Results for “Nonlinear programming.” — Page 26

DOE OSTI2016

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

A Bilevel Voltage Regulation Operation for Distribution Systems With Self-Operated Microgrids

The emerging of microgrids in distribution systems has significantly enhanced the resilience of power grids. However, the operators of a distribution system and microgrids therein can be different and have accessibility to different devices. To model the operation of such a grid, this work proposes a bilevel formulation and probes into the voltage regulation operation, considering the interaction between different systems. The proposed bilevel formulation considers the cooperation of active energy resources (AER), transformer tap-changers, and capacitor banks that are controlled by different operators. To facilitate the solution time of the target bilevel optimization, the lower-level problems with different objectives are modeled using deep neural networks (DNNs) which are then converted into a set of constraints. Hence, the bilevel problem can be reformed to a single-level problem. Lastly, the proposed solution procedures are validated using a customized joint system constructed by the IEEE 123-bus system and a real distribution system in Iowa. According to the numerical validation results, the solution time of the proposed nonlinear activation function based DNN model is 69 times faster than other methods in solving voltage regulation with a bilevel structure.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Automatic Differentiation in MetaPhysicL and Its Applications in MOOSE

Efficient solution via Newton’s method of nonlinear systems of equations requires an accurate representation of the Jacobian, corresponding to the derivatives of the component residual equations with respect to the degrees of freedom. In practice these systems of equations often arise from spatial discretization of partial differential equations used to model physical phenomena. These equations may involve domain motion or material equations that are complex functions of the systems’ degrees of freedom. Computing the Jacobian by hand in these situations is arduous and prone to error. Finite difference approximations of the Jacobian or its action are prone to truncation error, especially in multiphysics settings. Symbolic differentiation packages may be used, but often result in an excessive number of terms in realistic model scenarios. An alternative to symbolic and numerical differentiation is automatic differentiation (AD), which propagates derivatives with every elementary operation of a computer program, corresponding to continual application of the chain rule. Automatic differentiation offers the guarantee of an exact Jacobian at a relatively small overhead cost. In this work, we outline the adoption of AD in the Multiphysics Object Oriented Simulation Environment (MOOSE) via the MetaPhysicL package. We describe the application of MOOSE’s AD capability to several sets of physics that were previously infeasible to model via hand-coded or Jacobian-free simulation techniques, including arbitrary Lagrangian-Eulerian and level-set simulations of laser melt pools, phase-field simulations with free energies provided through neural networks, and metallic nuclear fuel simulations that require inner Newton loop calculation of nonlinear material properties.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2018

Extracting the turbulent flow-field from beam emission spectroscopy images using velocimetry

The 2D turbulent E × B flow-field is inferred from density fluctuation images obtained with the beam emission spectroscopy diagnostic on DIII-D using the orthogonal dynamic programming velocimetry algorithm. A synthetic turbulence model is used to test the algorithm and optimize it for measuring zonal flows. Zonal flow measurements are found to require a signal-to-noise ratio above ~10 and a zonal flow wavelength longer than ~2 cm. Comparison between the velocimetry-estimated flow-field and the E × B flow-field using a nonlinear gyrokinetic GENE simulation finds that the flow-fields have identical spatial structure and differ only by the mean turbulence phase velocity, which is spatially uniform in this flux tube simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Building Battery Energy Storage System Performance Data into an Economic Assessment

Economic assessments of battery energy storage systems (BESSs) rely on optimal dispatch methods to capture temporal interdependency of BESS operations and coupling among different grid applications. Many existing BESS economic assessment studies are based on a simplified first-order scalar model using BESS nameplate numbers. Such a method cannot accurately capture varying capabilities and nonlinear dynamics of a BESS, leading to inaccurate assessment results. This paper presents a practical implementation of performance data into the economic assessment of the BESSs recently developed within the Snohomish Public Utility District system in Washington State. Extensive testing conducted over multiple seasons is used to assess the technical performance and develop high-fidelity models of the BESSs. A dynamic programming algorithm is proposed to optimally dispatch the BESSs and assess the potential benefits from stacked value streams. The proposed method can be adapted for the economic assessment of other BESSs with different applications.

