTRS2007

UID...Now That's Gonna Leave A Mark

Since 1975 bar codes on products at the retail counter have been accepted as the standard for entering product identity for price determination. Since the beginning of the 21st century, the Data Matrix symbol has become accepted as the bar code format that is marked directly on a part, assembly or product that is durable enough to identify that item for its lifetime. NASA began the studies for direct part marking Data Matrix symbols on parts during the Return to Flight activities after the Challenger Accident. Over the 20 year period that has elapsed since Challenger, a mountain of studies, analyses and focused problem solutions developed by and for NASA have brought about world changing results. NASA Technical Standard 6002 and NASA Handbook 6003 for Direct Part Marking Data Matrix Symbols on Aerospace Parts have formed the basis for most other standards on part marking internationally. NASA and its commercial partners have developed numerous products and methods that addressed the difficulties of collecting part identification in aerospace operations. These products enabled the marking of Data Matrix symbols in virtually every situation and the reading of symbols at great distances, severe angles, under paint and in the dark without a light. Even unmarkable delicate parts now have a process to apply a chemical mixture, recently trademarked as Nanocodes, that can be converted to Data Matrix information through software. The accompanying intellectual property is protected by ten patents, several of which are licensed. Direct marking Data Matrix on NASA parts dramatically decreases data entry errors and the number ofparts that go through their life cycle unmarked, two major threats to sound configuration management and flight safety. NASA is said to only have people and stuff with information connecting them. Data Matrix is one of the most significant improvements since Challenger to the safety and reliability of that connection.

Schramm, Harry F., Jr.↗

NASA NTRS2008

UID...Now That's Gonna Leave a Mark

Since 1975 bar codes on products at the retail counter have been accepted as the standard for entering product identity for price determination. Since the beginning of the 21st century, the Data Matrix symbol has become accepted as the bar code format that is marked directly on a part, assembly or product that is durable enough to identify that item for its lifetime. NASA began the studies for direct part marking Data Matrix symbols on parts during the Return to Flight activities after the Challenger Accident. Over the 20 year period that has elapsed since Challenger, a mountain of studies, analyses and focused problem solutions developed by and for NASA have brought about world changing results. NASA Technical Standard 6002 and NASA Handbook 6003 for Direct Part Marking Data Matrix Symbols on Aerospace Parts have formed the basis for most other standards on part marking internationally. NASA and its commercial partners have developed numerous products and methods that addressed the difficulties of collecting part identification in aerospace operations. These products enabled the marking of Data Matrix symbols in virtually every situation and the reading of symbols at great distances, severe angles, under paint and in the dark without a light. Even unmarkable delicate parts now have a process to apply a chemical mixture, recently trademarked as Nanocodes, that can be converted to Data Matrix information through software. The accompanying intellectual property is protected by ten patents, several of which are licensed. Direct marking Data Matrix on NASA parts dramatically decreases data entry errors and the number of parts that go through their life cycle unmarked, two major threats to sound configuration management and flight safety. NASA is said to only have people and stuff with information connecting them. Data Matrix is one of the most significant improvements since Challenger to the safety and reliability of that connection.

Schramm, Harry F.↗

NASA NTRS2008

UID....Now That's Gonna Leave A Mark

Since 1975 bar codes on products at the retail counter have been accepted as the standard for entering product identity for price determination. Since the beginning of the 21 st century, the Data Matrix symbol has become accepted as the bar code format that is marked directly on a part, assembly or product that is durable enough to identify that item for its lifetime. NASA began the studies for direct part marking Data Matrix symbols on parts during the Return to Flight activities after the Challenger Accident. Over the 20 year period that has elapsed since Challenger, a mountain of studies, analyses and focused problem solutions developed by and for NASA have brought about world changing results. NASA Technical Standard 6002 and NASA Handbook 6003 for Direct Part Marking Data Matrix Symbols on Aerospace Parts have formed the basis for most other standards on part marking internationally. NASA and its commercial partners have developed numerous products and methods that addressed the difficulties of collecting part identification in aerospace operations. These products enabled the marking of Data Matrix symbols in virtually every situation and the reading of symbols at great distances, severe angles, under paint and in the dark without a light. Even unmarkable delicate parts now have a process to apply a chemical mixture, recently trademarked as Nanocodes, that can be converted to Data Matrix information through software. The accompanying intellectual property is protected by ten patents, several of which are licensed. Direct marking Data Matrix on NASA parts dramatically decreases data entry errors and the number of parts that go through their life cycle unmarked, two major threats to sound configuration management and flight safety. NASA is said to only have people and stuff with information connecting them. Data Matrix is one of the most significant improvements since Challenger to the safety and reliability of that connection.

