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NASA NTRS2005

Parallel Adaptive Mesh Refinement Library

Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.

Mac-Neice, Peter↗

NASA NTRS2021

How Well Do Multisatellite Products Capture the Space–Time Dynamics of Precipitation? Part I: Five Products Assessed via a Wavenumber–Frequency Decomposition

As more global satellite-derived precipitation products become available, it is imperative to evaluate them more carefully for providing guidance as to how well precipitation space–time features are captured for use in hydrologic modeling, climate studies, and other applications. Here we propose a space–time Fourier spectral analysis and define a suite of metrics that evaluate the spatial organization of storm systems, the propagation speed and direction of precipitation features, and the space–time scales at which a satellite product reproduces the variability of a reference “ground-truth” product (“effective resolution”). We demonstrate how the methodology relates to our physical intuition using the case study of a storm system with rich space–time structure. We then evaluate five high-resolution multisatellite products (CMORPH, GSMaP, IMERG-Early, IMERG-Final, and PERSIANN-CCS) over a period of 2 years over the southeastern United States. All five satellite products show generally consistent space–time power spectral density when compared to a reference ground gauge–radar dataset (GV-MRMS), revealing agreement in terms of average morphology and dynamics of precipitation systems. However, a deficit of spectral power at wavelengths shorter than 200 km and periods shorter than 4 h reveals that all satellite products are excessively “smooth.” The products also show low levels of spectral coherence with the gauge–radar reference at these fine scales, revealing discrepancies in capturing the location and timing of precipitation features. From the space–time spectral coherence, the IMERG-Final product shows superior ability in resolving the space–time dynamics of precipitation down to 200-km and 4-h scales compared to the other products.

Clement Guilloteau↗

DOE OSTI2022

Subsystem Estimation: A Modal Decomposition Approach

In structural analysis it is often the requirement that the response of a critical subsystem must be extracted from the response of the overall structure even when not directly excited or sometimes even measured. Based on this requirement, a number of signal processing approaches evolve that can provide a meaningful solution to this troubling problem; however, there is a variety of prior information (parameters or data) that must be available. For instance, knowledge of subsystem bandwidth may be enough to design a simple filter if there is little or no overlap with other component systems. If this is not satisfactory and a specific spectral response is required, then a model-based approach can be applied using an available free-free response of the subsystem from calibration or acceptance tests. However, when assembled and coupled with the overall system, the subsystem boundary conditions have been altered and therefore its response is altered as well.

42 ENGINEERING↗

DOE OSTI2024

Progressive Hedging Decomposition for Solutions of Large-Scale Process Family Design Problems

In previous work, we have introduced a mathematical model for solving a discretized version of the process family design problem. This involves two sets of decision variables. One set selects which unit module designs are included in the process platform out of a candidate set of options; the other set determines which of these unit module designs are assigned to each variant. In this work, we exploit a parallelized Progressive Hedging (PH) algorithm to solve even larger scale design problems. PH is a well-known algorithm traditionally used to solve stochastic programming problems. While our problem is not a two-stage stochastic programming problem, the structure is similar, and it can be directly mapped to the PH approach, which we employ here to solve this deterministic optimization problem. We decompose our problem by process variant. We treat the platform unit module design variables as first-stage and the assignment of unit module designs to variants as second-stage, solving the problem using mpi-sppy. We demonstrate this approach on case studies of CC, water desalination, and refrigeration.

Stinchfield, Georgia↗

DOE OSTI2022

How Cooperatively Folding Are Homopolymer Molecular Knots?

Detailed thermodynamic analysis of complex systems with multiple stable configurational states allows for insight into the cooperativity of each individual transition. In this work, we derive a heat capacity decomposition comprising contributions from each individual configurational state, which together sum to a baseline heat capacity, and contributions from each state-to-state transition. We apply this analysis framework to a series of replica exchange molecular dynamics simulations of linear and 1-1 coarse-grained homo-oligomer models, which fold into stable, configurationally well-defined molecular knots, in order to better understand the parameters leading to stable and cooperative folding of these knots. We find that a stiff harmonic backbone bending angle potential is key to achieving knots with specific 3D structures. Tuning the backbone equilibrium angle in small increments yields a variety of knot topologies. Populations of different knotted states as a function of temperature can also be manipulated by tuning the backbone torsion stiffness or by adding side-chain beads. We find that sharp total heat capacity peaks for the homo-oligomer knots are largely due to a coil-to-globule transition rather than a cooperative knotting step. Furthermore, in some cases, the cooperativity of globule-to-knot and coil-to-globule transitions is comparable, suggesting that highly cooperative folding to knotted structures can be achieved by refining the model parameters or adding sequence specificity.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Seismic fault weakening via CO 2 pressurization enhanced by mechanical deformation of dolomite fault gouges