Wu, Di↗

DOE OSTI2015

Dynamic force matching: A method for constructing dynamical coarse-grained models with realistic time dependence

Coarse-grained (CG) models of molecular systems, with fewer mechanical degrees of freedom than an all-atom model, are used extensively in chemical physics. It is generally accepted that a coarse-grained model that accurately describes equilibrium structural properties (as a result of having a well constructed CG potential energy function) does not necessarily exhibit appropriate dynamical behavior when simulated using conservative Hamiltonian dynamics for the CG degrees of freedom on the CG potential energy surface. Attempts to develop accurate CG dynamic models usually focus on replacing Hamiltonian motion by stochastic but Markovian dynamics on that surface, such as Langevin or Brownian dynamics. However, depending on the nature of the system and the extent of the coarse-graining, a Markovian dynamics for the CG degrees of freedom may not be appropriate. In this paper, we consider the problem of constructing dynamic CG models within the context of the Multi-Scale Coarse-graining (MS-CG) method of Voth and coworkers. We propose a method of converting a MS-CG model into a dynamic CG model by adding degrees of freedom to it in the form of a small number of fictitious particles that interact with the CG degrees of freedom in simple ways and that are subject to Langevin forces. The dynamic models are members of a class of nonlinear systems interacting with special heat baths that were studied by Zwanzig [J. Stat. Phys. 9, 215 (1973)]. The properties of the fictitious particles can be inferred from analysis of the dynamics of all-atom simulations of the system of interest. This is analogous to the fact that the MS-CG method generates the CG potential from analysis of equilibrium structures observed in all-atom simulation data. The dynamic models generate a non-Markovian dynamics for the CG degrees of freedom, but they can be easily simulated using standard molecular dynamics programs. We present tests of this method on a series of simple examples that demonstrate that the method provides realistic dynamical CG models that have non-Markovian or close to Markovian behavior that is consistent with the actual dynamical behavior of the all-atom system used to construct the CG model. Both the construction and the simulation of such a dynamic CG model have computational requirements that are similar to those of the corresponding MS-CG model and are good candidates for CG modeling of very large systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Modeling Multiscale-Multiphase-Multicomponent Subsurface Reactive Flows Using Advanced Computing

The DOE SciDAC program funded a team that developed PFLOTRAN, the next-generation (peta-scale) massively parallel, multiphase, multicomponent reactive flow and transport code. These codes are required to improve understanding and risk management of subsurface contaminant migration and geological sequestration of carbon dioxide. The important fate and transport processes occurring in the subsurface span a wide range of spatial and temporal scales, and involve nonlinear interactions among many different chemical constituents. Due to the complexity of this problem, modeling subsurface processes normally requires simplifying assumptions. However, tools of advanced scientific computing that have been used in other areas such as energy and materials research can also help address challenging problems in the environmental and geoscience fields. The overall project was led by Los Alamos National Laboratory and included Argonne, Oak Ridge and Pacific Northwest National Laboratories, in addition to the University of Illinois. This report summarizes the results of the research done at the University of Illinois, which focused on improvements to the underlying physical and computational modeling of certain transport and mixing processes.

58 GEOSCIENCES↗

DOE OSTI2010

QMU as an Approach to Strengthening the Predictive Capabilities of Complex Models

Complex systems are made up of multiple interdependent parts, and the behavior of the entire system cannot always be directly inferred from the behavior of the individual parts. They are nonlinear and system responses are not necessarily additive. Examples of complex systems include energy, cyber and telecommunication infrastructures, human and animal social structures, and biological structures such as cells. To meet the goals of infrastructure development, maintenance, and protection for cyber-related complex systems, novel modeling and simulation technology is needed. Sandia has shown success using M&S in the nuclear weapons (NW) program. However, complex systems represent a significant challenge and relative departure from the classical M&S exercises, and many of the scientific and mathematical M&S processes must be re-envisioned. Specifically, in the NW program, requirements and acceptable margins for performance, resilience, and security are well-defined and given quantitatively from the start. The Quantification of Margins and Uncertainties (QMU) process helps to assess whether or not these safety, reliability and performance requirements have been met after a system has been developed. In this sense, QMU is used as a sort of check that requirements have been met once the development process is completed. In contrast, performance requirements and margins may not have been defined a priori for many complex systems, (i.e. the Internet, electrical distribution grids, etc.), particularly not in quantitative terms. This project addresses this fundamental difference by investigating the use of QMU at the start of the design process for complex systems. Three major tasks were completed. First, the characteristics of the cyber infrastructure problem were collected and considered in the context of QMU-based tools. Second, UQ methodologies for the quantification of model discrepancies were considered in the context of statistical models of cyber activity. Third, Bayesian methods for optimal testing in the QMU framework were developed. This completion of this project represent an increased understanding of how to apply and use the QMU process as a means for improving model predictions of the behavior of complex systems.

