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NASA NTRS1996

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Molenaar, J.↗
NASA NTRS1996

Rhenium Mechanical Properties and Joining Technology

Iridium-coated rhenium (Ir/Re) provides thermal margin for high performance and long life radiation cooled rockets. Two issues that have arisen in the development of flight Ir/Re engines are the sparsity of rhenium (Re) mechanical property data (particularly at high temperatures) required for engineering design, and the inability to directly electron beam weld Re chambers to C103 nozzle skirts. To address these issues, a Re mechanical property database is being established and techniques for creating Re/C103 transition joints are being investigated. This paper discusses the tensile testing results of powder metallurgy Re samples at temperatures from 1370 to 2090 C. Also discussed is the evaluation of Re/C103 transition pieces joined by both, explosive and diffusion bonding. Finally, the evaluation of full size Re transition pieces, joined by inertia welding, as well as explosive and diffusion bonding, is detailed.

Reed, Brian D.↗
NASA NTRS1997

PLATSIM: A Simulation and Analysis Package for Large-Order Flexible Systems

The software package PLATSIM provides efficient time and frequency domain analysis of large-order generic space platforms. PLATSIM can perform open-loop analysis or closed-loop analysis with linear or nonlinear control system models. PLATSIM exploits the particular form of sparsity of the plant matrices for very efficient linear and nonlinear time domain analysis, as well as frequency domain analysis. A new, original algorithm for the efficient computation of open-loop and closed-loop frequency response functions for large-order systems has been developed and is implemented within the package. Furthermore, a novel and efficient jitter analysis routine which determines jitter and stability values from time simulations in a very efficient manner has been developed and is incorporated in the PLATSIM package. In the time domain analysis, PLATSIM simulates the response of the space platform to disturbances and calculates the jitter and stability values from the response time histories. In the frequency domain analysis, PLATSIM calculates frequency response function matrices and provides the corresponding Bode plots. The PLATSIM software package is written in MATLAB script language. A graphical user interface is developed in the package to provide convenient access to its various features.

Maghami, Peiman G.↗
NASA NTRS1998

Algorithms for Efficient Computation of Transfer Functions for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, still-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open- and closed-loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, the present method was up to two orders of magnitude faster than a traditional method. The present method generally showed good to excellent accuracy throughout the range of test frequencies, while traditional methods gave adequate accuracy for lower frequencies, but generally deteriorated in performance at higher frequencies with worst case errors being many orders of magnitude times the correct values.

Maghami, Peiman G.↗
NASA NTRS1998

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Kandil, Osama A.↗
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 NTRS1999

El Nino and the Global Ocean Observing System

Until a decade ago, an often-quoted expression in oceanography is that very few observations are recorded throughout the ocean. Now, the sentiment is no longer valid in the uppermost 10% of the tropical Pacific Ocean nor at the surface of the global ocean. One of the remarkable legacies of the 1985-1994 Tropical Oceans Global Atmosphere (TOGA) Program is an in situ marine meteorological and upper oceanographic measurement array throughout the equatorial Pacific to monitor the development and maintenance of El Nino episodes. The TOGA Observing System, which initially consisted of moored- and drifting-buoy arrays, a network of commercial ships, and coastal and island stations, now includes a constellation of satellites and data-assimilating models to simulate subsurface oceanographic conditions. The El Nino and La Nina tropical Pacific Ocean observing system represents the initial phase of an integrated global ocean observing system. Remarkable improvements have been made in ocean model simulation of subsurface currents, but some problems persist. For example, the simulation of the South Equatorial Current (SEC) remains an important challenge in the 2S-2N Pacific equatorial wave guide. During El Nino the SEC at the equator is reduced and sometimes the direction is reversed, becoming eastward. Both conditions allow warm water stored in the western Pacific to invade the eastern region, creating an El Nino episode. Assimilation of data is a tenet of faith to correct simulation errors caused by deficiencies in surface fluxes (especially wind stress) and parameterizations of subgrid-scale physical processes. In the first of two numerical experiments, the Pacific SEC was simulated with and without assimilation of subsurface temperature data. Along the equator, a very weak SEC occurred throughout the eastern Pacific, independent of assimilation of data. However, as displayed in the diagram, in the western Pacific there was no satisfactory agreement between the two simulations. To help determine reliability of the simulated SEC in the western Pacific, current measurements recorded during the 9-19 October 1994 voyage of the French research vessel L'Atalante are also shown in the diagram. With data assimilation, the simulated SEC was in much better agreement with L'Atalante observations. The simulated SEC with data assimilation was far from perfect, in part because of the sparsity of subsurface temperature observations. In the next experiment, TOPEX/POSEIDON sea surface height data in combination with subsurface temperatures will be assimilated to assess further improvement of the simulation of the SEC.

