Performance of Numerical Integration Methods for High-Dimensional Functions.
Abstract not provided.
de Bord, Sarah Irene↗
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Results for “FUNCTIONAL INTEGRATION”
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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Integrated Nanomaterials
Nanomaterials offer exceptional properties for photonic, electronic, magnetic, structural, mechanical, chemical, nuclear, and biological functionality. Real access to enhanced functionality remains limited, however, without connecting the nanoscale across the mesoscale to macroscale assemblies and the ability to define and control nanomaterials organization, interactions, and interfaces. Integration is essential for accessing and controlling functionality to harness nanomaterials properties while also generating new behaviors and function. Integration thus provides a route to discovering, generating, and using intrinsic and emergent nanomaterials properties, which define the two focus areas of this leadership theme.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
ASCR Workshop Position Paper: Challenges and Opportunities in High Energy Physics
High energy particle physics and cosmology concern themselves with estimating fundamental parameters of nature, such as the masses and interactions of fundamental particles like the Higgs boson and the rate of expansion of the universe. In doing so, they analyze exabyte-scale datasets, some of the largest in all of science, and face many challenges in subsequent data analysis. These challenges are shared between the two disciplines, but we focus on particle physics to highlight one specific domain. In particle physics, the standard method for estimating parameters involves performing Monte Carlo (MC) integration as a function of both parameters of interest and nuisance parameters using an expensive simulator, counting the number of observed collision events (i.i.d. samples) from an experiment in the corresponding integration domains, and forming a Poisson likelihood function. This likelihood function is then used in a Frequentist manner to construct a maximum likelihood point estimate (MLE) and confidence set for the parameters. To sufficiently populate the high-dimensional integration domains, simulators consume billions of CPU-hours annually and produce hundreds of petabytes of intermediate output data. Several techniques have been developed to: optimize definitions of the integration domains so as to be maximally sensitive to a particular subset of parameters, efficiently estimate the integrals, and build robust surrogate models by interpolating between integral evaluations at different parameter points. One can view this whole endeavor as classical Simulation-Based Inference (SBI).
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
A systematic way for the cost reduction of density fitting methods
We present a simple approach for the reduction of the size of auxiliary basis sets used in methods exploiting the density fitting (resolution of identity) approximation for electron repulsion integrals. Starting out of the singular value decomposition of three-center two-electron integrals, new auxiliary functions are constructed as linear combinations of the original fitting functions. The new functions, which we term natural auxiliary functions (NAFs), are analogous to the natural orbitals widely used for the cost reduction of correlation methods. The use of the NAF basis enables the systematic truncation of the fitting basis, and thereby potentially the reduction of the computational expenses of the methods, though the scaling with the system size is not altered. The performance of the new approach has been tested for several quantum chemical methods. It is demonstrated that the most pronounced gain in computational efficiency can be expected for iterative models which scale quadratically with the size of the fitting basis set, such as the direct random phase approximation. The approach also has the promise of accelerating local correlation methods, for which the processing of three-center Coulomb integrals is a bottleneck.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On the integration of image sources in exact image method of field analysis
Convergence conditions of image integration in the exact image method of field calculation have been investigated, and the method is extended to include more general media than previously considered. It is demonstrated that the integral is well behaved and the method works best when the field is calculated in a medium with less loss. If the medium has more loss, it is shown that the image line may enter the improper half-space and still produce valid results. Means of correctly selecting the integration path branch for the case of crossing branch cuts of the Green function in complex integration planes are proposed.
Lindell, I. V.↗
Determination of equivalent model geometry for tunnel wall interference assessment/correction
A formula for the determination of equivalent model geometry with two variables measured at the interface is derived, based on two dimensional subsonic flow. This predicted model profile is a reasonable initial estimate for transonic flow as long as the sonic region does not reach the interface. A general formula is given in two forms. One is in terms of complex variable functions and the other is an integral equation. The complex-function formula has the advantage of using analytic expressions. The integral equation form requires a numerical solution after assuming the model geometry as a polynomial function. Examples are given to illustrate the application of the formulas.