Schramm, Harry F., Jr.↗

NASA NTRS2008

UID...Leaving Its Mark on the Universe

Since 1975 bar codes on products at the retail counter have been accepted as the standard for entering product identity for price determination. Since the beginning of the 21 st century, the Data Matrix symbol has become accepted as the bar code format that is marked directly on a part, assembly or product that is durable enough to identify that item for its lifetime. NASA began the studies for direct part marking Data Matrix symbols on parts during the Return to Flight activities after the Challenger Accident. Over the 20 year period that has elapsed since Challenger, a mountain of studies, analyses and focused problem solutions developed by and for NASA have brought about world changing results. NASA Technical Standard 6002 and NASA Handbook 6003 for Direct Part Marking Data Matrix Symbols on Aerospace Parts have formed the basis for most other standards on part marking internationally. NASA and its commercial partners have developed numerous products and methods that addressed the difficulties of collecting part identification in aerospace operations. These products enabled the marking of Data Matrix symbols in virtually every situation and the reading of symbols at great distances, severe angles, under paint and in the dark without a light. Even unmarkable delicate parts now have a process to apply a chemical mixture, recently trademarked as Nanocodes, that can be converted to Data Matrix information through software. The accompanying intellectual property is protected by ten patents, several of which are licensed. Direct marking Data Matrix on NASA parts dramatically decreases data entry errors and the number of parts that go through their life cycle unmarked, two major threats to sound configuration management and flight safety. NASA is said to only have people and stuff with information connecting them. Data Matrix is one of the most significant improvements since Challenger to the safety and reliability of that connection.

Schramm, Harry F., Jr.↗

NASA NTRS1993

Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations

We present ideas on how to use wavelets in the solution of boundary value ordinary differential equations. Rather than using classical wavelets, we adapt their construction so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. We show how one can construct an O(N) algorithm for various constant and variable coefficient operators.

Jawerth, Bjoern↗

NASA NTRS1975

Diagrammatic technique for calculating matrix elements of collective operators in superradiance

Adopting the so-called genealogical construction, one can express the eigenstates of collective operators corresponding to a specified mode for an N-atom system in terms of those for an (N-1) atom system. Using these Dicke states as bases and using the Wigner-Eckart theorem, a matrix element of a collective operator of an arbitrary mode can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME is obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups is then introduced. This gives a simple and systematic way of calculating the RME. This method is especially useful when the cooperation number r is close to N/2, where almost exact asymptotic expressions can be obtained easily. The result shows explicity the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes.

Lee, C. T.↗

NASA NTRS1975

Superradiant effects on pulse propagation in resonant media

Adopting the so-called genealogical construction, the eigenstates of collective operators can be expressed corresponding to a specified mode for an N-atom system in terms of those for an (N-1)-atom system. Matrix element of a collective operator of an arbitrary mode is presented which can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME was obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups was then introduced. This gave a simple and systematic way of calculating the RME. Results show explicitly the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes and clears up the chief difficulty encounted in the problem of N two-level atoms, spread over large regions, interacting with a multimode radiation field.

Lee, C.↗

NASA NTRS1975

Study of flutter related computational procedures for minimum weight structural sizing of advanced aircraft, supplemental data

Computational aspects of (1) flutter optimization (minimization of structural mass subject to specified flutter requirements), (2) methods for solving the flutter equation, and (3) efficient methods for computing generalized aerodynamic force coefficients in the repetitive analysis environment of computer-aided structural design are discussed. Specific areas included: a two-dimensional Regula Falsi approach to solving the generalized flutter equation; method of incremented flutter analysis and its applications; the use of velocity potential influence coefficients in a five-matrix product formulation of the generalized aerodynamic force coefficients; options for computational operations required to generate generalized aerodynamic force coefficients; theoretical considerations related to optimization with one or more flutter constraints; and expressions for derivatives of flutter-related quantities with respect to design variables.

Oconnell, R. F.↗

NASA NTRS2019

Electron Beam Welding of Pure Tungsten Hex Cans for Nuclear Thermal Propulsion Engines