Halpern, David↗
NASA NTRS2000

Model Refinement Using Eigensystem Assignment

IA novel approach for the refinement of finite-element-based analytical models of flexible structures is presented. The proposed approach models the possible refinements in the mass, damping, and stiffness matrices of the finite element model in the form of a constant gain feedback with acceleration, velocity, and displacement measurements, respectively. Once the free elements of the structural matrices have been defined, the problem of model refinement reduces to obtaining position, velocity, and acceleration gain matrices with appropriate sparsity that reassign a desired subset of the eigenvalues of the model, along with partial mode shapes, from their baseline values to those obtained from system identification test data. A sequential procedure is used to assign one conjugate pair of eigenvalues at each step using symmetric output feedback gain matrices, and the eigenvectors are partially assigned, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The procedure can also impose that gain matrices be dissipative to guarantee the stability of the refined model. A numerical example, involving finite element model refinement for a structural testbed at NASA Langley Research Center (Controls-Structures-Interaction Evolutionary model) is presented to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗
NASA NTRS2002

Consistency of ARESE II Cloud Absorption Estimates and Sampling Issues

Data from three cloudy days (March 3, 21, 29, 2000) of the ARM Enhanced Shortwave Experiment II (ARESE II) were analyzed. Grand averages of broadband absorptance among three sets of instruments were compared. Fractional solar absorptances were approx. 0.21-0.22 with the exception of March 3 when two sets of instruments gave values smaller by approx. 0.03-0.04. The robustness of these values was investigated by looking into possible sampling problems with the aid of 500 nm spectral fluxes. Grand averages of 500 nm apparent absorptance cover a wide range of values for these three days, namely from a large positive (approx. 0.011) average for March 3, to a small negative (approximately -0.03) for March 21, to near zero (approx. 0.01) for March 29. We present evidence suggesting that a large part of the discrepancies among the three days is due to the different nature of clouds and their non-uniform sampling. Hence, corrections to the grand average broadband absorptance values may be necessary. However, application of the known correction techniques may be precarious due to the sparsity of collocated flux measurements above and below the clouds. Our analysis leads to the conclusion that only March 29 fulfills all requirements for reliable estimates of cloud absorption, that is, the presence of thick, overcast, homogeneous clouds.

Oreopoulos, L.↗
NASA NTRS2002

An Efficient Scheme for Updating Sparse Cholesky Factors

Raghavan had earlier developed the software package DCSPACK which can be used for solving sparse linear systems where the coefficient matrix is symmetric and positive definite (this project was not funded by NASA but by agencies such as NSF). DSCPACK-S is the serial code and DSCPACK-P is a parallel implementation suitable for multiprocessors or networks-of-workstations with message passing using MCI. The main algorithm used is the Cholesky factorization of a sparse symmetric positive positive definite matrix A = LL(T). The code can also compute the factorization A = LDL(T). The complexity of the software arises from several factors relating to the sparsity of the matrix A. A sparse N x N matrix A has typically less that cN nonzeroes where c is a small constant. If the matrix were dense, it would have O(N2) nonzeroes. The most complicated part of such sparse Cholesky factorization relates to fill-in, i.e., zeroes in the original matrix that become nonzeroes in the factor L. An efficient implementation depends to a large extent on complex data structures and on techniques from graph theory to reduce, identify, and manage fill. DSCPACK is based on an efficient multifrontal implementation with fill-managing algorithms and implementation arising from earlier research by Raghavan and others. Sparse Cholesky factorization is typically a four step process: (1) ordering to compute a fill-reducing numbering, (2) symbolic factorization to determine the nonzero structure of L, (3) numeric factorization to compute L, and, (4) triangular solution to solve L(T)x = y and Ly = b. The first two steps are symbolic and are performed using the graph of the matrix. The numeric factorization step is of dominant cost and there are several schemes for improving performance by exploiting the nested and dense structure of groups of columns in the factor. The latter are aimed at better utilization of the cache-memory hierarchy on modem processors to prevent cache-misses and provide execution rates (operations/second) that are close to the peak rates for dense matrix computations. Currently, EPISCOPACY is being used in an application at NASA directed by J. Newman and M. James. We propose the implementation of efficient schemes for updating the LL(T) or LDL(T) factors computed in DSCPACK-S to meet the computational requirements of their project. A brief description is provided in the next section.