Carbon dioxide emissions from dolomite decarbonation play an essential role in the weakening of carbonate faults by lowering the effective normal stress, which is thermally activated at temperatures above 600–700 °C. However, the mechanochemical effect of low-crystalline ultrafine fault gouge on the decarbonation and slip behavior of dolomite-bearing faults remains unclear. In this study, we obtained a series of artificial dolomite fault gouges with systematically varying particle sizes and dolomite crystallinities using a high-energy ball mill. The laboratory-scale pulverization of dolomite yielded MgO at temperatures below 50 °C, indicating that mechanical decarbonation without significant heating occurred due to the collapse of the crystalline structure, as revealed by X-ray diffraction and solid-state nuclear magnetic resonance results. Furthermore, the onset temperature of thermal decarbonation decreased to ~400 °C. Numerical modeling reproduced this two-stage decarbonation, where the pore pressure increased due to low-temperature thermal decarbonation, leading to slip weakening on the fault plane even at 400–500 °C; i.e., 200–300 °C lower than previously reported temperatures. Thus, the presence of small amounts of low-crystalline dolomite in a fault plane may lead to a severely reduced shear strength due to thermal decomposition at ~400 °C with a small slip weakening distance.

58 GEOSCIENCES↗

DOE OSTI2024

Convergence of Weak-SINDy Surrogate Models

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Tensor force role in β decays analyzed within the Gogny-interaction shell model

The half-life of the famous C 14 β decay is anomalously long, with different mechanisms: the tensor force, cross-shell mixing, and three-body forces, proposed to explain the cancellations that lead to a small transition matrix element. In this study, we revisit and analyze the role of the tensor force for the β decay of C 14 as well as of neighboring isotopes. We add a tensor force to the Gogny interaction, and derive an effective Hamiltonian for shell-model calculations. The calculations were carried out in a p – s d model space to investigate cross-shell effects. Furthermore, we decompose the wave functions according to the total orbital angular momentum L in order to analyze the effects of the tensor force and cross-shell mixing. The inclusion of the tensor force significantly improves the shell-model calculations of the β -decay properties of carbon isotopes. In particular, the anomalously slow β decay of C 14 can be explained by the isospin T = 0 part of the tensor force, which changes the components of N 14 with the orbital angular momentum L = 0 , 1 , and results in a dramatic suppression of the Gamow-Teller transition strength. At the same time, the description of other nearby β decays are improved. Decomposition of wave function into L components illuminates how the tensor force modifies nuclear wave functions, in particular suppression of β -decay matrix elements. Cross-shell mixing also has a visible impact on the β -decay strength. Inclusion of the tensor force does not seem to significantly change, however, binding energies of the nuclei within the phenomenological interaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2019

Pressio

Reduced-order Models (ROMs). ROMs are "compressed" approximations of high-fidelity computational models. Implementing ROM methods in production codes is typically intrusive, i.e. the native codes must be adapted and modified, with individual ROM methods reimplemented in every application code. This clearly constitutes an obstacle to users who want to use ROMs. To address this, we have developed Pressio, which is a C++ header-only ROM library that can be used by an application code in a non-intrusive fashion. The main objectives behind the design of Pressio are: (a) support for general computational models (data structures, PDE types); (b) heterogeneous hardware (CPU, GPU); (c) performance; and (d) extensibility. Using metaprogramming techniques, Pressio detects and leverages the application?s native linear algebra data structures (e.g. vector and matrix) to run the ROM methods. The application only needs to expose the velocity vector and Jacobian matrix via an adapter class. Pressio checks at compile time that the target application meets the correct API. The library is structured in several modular packages including (a) non-linear least-square solvers (e.g. Gauss-Newton with and without line-search); (b) singular value decomposition (for the computation of the ROM generalized coordinates) and (c) algebraic hyper-reduction.SAND2019-5878 M

Blonigan, Patrick↗

DOE OSTI2019

Pressio v.1.0

Blonigan, Patrick↗

DOE OSTI2019

Metabolic tradeoffs and heterogeneity in microbial responses to temperature determine the fate of litter carbon in simulations of a warmer world