Nuclear thermal propulsion (NTP) is an in-space propulsion method currently being developed at the NASA Marshall Space Flight Center (MSFC). NTP systems are a high specific impulse (750–1,100 s), high thrust (15,000–250,000 lbf ) method of propulsion which have the potential to allow for faster transit times when optimizing for high ΔV. In the nuclear rocket engine, the heat from the nuclear fission reaction is transferred to a low molecular mass propellant (such as hydrogen). Hot propellant is expanded through a nozzle to generate thrust. Development of ceramic metal (cermet) fuel systems for NTP applications is currently ongoing at MSFC. In cermet fuel systems, ceramic fissile fuel particles such as uranium nitride or uranium dioxide are dispersed within a net-shaped, high-density structural matrix. The composite material is cladded by a protective metal structure to make up an NTP fuel element. Cladding materials must be able to withstand the demanding operating conditions required of the engine as well as retain a hermetic seal to allow for retention of fuel element structural integrity, prevent hydrogen attack or migration of the ceramic fuel, and limit release of fission products during operation. For NTP applications, tungsten is a prime material for both the metal matrix and cladding in cermet fuel systems because of its high melting point, high temperature strength, and compatibility with hot hydrogen. If a weld in tungsten with the capability of holding a hermetic seal is achievable, tungsten becomes a strong candidate for NTP applications. This Technical Memorandum focuses on determining the weldability of pure tungsten using electron beam welding (EBW). Tungsten appears well suited for NTP applications, but it has a high ductile to brittle transition temperature (DBTT) dependent upon chemical composition, structure/stress distribution, and mechanical conditions. Therefore, it is highly subject to brittle fracture. Because of its high susceptibility to brittle fracture, it is very difficult to weld. EBW was chosen for joining pure tungsten because of its low heat input compared to gas tungsten arc welding. Reduced heat input can be directly correlated with an increase in ductility of a tungsten weld. EBW is a high energy density welding process in which a stream of electrons penetrates a weld joint in a deep, narrow spike in contrast to a broad gas tungsten arc weld pool. The investigation initially focused on EBW of tungsten plates of both 0.01 in and 0.03 in thickness to determine if EBW could weld pure tungsten without the presence of visual defects—particularly cracking—in the welds. Variation in the weld procedure and post-weld heat treatment (PWHT) was used to improve the surface appearance of flat EBWs on a pure tungsten sheet. The investigation moved on to weld 0.05-in-thick hexagonal tungsten cans with a weld joint thickness of 0.025 in. The goal for welding the pure tungsten hex cans was to avoid any visual surface defects and generate a weld capable of a hermetic seal. This proved difficult. Cold welds commonly exhibited porosity that leaked air. Hot welds exhibited cracks, typically observed immediately after welding. Later welds were preheated to increase ductility and decrease the likelihood of through-thickness cracking. PWHT was used to arrest microcrack growth both in the flat weld samples and hexagonal weld samples.

Courtright, Z. S.↗

NASA NTRS1983

Matrix differentiation formulas

A compact differentiation technique (without using indexes) is developed for scalar functions that depend on complex matrix arguments which are combined by operations of complex conjugation, transposition, addition, multiplication, matrix inversion and taking the direct product. The differentiation apparatus is developed in order to simplify the solution of extremum problems of scalar functions of matrix arguments.

Usikov, D. A.↗

NASA NTRS2000

Biological removal of gaseous ammonia in biofilters: space travel and earth-based applications

Gaseous NH3 removal was studied in laboratory-scale biofilters (14-L reactor volume) containing perlite inoculated with a nitrifying enrichment culture. These biofilters received 6 L/min of airflow with inlet NH3 concentrations of 20 or 50 ppm, and removed more than 99.99% of the NH3 for the period of operation (101, 102 days). Comparison between an active reactor and an autoclaved control indicated that NH3 removal resulted from nitrification directly, as well as from enhanced absorption resulting from acidity produced by nitrification. Spatial distribution studies (20 ppm only) after 8 days of operation showed that nearly 95% of the NH3 could be accounted for in the lower 25% of the biofilter matrix, proximate to the port of entry. Periodic analysis of the biofilter material (20 and 50 ppm) showed accumulation of the nitrification product NO3- early in the operation, but later both NO2- and NO3- accumulated. Additionally, the N-mass balance accountability dropped from near 100% early in the experiments to approximately 95 and 75% for the 20- and 50-ppm biofilters, respectively. A partial contributing factor to this drop in mass balance accountability was the production of NO and N2O, which were detected in the biofilter exhaust.

NASA Discipline Life Support Systems↗

NASA NTRS1972

Insolubilized enzymes for food synthesis

Cellulose matrix with numerous enzyme-coated silica particles of colloidal size permanently bound at various sites within matrix was produced that has high activity and possesses requisite physical characteristics for filtration or column operations. Product also allows coupling step in synthesis of edible food to proceed under mild conditions.

Marshall, D. L.↗

NASA NTRS1993

Nested Krylov methods and preserving the orthogonality

Recently the GMRESR inner-outer iteraction scheme for the solution of linear systems of equations was proposed by Van der Vorst and Vuik. Similar methods have been proposed by Axelsson and Vassilevski and Saad (FGMRES). The outer iteration is GCR, which minimizes the residual over a given set of direction vectors. The inner iteration is GMRES, which at each step computes a new direction vector by approximately solving the residual equation. However, the optimality of the approximation over the space of outer search directions is ignored in the inner GMRES iteration. This leads to suboptimal corrections to the solution in the outer iteration, as components of the outer iteration directions may reenter in the inner iteration process. Therefore we propose to preserve the orthogonality relations of GCR in the inner GMRES iteration. This gives optimal corrections; however, it involves working with a singular, non-symmetric operator. We will discuss some important properties, and we will show by experiments that, in terms of matrix vector products, this modification (almost) always leads to better convergence. However, because we do more orthogonalizations, it does not always give an improved performance in CPU-time. Furthermore, we will discuss efficient implementations as well as the truncation possibilities of the outer GCR process. The experimental results indicate that for such methods it is advantageous to preserve the orthogonality in the inner iteration. Of course we can also use iteration schemes other than GMRES as the inner method; methods with short recurrences like GICGSTAB are of interest.

Desturler, Eric↗