Raghavan, Padma↗
NASA NTRS1999

Efficient Implementations of the Quadrature-Free Discontinuous Galerkin Method

The efficiency of the quadrature-free form of the dis- continuous Galerkin method in two dimensions, and briefly in three dimensions, is examined. Most of the work for constant-coefficient, linear problems involves the volume and edge integrations, and the transformation of information from the volume to the edges. These operations can be viewed as matrix-vector multiplications. Many of the matrices are sparse as a result of symmetry, and blocking and specialized multiplication routines are used to account for the sparsity. By optimizing these operations, a 35% reduction in total CPU time is achieved. For nonlinear problems, the calculation of the flux becomes dominant because of the cost associated with polynomial products and inversion. This component of the work can be reduced by up to 75% when the products are approximated by truncating terms. Because the cost is high for nonlinear problems on general elements, it is suggested that simplified physics and the most efficient element types be used over most of the domain.

Lockard, David P.↗
NASA NTRS1997

Efficient Computation of Closed-loop Frequency Response for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, full-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open and closed loop loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, a speed-up of almost two orders of magnitude was observed while accuracy improved by up to 5 decimal places.

Maghami, Peiman G.↗
NASA NTRS2005

Parallel Finite Element Domain Decomposition for Structural/Acoustic Analysis

A domain decomposition (DD) formulation for solving sparse linear systems of equations resulting from finite element analysis is presented. The formulation incorporates mixed direct and iterative equation solving strategics and other novel algorithmic ideas that are optimized to take advantage of sparsity and exploit modern computer architecture, such as memory and parallel computing. The most time consuming part of the formulation is identified and the critical roles of direct sparse and iterative solvers within the framework of the formulation are discussed. Experiments on several computer platforms using several complex test matrices are conducted using software based on the formulation. Small-scale structural examples are used to validate thc steps in the formulation and large-scale (l,000,000+ unknowns) duct acoustic examples are used to evaluate the ORIGIN 2000 processors, and a duster of 6 PCs (running under the Windows environment). Statistics show that the formulation is efficient in both sequential and parallel computing environmental and that the formulation is significantly faster and consumes less memory than that based on one of the best available commercialized parallel sparse solvers.

Nguyen, Duc T.↗
NASA NTRS2006

Compilation of a Global Emission Inventory from 1980 to 2000 for Global Model Simulations of the Long-term Trend of Tropospheric Aerosols

The approach to create a comprehensive emission inventory for the time period 1980 to 2000 is described in this paper. We have recently compiled an emission database, which we will use for a 21 year simulation of tropospheric aerosols with the GOCART model. Particular attention was paid to the time-dependent SO2, black carbon and organic carbon aerosol emissions. For the emission of SO2 from sporadically erupting volcanoes, we assembled emission data from the Global Volcanism Program of the Smithsonian Institution, using the VEI to derive the volcanic cloud height and the SO2 amount, and amended this dataset by the SO2 emission data from the TOMS instrument when available. 3-dimensional aircraft emission data was obtained for a number of years from the AEAP project, converted from burned fuel to SO2 and interpolated to each year, taking the sparsity of the flight patterns into account. Other anthropogenic SO2 emissions are based on gridded emissions from the EDGAR 2000 database (excluding sources from aircraft, biomass burning and international ship traffic), which were scaled to individual years with country/regional based emission inventories. Gridded SO2 emissions from international ship traffic for 2000 and the scaling factors for other years are from [Eyring et al., 2005]. We used gridded anthropogenic black and organic carbon emissions for 1996 [Bond et al., 2005], again excluding aircraft, biomass burning and ship sources. These emissions were scaled with regional based emission inventories from 1980 to 2000 to derive gridded emissions for each year. The biomass burning emissions are based on a climatology, which is scaled with regional scaling factors derived from the TOMS aerosol index and the AVHRR/ASTR fire counts to each year [Duncan et al., 2003]. Details on the integration of the information from the various sources will be provided and the distribution patterns and total emissions in the final product will be discussed.

Diehl, Thomas L.↗
NASA NTRS2006

On the Development of an Efficient Parallel Hybrid Solver with Application to Acoustically Treated Aero-Engine Nacelles

A finite element solution to the convected Helmholtz equation in a nonuniform flow is used to model the noise field within 3-D acoustically treated aero-engine nacelles. Options to select linear or cubic Hermite polynomial basis functions and isoparametric elements are included. However, the key feature of the method is a domain decomposition procedure that is based upon the inter-mixing of an iterative and a direct solve strategy for solving the discrete finite element equations. This procedure is optimized to take full advantage of sparsity and exploit the increased memory and parallel processing capability of modern computer architectures. Example computations are presented for the Langley Flow Impedance Test facility and a rectangular mapping of a full scale, generic aero-engine nacelle. The accuracy and parallel performance of this new solver are tested on both model problems using a supercomputer that contains hundreds of central processing units. Results show that the method gives extremely accurate attenuation predictions, achieves super-linear speedup over hundreds of CPUs, and solves upward of 25 million complex equations in a quarter of an hour.