Gray, Genetha Anne↗

DOE OSTI2011

PyRAT - python radiography analysis tool (u)

PyRAT is a radiography analysis tool used to reconstruction images of unknown 1-0 objects. The tool is written in Python and developed for use on LINUX and Windows platforms. The tool is capable of performing nonlinear inversions of the images with minimal manual interaction in the optimization process. The tool utilizes the NOMAD mixed variable optimization tool to perform the optimization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Carbon Monoxide Mediated Hydrogen Release from PtCu Single-Atom Alloys: The Punctured Molecular Cork Effect

Pt-based materials are used extensively in heterogeneous catalytic processes, yet they are notoriously susceptible to poisoning by CO. In contrast, highly dilute binary alloys formed of isolated Pt atoms in a Cu metal host, known as PtCu single-atom alloys (SAAs), are more resilient to CO poisoning during catalytic hydrogenation reactions. In this article, we describe how CO affects the adsorption and desorption of H 2 from a model PtCu(111) SAA surface and gain a microscopic understanding of these species’ interaction at the Pt atom active sites. By combining temperature-programmed desorption and scanning tunneling microscopy with first-principles kinetic Monte Carlo, we identify CO as a Pt site blocker that prevents the low temperature adsorption and desorption of H 2 , the so-called molecular cork effect , first realized when examining PdCu SAAs. Intriguingly, for the case of PtCu, H 2 desorption occurs before CO release is detected. Additionally, desorption experiments show a nonlinear relationship between CO coverage of the Pt sites and H 2 desorption peak temperature. When all the Pt atoms are saturated by CO, a very sharp H 2 desorption feature is observed 55 K above the regular desorption temperature of H 2 . Our simulations reveal that the origin of these effects is the fact that desorption of just one CO molecule from a Pt site facilitates the fast release of many molecules of H 2 . In fact, just 0.7% of the CO adsorbed at Pt sites has desorbed when the H 2 desorption peak maximum is reached. The release of H 2 from CO-corked PtCu SAA surfaces is analogous to the escape of gas from a pressurized container with a small puncture. Given that small changes in CO surface coverage lead to large changes in H 2 evolution energetics, the punctured molecular cork effect must be considered when modeling reaction mechanisms on similar alloy systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Physics of the thermal quench in MST tokamak plasmas (Final Technical Report)

This project at the University of Wisconsin-Madison targeted measurements in tokamak plasmas in the Madison Symmetric Torus (MST) to help elucidate the physics of the tokamak disruption. We intended to focus on the thermal quench, during which energy is lost from the plasma in a very short time. Understanding and ultimately mitigating the thermal quench are among the highest priority research thrusts for ITER, a large international fusion experiment presently under construction. The measurements in MST exploited an advanced set of diagnostics for internal measurements with high time resolution, targeting linear and nonlinear magnetohydrodynamic (MHD) activity as well as the electron temperature and density profiles. We also exploited other features of the MST device, including very flexible power supplies for the toroidal magnetic field and toroidal plasma current that are capable of producing almost arbitrary waveforms. While the work funded by this project was purely experimental, we continued and expanded an existing collaboration with UW-Madison experts in nonlinear MHD computational modeling of tokamak plasmas. That modeling incorporated realistic, experimentally measured parameters. The results of the modeling were anticipated to deepen considerably our understanding of the experimental measurements, and in turn, the experimental measurements were anticipated to help validate the modeling results. The science of transients such as disruptions is one of the highest priority research areas in the U.S. and international fusion programs. The work carried out in this project was targeted to help advance the science of tokamak disruptions which will in turn contribute to the success of ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Optimal Transmission Switching Using the IV-ACOPF Linearization

In this paper we seek to investigate the performance of transmission switching using the iterative linear program approximation to the Current Voltage AC Optimal Power Flow (IV-ACOPF). Several different methods of using this switching are investigated to find a method that addresses the MIP challenges and is both fast and accurate. We consider opening only one line, opening up to five lines, and progressively opening one line at a time. The linear method with switching is much faster than the nonlinear ACOPF and generally finds solutions within 1% of the nonlinear ACOPF.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2020

PETSc Users Manual (Rev. 3.13)

This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear solvers, nonlinear solvers, and time integrators that may be used in application codes written in Fortran, C, C++, and Python. PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++, python, or Fortran and experience using a debugger such as gdb or dbx, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than \rolling them" yourself.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

First Results of the IOTA Ring Research at Fermilab

The IOTA ring at Fermilab is a unique machine exclusively dedicated to accelerator beam physics R&D. The research conducted at IOTA includes topics such as nonlinear integrable optics, suppression of coherent beam instabilities, optical stochastic cooling and quantum science experiments. In this talk we report on the first results of experiments with implementations of nonlinear integrable beam optics. The first of its kind practical realization of a two-dimensional integrable system in a strongly-focusing storage ring was demonstrated allowing among other things for stable beam circulation near or at the integer resonance. Also presented will be the highlights of the world’s first demonstration of optical stochastic beam cooling and other selected results of IOTA’s broad experimental program.