Lo, C. F.↗
Calculation of potential flow past airship bodies in yaw
An outline of Von Karman's method of computing the potential flow of airships in yaw by means of partially constant dipolar superposition on the axis of the body is followed by several considerations for beginning and end of the superposition. Then this method is improved by postulating a continuous, in part linearly variable dipolar superposition on the axis. The second main part of the report brings the calculation of the potential flow by means of sources and sinks, arranged on the surface of the airship body. The integral equation which must satisfy this surface superposition is posed, and the core reduced to functions developed from whole elliptical normal integrals. The functions are shown diagrammatically. The integration is resolvable by iteration. The consequence of the method is good. The formulas for computing the velocity on the surface and of the potential for any point conclude the report.
Lotz, I↗
NEXT Single String Integration Test Results
As a critical part of NASA's Evolutionary Xenon Thruster (NEXT) test validation process, a single string integration test was performed on the NEXT ion propulsion system. The objectives of this test were to verify that an integrated system of major NEXT ion propulsion system elements meets project requirements, to demonstrate that the integrated system is functional across the entire power processor and xenon propellant management system input ranges, and to demonstrate to potential users that the NEXT propulsion system is ready for transition to flight. Propulsion system elements included in this system integration test were an engineering model ion thruster, an engineering model propellant management system, an engineering model power processor unit, and a digital control interface unit simulator that acted as a test console. Project requirements that were verified during this system integration test included individual element requirements ; integrated system requirements, and fault handling. This paper will present the results of these tests, which include: integrated ion propulsion system demonstrations of performance, functionality and fault handling; a thruster re-performance acceptance test to establish baseline performance: a risk-reduction PMS-thruster integration test: and propellant management system calibration checks.
Soulas, George C.↗
Variational solutions by the use of stepwise constant functions. I - Linear case.
Demonstration that accurate solutions to the integral equation or to the extremal function can be easily obtained by the variational method in many cases when a stepwise constant function is used for the trial function. The evaluation procedure is simple and straightforward; integrals of the kernel function can be evaluated analytically; the method provides, when the solution involves singularities, the best mean value across the singularity; the results are accurate in both the detailed physical quantities and their averages; the resultant solution can be further integrated analytically over the parameters associated with the problem; and the method can be readily applied to nonlinear integral equations.
Yoshikawa, K. K.↗
A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids
A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.
97 MATHEMATICS AND COMPUTING↗
Exergy surface shaping and thermodynamic flow control of electro-mechanical-thermal systems
Our work extends the concepts and tools of Hamiltonian Surface Shaping and Power Flow Control (HS SPFC) for electro-mechanical (EM) systems(i.e., adiabatic irreversible work processes and Hamiltonian natural systems)to Exergy Surface Shaping and Thermodynamic Flow Control (ESSTFC) for electro-mechanical-thermal (EMT) systems (i.e., irreversible work processes with heat and mass flows). The extension of HSSPFC requires the development of exergy potential functions, irreversible entropy production terms of the entropy balance equation to obtain the exergy destruction terms for inclusion in the exergy balance equation, and variational principles for producing consistent equations of motion for coupled EMT systems. The Hamiltonian for natural EM systems is an exergy potential function which leaves the development of exergy potential functions for the thermal part of the coupled models. This development is completed by integrating the exergy function over the control volume subject to the modeling assumptions. The irreversible entropy production terms are the exergy destruction terms of the exergy balance equation and the generalization of the mechanical dissipation and electrical resistance within EM systems. These generalized dissipation terms enable the derivation of a consistent set of coupled equations of motion for EMT systems. For this paper, Extended Irreversible Thermodynamics will be utilized to produce consistent thermal equations of motion that directly include the exergy destruction terms. There are several variational principles that are available for application to EMT systems. We focus on the variational principles developed by Biot and Fung [1, 2]. Furthermore, a simplified EMT system that models the EMT dynamics of a Navy ship equipped with a railgun is used to demonstrate the application of ESSTFC for designing high performance, stable nonlinear controllers for EMT systems.