Watson, Willie R.↗
NASA NTRS2007

Compilation of a Global Emission Inventory from 1980 to 2000 for Global Model Simulations of the Long-term Trend of Tropospheric Aerosols

The approach to create a comprehensive emission inventory for the time period 1980 to 2000 is described in this paper. We have recently compiled an emission database, which we will use for a 21 year simulation of tropospheric aerosols with the GOCART model. Particular attention was paid to the time-dependent SO2, black carbon and organic carbon aerosol emissions. For the emission of SO2 from sporadically erupting volcanoes, we assembled emission data from the Global Volcanism Program of the Smithsonian Institution, using the VEI to derive the volcanic cloud height and the SO2 amount, and amended this dataset by the SO2 emission data from the TOMS instrument when available. 3-dimensional aircraft emission data was obtained for a number of years from the AEAP project, converted from burned fuel to SO2 and interpolated to each year, taking the sparsity of the flight patterns into account. Other anthopogenic SO2 emissions are based on gridded emissions from the EDGAR 2000 database (excluding sources from aircraft, biomass burning and international ship traffic), which were scaled to individual years with country/regional based emission inventories. Gridded SO2 emissions from international ship traffic for 2000 and the scaling factors for other years are from [Eyring et al., 2005]. We used gridded anthropogenic black and organic carbon emissions for 1996 [Bond et al., 2005], again excluding aircraft, biomass burning and ship sources. These emissions were scaled with regional based emission inventories from 1980 to 2000 to derive gridded emissions for each year. The biomass burning emissions are based on a climatology, which is scaled with regional scaling factors derived from the TOMS aerosol index and the AVHRR/ATSR fire counts to each year [Duncan et al., 2003]. Details on the integration of the information from the various sources will be provided and the distribution patterns and total emissions in the final product will be discussed.

Diehl, T. L.↗
NASA NTRS1989

Vector excitation speech or audio coder for transmission or storage

A vector excitation coder compresses vectors by using an optimum codebook designed off line, using an initial arbitrary codebook and a set of speech training vectors exploiting codevector sparsity (i.e., by making zero all but a selected number of samples of lowest amplitude in each of N codebook vectors). A fast-search method selects a number N.sub.c of good excitation vectors from the codebook, where N.sub.c is much smaller tha ORIGIN OF INVENTION The invention described herein was made in the performance of work under a NASA contract, and is subject to the provisions of Public Law 96-517 (35 USC 202) under which the inventors were granted a request to retain title.

Davidson, Grant↗
NASA NTRS2009

Satellite Contributions to Global Change Studies

By providing a global view with a level playing field (no region missed because of unfavorable surface conditions or political boundaries), satellites have made major contributions to improved monitoring and understanding of our constantly changing planet. The global view has allowed surprising realizations like the relative sparsity of lightning strikes over oceans and the large-scale undulations on the massive Antarctic ice sheet. It has allowed the tracking of all sorts of phenomena, including aerosols, both natural and anthropogenic, as they move with the atmospheric circulation and impact weather and human health. But probably nothing that the global view allows is more important in the long term than its provision. of unbiased data sets to address the issue of global change, considered by many to be among the most important issues facing humankind today. With satellites we can monitor atmospheric temperatures at all latitudes and longitudes, and obtain a global average that lessens the likelihood of becoming endlessly mired in the confusions brought about by the certainty of regional differences. With satellites we can monitor greenhouse gases such as CO2 not just above individual research stations but around the globe. With satellites we can monitor the polar sea ice covers, as we have done since the late 1970s, determining and quantifying the significant reduction in Arctic sea ice and the slight growth in Antarctic sea ice over that period, With satellites we can map the full extent and changes in the Antarctic stratospheric ozone depletions that were first identified from using a single ground station; and through satellite data we have witnessed from afar land surface changes brought about by humans both intentionally, as with wide-scale deforestation, and unintentionally, as with the decay of the Aral Sea. The satellite data are far from sufficient for all that we need in order to understand the global system and forecast its changes, as we also need sophisticated climate models, in situ process studies, and data sets that extend back well before the introduction of satellite technology. Nonetheless, the repetitive, global view provided by satellites is contributing in a major way to our improved recognition of how the Earth im changing, a recognition that is none too soon in view of the magnitude of the impacts that humans can now have.

Parkinson, Claire L.↗