Abstract. Climate change has the potential to destabilize the Earth's massive terrestrial carbon (C) stocks, but the degree to which models project this destabilization to occur depends on the kinds and complexities of microbial processes they simulate. Of particular note is carbon use efficiency (CUE), which determines the fraction of C processed by microbes that is anabolized into microbial biomass rather than lost to the atmosphere and soil as carbon dioxide and extracellular products. The temperature sensitivity of CUE is often modeled as an intrinsically fixed (homogeneous) property of the community, which contrasts with empirical data and has unknown impacts on projected changes to the soil C cycle under global warming. We used the Decomposition Model of Enzymatic Traits (DEMENT) – which simulates taxon-level litter decomposition dynamics – to explore the effects of introducing organism-level heterogeneity into the CUE response to temperature for decomposition of leaf litter under 5 ∘C of warming. We found that allowing the CUE temperature response to differ between taxa facilitated increased loss of litter C, unless fungal taxa were specifically restricted to decreasing CUE with temperature. Litter C loss was exacerbated by variable and elevated CUE at higher temperature, which effectively lowered costs for extracellular enzyme production. Together these results implicate a role for diversity of taxon-level CUE responses in driving the fate of litter C in a warmer world within DEMENT, which should be explored within the framework of additional model structures and validated with empirical studies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Model Reduction for Compressible Cavity Simulations Towards Uncertainty Quantification of Structural Loading

This report summarizes FY16 progress towards enabling uncertainty quantification for compressible cavity simulations using model order reduction (MOR). The targeted application is the quantification of the captive-carry environment for the design and qualification of nuclear weapons systems. To accurately simulate this scenario, Large Eddy Simulations (LES) require very fine meshes and long run times, which lead to week-long runs even on parallel state-of-the-art super- computers. MOR can reduce substantially the CPU-time requirement for these simulations. We describe two approaches for model order reduction for nonlinear systems, which can yield significant speed-ups when combined with hyper-reduction: the Proper Orthogonal Decomposition (POD)/Galerkin approach and the POD/Least-Squares Petrov Galerkin (LSPG) approach. The implementation of these methods within the in-house compressible flow solver SPARC is discussed. Next, a method for stabilizing and enhancing low-dimensional reduced bases that was developed as a part of this project is detailed. This approach is based on a premise termed "minimal subspace rotation", and has the advantage of yielding ROMs that are more stable and accurate for long-time compressible cavity simulations. Numerical results for some laminar cavity problems aimed at gauging the viability of the proposed model reduction methodologies are presented and discussed.

42 ENGINEERING↗

DOE OSTI2022

Electronic Structure Calculations of the Fundamental Interactions in Solvent Extraction Desalination

Solvent extraction desalination (SED) is a promising membrane-free desalination technology, but new solvents are still needed that can improve the molecular-level water selectivity, while minimizing solvent contamination in the aqueous phase. Improvements in solvent design for SED require a fundamental understanding of the molecular interactions governing solvation behavior. Herein, quantum chemical calculations are used to delineate different fundamental interactions in water-solvent systems involving 38 different solvents, with a particular focus on the role of the electrostatic potential characteristics. Furthermore, these interactions are rigorously analyzed using the independent gradient model based on Hirshfeld partition (IGMH), Symmetry-Adapted Perturbation Theory (SAPT), as well as the energy decomposition analysis based on force field (EDA-FF) to compare against a standard force field model. The solvation free energies and partition coefficients are also calculated to estimate water extraction performance in a bulk solvent system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1979

Investigations on the hierarchy of reference frames in geodesy and geodynamics

Problems related to reference directions were investigated. Space and time variant angular parameters are illustrated in hierarchic structures or towers. Using least squares techniques, model towers of triads are presented which allow the formation of linear observation equations. Translational and rotational degrees of freedom (origin and orientation) are discussed along with and the notion of length and scale degrees of freedom. According to the notion of scale parallelism, scale factors with respect to a unit length are given. Three-dimensional geodesy was constructed from the set of three base vectors (gravity, earth-rotation and the ecliptic normal vector). Space and time variations are given with respect to a polar and singular value decomposition or in terms of changes in translation, rotation, deformation (shear, dilatation or angular and scale distortions).