42 ENGINEERING↗
Integrated Safety Management System Description, Revision 9, PG470252
Personnel at Sandia National Laboratories (hereinafter referred to as Sandia) comply with U.S. Department of Energy (DOE) P 450.4A, Chg 1, Integrated Safety Management Policy, and implement an Integrated Safety Management System (ISMS) to ensure safe operations. Sandia personnel integrate safety into management and work practices at all levels so that missions are accomplished while protecting Members of the Workforce, the public, and the environment. As a result, safety is effectively integrated into all facets of work planning and execution. Thus, the management of safety functions becomes an integral part of mission accomplishment and meets the requirements outlined in the DOE Acquisition Regulation (DEAR) 970.5223-1, Integration of Environment, Safety, and Health into Work Planning and Execution clause incorporated into the Prime Contract. The DEAR 970.5223-1, Integration of Environment, Safety, and Health into Work Planning and Execution clause requires DOE contractors to manage and perform work in accordance with a documented Safety Management System that fulfills conditions of the DEAR clause, at a minimum. For purposes of this clause, safety encompasses environment, safety, and health, including pollution prevention and waste minimization.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Integrated Safety Management System Description
Personnel at Sandia National Laboratories (hereinafter referred to as Sandia) comply with United States Department of Energy (DOE) Policy 450.4A, Chg 1, Integrated Safety Management Policy, and implement an Integrated Safety Management System (ISMS) to ensure safe operations. Safety is integrated into management and work practices at all levels so missions are accomplished while protecting Members of the Workforce, the public, and the environment. As a result, safety is effectively integrated into all facets of work planning and execution. Thus the management of safety functions becomes an integral part of mission accomplishment and meets the requirements outlined in the DOE Acquisition Regulation (DEAR) 970.5223-1, Integration of Environment, 4/.01, and Health into Work Planning and Execution, clause incorporated by reference into the Prime Contract.
96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids. LDRD Final Report
This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. In this project, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality. At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5x improvement in accuracy and allows for taking an 8x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method. The report concludes with a brief summary of ongoing projects and collaborations that utilize or extend the products of this work.
97 MATHEMATICS AND COMPUTING↗
Integrated Safety Management System Description (PG470252) (V.10)
Personnel at Sandia National Laboratories (hereinafter referred to as Sandia) comply with United States Department of Energy (DOE) Policy 450.4A, Chg 1, Integrated Safety Management Policy, and implement an Integrated Safety Management System (ISMS) to ensure safe operations. Sandia personnel integrate safety into management and work practices at all levels so missions are accomplished while protecting Members of the Workforce, the public, and the environment. As a result, safety is effectively integrated into all facets of work planning and execution. Thus the management of safety functions becomes an integral part of mission accomplishment and meets the requirements outlined in the DOE Acquisition Regulation (DEAR) 970.5223-1, Integration of Environment, Safety, and Health into Work Planning and Execution, clause incorporated by reference into the Prime Contract. The DEAR 970.5223-1, Integration of Environment, Safety, and Health into Work Planning and Execution, clause requires DOE contractors to manage and perform work in accordance with a documented Safety Management System that fulfills conditions of the DEAR clause at a minimum. For purposes of this clause, safety encompasses environment, safety, and health (ES&H), including pollution prevention and waste minimization.
99 GENERAL AND MISCELLANEOUS↗
Integration of thermal and environmental control systems during Space Station Freedom early assembly phase
An overview of Space Station Freedom Thermal Control System (TCS) and Environmental Control and Life Support System (ECLSS) integration is presented for Stages 2-6. Particular attention is given to issues associated with integrating five distinct, functioning spacecraft with hardware not specifically designed for intermediate stages. Areas specifically addressed include integrated ECLSS temperature and humidity control performance, thermal load balancing, performance and verification requirements, interface verification procedures, TCS activation sequence, resource allocation and Space Shuttle integration.
Di Pietro, David A.↗
Functional Groups Based on Leaf Physiology: Are they Spatially and Temporally Robust?
The functional grouping hypothesis, which suggests that complexity in function can be simplified by grouping species with similar responses, was tested in the Florida scrub habitat. Functional groups were identified based on how species in fire maintained FL scrub function in terms of carbon, water and nitrogen dynamics. The suite of physiologic parameters measured to determine function included both instantaneous gas exchange measurements obtained from photosynthetic light response curves and integrated measures of function. Using cluster analysis, five distinct physiologically-based functional groups were identified. Using non-parametric multivariate analyses, it was determined that these five groupings were not altered by plot differences or by the three different management regimes; prescribed burn, mechanically treated and burn, and fire-suppressed. The physiological groupings also remained robust between the two years 1999 and 2000. In order for these groupings to be of use for scaling ecosystem processes, there needs to be an easy-to-measure morphological indicator of function. Life form classifications were able to depict the physiological groupings more adequately than either specific leaf area or leaf thickness. THe ability of life forms to depict the groupings was improved by separating the parasitic Ximenia americana from the shrub category.
Foster, Tammy E.↗
Stochastic many-body perturbation theory for anharmonic molecular vibrations
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