43 PARTICLE ACCELERATORS↗

DOE OSTI2017

Algorithm and program for precise determination of unit-cell parameters of single crystal taking into account the sample eccentricity

A technique has been developed to refine the unit-cell parameters of single crystals with minimization of the influence of instrumental errors on the result. The corresponding computational procedure HuberUB is added to the software package of Huber-5042 diffractometer with a point detector and closedcycle helium cryostat Displex DE-202. The parameters of unit cell, its orientation, the goniometer zero angles, the sample eccentricity, the distances in the goniometer, and the radiation wavelength were refined by the nonlinear least-squares method, which allows imposition of constraints on the unit-cell parameters, depending on the crystal symmetry. The technique is approved on a LuB{sub 12} single crystal. The unit-cell parameters are determined in a temperature range of 20–295 K, with an absolute error not larger than 0.0004 Å (the relative error is of ~5 × 10{sup –5}). The estimates of the unit-cell parameters obtained by the proposed method are evidenced to be unbiased. Some specific features of the behavior of parameters in the ranges of 120–140 and 20–50 K are revealed, which correlate with the anomalies of the physical properties of the crystal.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2013

Light Water Reactor Sustainability Program Status Report on the Grizzly Code Enhancements

This report summarizes work conducted during fiscal year 2013 to work toward developing a full capability to evaluate fracture contour J-integrals to the Grizzly code. This is a progress report on ongoing work. During the next fiscal year, this capability will be completed, and Grizzly will be capable of evaluating these contour integrals for 3D geometry, including the effects of thermal stress and large deformation. A usable, limited capability has been developed, which is capable of evaluating these integrals on 2D geometry, without considering the effects of material nonlinearity, thermal stress or large deformation. This report presents an overview of the approach used, along with a demonstration of the current capability in Grizzly, including a comparison with an analytical solution.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2013

PETSc Users Manual (Rev. 3.3)

This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear, nonlinear equation solvers and time integrators that may be used in application codes written in Fortran, C, C++, Python, and MATLAB (sequential). PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++ or Fortran and experience using a debugger such as gdb or dbx, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than “rolling them” yourself; For many tasks a package such as MATLAB is often the best tool; PETSc is not intended for the classes of problems for which effective MATLAB code can be written. PETSc also has a MATLAB interface, so portions of your code can be written in MATLAB to “try out” the PETSc solvers. The resulting code will not be scalable however because currently MATLAB is inherently not scalable; and PETSc should not be used to attempt to provide a “parallel linear solver” in an otherwise sequential code. Certainly all parts of a previously sequential code need not be parallelized but the matrix generation portion must be parallelized to expect any kind of reasonable performance. Do not expect to generate your matrix sequentially and then “use PETSc” to solve the linear system in parallel. Since PETSc is under continued development, small changes in usage and calling sequences of routines will occur. PETSc is supported; see the web site http://www.mcs.anl.gov/petsc for information on contacting support. A http://www.mcs.anl.gov/petsc/publications may be found a list of publications and web sites that feature work involving PETSc. We welcome any reports of corrections for this document.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

PETSc Users Manual (Rev. 3.4)

This manual describes the use of PETSc for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear, nonlinear equation solvers and time integrators that may be used in application codes written in Fortran, C, C++, Python, and MATLAB (sequential). PETSc provides many of the mechanisms needed within parallel application codes, such as parallel matrix and vector assembly routines. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background, experience programming in C, C++ or Fortran and experience using a debugger such as gdb or dbx, it may require a significant amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates may make the efficient implementation of many application codes simpler than “rolling them” yourself; For many tasks a package such as MATLAB is often the best tool; PETSc is not intended for the classes of problems for which effective MATLAB code can be written. PETSc also has a MATLAB interface, so portions of your code can be written in MATLAB to “try out” the PETSc solvers. The resulting code will not be scalable however because currently MATLAB is inherently not scalable; and PETSc should not be used to attempt to provide a “parallel linear solver” in an otherwise sequential code. Certainly all parts of a previously sequential code need not be parallelized but the matrix generation portion must be parallelized to expect any kind of reasonable performance. Do not expect to generate your matrix sequentially and then “use PETSc” to solve the linear system in parallel. Since PETSc is under continued development, small changes in usage and calling sequences of routines will occur. PETSc is supported; see the web site http://www.mcs.anl.gov/petsc for information on contacting support. A http://www.mcs.anl.gov/petsc/publications may be found a list of publications and web sites that feature work involving PETSc. We welcome any reports of corrections for this document.

97 MATHEMATICS AND COMPUTING↗