Grafarend, E. W.↗

NASA NTRS1987

Coherent structures

In order to develop more quantitative measures of coherent structures that would have comparative value over a range of experiments, it is essential that such measures be independent of the observer. It is only through such a general framework that theories with a fundamental predictive value can be developed. The triple decomposition phi = bar-phi + phi(c) + phi(r) (where bar-phi is the mean, phi(c) is the coherent part, and phi(r) is the random part of any turbulent field phi) serves this purpose. The equations of motion for the mean and coherent flow fields, based on the triple decomposition, are presented and modeling methods for the time-averaged and phase-averaged Reynolds stress are discussed.

Speziale, Charles G.↗

DOE OSTI2017

A generalized Ewald decomposition for screened Coulomb interactions

Medium-range interactions occur in a wide range of systems, including charged-particle systems with varying screening lengths. We generalize the Ewald method to charged systems described by interactions involving an arbitrary dielectric response function ϵ(𝐤). We provide an error estimate and optimize the generalization to find the break-even parameters that separate a neighbor list-only algorithm from the particle-particle particle-mesh algorithm. We examine the implications of different choices of the screening length for the computational cost of computing the dynamic structure factor. We then use our new method in molecular dynamics simulations to compute the dynamic structure factor for a model plasma system and examine the wave-dispersion properties of this system.

Dharuman, Gautham↗

NASA NTRS1996

Concurrent Probabilistic Simulation of High Temperature Composite Structural Response

A computational structural/material analysis and design tool which would meet industry's future demand for expedience and reduced cost is presented. This unique software 'GENOA' is dedicated to parallel and high speed analysis to perform probabilistic evaluation of high temperature composite response of aerospace systems. The development is based on detailed integration and modification of diverse fields of specialized analysis techniques and mathematical models to combine their latest innovative capabilities into a commercially viable software package. The technique is specifically designed to exploit the availability of processors to perform computationally intense probabilistic analysis assessing uncertainties in structural reliability analysis and composite micromechanics. The primary objectives which were achieved in performing the development were: (1) Utilization of the power of parallel processing and static/dynamic load balancing optimization to make the complex simulation of structure, material and processing of high temperature composite affordable; (2) Computational integration and synchronization of probabilistic mathematics, structural/material mechanics and parallel computing; (3) Implementation of an innovative multi-level domain decomposition technique to identify the inherent parallelism, and increasing convergence rates through high- and low-level processor assignment; (4) Creating the framework for Portable Paralleled architecture for the machine independent Multi Instruction Multi Data, (MIMD), Single Instruction Multi Data (SIMD), hybrid and distributed workstation type of computers; and (5) Market evaluation. The results of Phase-2 effort provides a good basis for continuation and warrants Phase-3 government, and industry partnership.

Abdi, Frank↗

DOE OSTI2024

Precision Calcination Mechanism of CaCO 3 to High-Porosity Nanoscale CaO CO 2 Sorbent Revealed by Direct In Situ Observations

Deploying energy storage and carbon capture at scale is hindered by the substantial endothermic penalty of decomposing CaCO 3 to CaO and CO 2 , and the rapid loss of CO 2 absorption capacity by CaO sorbent particles due to sintering at the high requisite decomposition temperatures. The decomposition reaction mechanism underlying sorbent deactivation remains unclear at the atomic level and nanoscale due to past reliance on postmortem characterization methods with insufficient spatial and temporal resolution. Thus, elucidating the important CaCO 3 decomposition reaction pathway requires direct observation by time-resolved (sub-)nanoscale methods. Here, chemical and structural dynamics during the decomposition of CaCO 3 nanoparticles to nanoporous CaO particles comprising high-surface-area CaO nanocrystallites are examined. Comparing in situ transmission electron microscopy (TEM) and synchrotron X-ray diffraction experiments gives key insights into the dynamics of nanoparticle calcination, involving anisotropic CaCO 3 thermal distortion before conversion to thermally dilated energetically stable CaO crystallites. Time-resolved TEM uncovered a novel CaO formation mechanism involving heterogeneous nucleation at extended CaCO 3 defects followed by sweeping reaction front motion across the initial CaCO 3 particle. These observations clarify longstanding, yet incomplete, reaction mechanisms and kinetic models lacking accurate information about (sub-)nanoscale dynamics, while also demonstrating calcination of CaCO 3 without sintering through rapid heating and precise temperature control.

36 MATERIALS SCIENCE↗