Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “discretization”

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.

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

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Block encodings of discrete subgroups on a quantum computer

We introduce a block encoding method for mapping discrete subgroups to qubits on a quantum computer. This method is applicable to general discrete groups, including crystal-like subgroups such as BI of S U ( 2 ) and V of S U ( 3 ) . We detail the construction of primitive gates—the inversion gate, the group multiplication gate, the trace gate, and the group Fourier gate—utilizing this encoding method for BT and for the first time BI group. We also provide resource estimations to extract the gluon viscosity. The inversion gates for BT and BI are benchmarked on the quantum computer with estimated fidelities of 40 − 4 + 5 % and 4 − 3 + 5 % , respectively. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Extended families of critical and stationary droplets for nonequilibrium phase transitions in spatially discrete bistable systems

Bistable nonequilibrium systems are realized in catalytic reaction-diffusion processes, biological transport and regulation, spatial epidemics, etc. Behavior in spatially continuous formulations, described at the mean-field level by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, p eq , of a control parameter, p , with metastability and hysteresis around p eq . For each p , there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as p → p eq . Spatially discrete analogs of these mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. Herein, we show that this feature, together with an orientation dependence of planar interface propagation also deriving from spatial discreteness, results in the occurrence of entire families of stationary droplets. The extent of these families increases approaching the transition and can be infinite if propagation failure is realized. In addition, there can exist a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Discrete generative diffusion models without stochastic differential equations: A tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025

Causer, Luke (ORCID:0000000194243473)↗
DOE OSTI2021

Variational Discrete Action Theory

In this work, we propose the variational discrete action theory (VDAT) to study the ground state properties of quantum many-body Hamiltonians. VDAT is a variational theory based on the sequential product density matrix (SPD) ansatz, characterized by an integer $\mathscr{N}$, which monotonically approaches the exact solution with increasing $\mathscr{N}$. To evaluate the SPD, we introduce a discrete action and a corresponding integer time Green’s function. We use VDAT to exactly evaluate the SPD in two canonical models of interacting electrons: the Anderson impurity model and the d = ∞ Hubbard model. For the latter, we evaluate $\mathscr{N}$ = 2 – 4, where $\mathscr{N}$ = 2 recovers the Gutzwiller approximation (GA), and we show that $\mathscr{N}$ = 3, which exactly evaluates the Gutzwiller-Baeriswyl wave function, provides a truly minimal yet precise description of Mott physics with a cost similar to that of the GA. VDAT is a flexible theory for studying quantum Hamiltonians, competing both with state-of-the-art methods and simple, efficient approaches all within a single framework.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Laser wakefield acceleration driven by a discrete flying focus

Laser wakefield acceleration (LWFA) may enable the next generation of TeV-scale lepton colliders. Reaching such energies will likely require multiple LWFA stages to overcome limitations on the energy gain achievable in a single stage. The use of stages, however, introduces challenges such as alignment, adiabatic matching between stages, and a lower average accelerating gradient. Here, we propose a discrete flying focus that can deliver higher energy gain in a single stage, thereby reducing the number of stages required for a target energy. A sequence of laser pulses with staggered focal points and delays drives a plasma wave in which an electron beam experiences a near-constant accelerating gradient over distances beyond those attainable with a conventional pulse. Simulations demonstrate that a discrete flying focus with a total energy of 150 J can transfer 40 GeV per electron to a 50-pC beam in a single 30-cm stage, corresponding to 50 dephasing lengths.

laser wakefield acceleration↗
DOE OSTI2022

Discrete and Integrated Solutions for Hybrid PV Plants Without Momentary Cessation in Low SCR and High Penetration PE Grids

With the increased penetration of power electronic (PE) based loads and sources, advanced solutions may be required for the enhancement of grid stability in regions with low short circuit ratio (SCR) and high penetration PE grids. The requirement of advanced solutions arises from the gradual paradigm shift of the electric grid from the traditional electric machine dominant system to a high penetration of PE-based system. One of the major challenges with such systems in recent times is the momentary cessation during alternating current (ac) grid transmission faults. During momentary cessation, PE-based resources cease to operate, thus creating probable reliability challenges for the grid. In this paper, potential feasible options to provide continuity of operation during such scenarios are presented. The options are considered through identifying upgrades in existing and upcoming discrete development of photovoltaic (PV) and energy storage systems (ESS) termed as discrete hybrid PV plants. Additionally, an advanced concept of integrated development of PV and ESS connecting to ac transmission grid links called multi-port autonomous reconfigurable solar power plant (MARS) is evaluated. The developed new solutions are evaluated for different grid use cases and scenarios in PSCAD.

Marthi, Phani Ratna Vanamali↗
DOE OSTI2020

A Hierarchical Volt-var Optimization with Discrete Variables in Unbalanced Distribution Systems

This paper proposes a framework to determine the optimal active and reactive power dispatch of distributed photovoltaic (PV) generation, switched capacitors, and voltage regulators in multi-phase unbalanced distribution systems. The objectives of the optimal dispatch are minimization of the energy loss, PV real power curtailment, and switching operations of capacitors and voltage regulators, in addition to elimination of voltage violation and reverse power flow. The optimization problem is formulated in rectangular coordinates as a nonlinear, nonconvex problem with discrete variables. A hierarchical twostage framework is proposed to effectively handle those discrete variables and reduce the computational time compared to the unified approach in which all variables are solved simultaneously. The efficacy of the proposed approach and the accuracy of the obtained numerical solution is validated using the unbalanced multi-phase IEEE 34-bus with 15-minute load and PV data.

Nguyen, Quan H.↗
DOE OSTI2024

Thermal Management of Discretized Heaters Using CuW Microchannel Heat Sinks and FC3283

Single-phase cooling using microchannel heat sinks (MCHS) has become a popular approach for overcoming the thermal challenges associated with high-powered microelectronic devices. Thermal management is one of the largest barriers to higher power densities in electronics and frequently limits overall device performance. The implementation of forced convective cooling via single-phase liquid cooling in MCHS reduces the thermal resistance resulting in lower device temperatures at high-power conditions, which can decrease the package size and extend the lifespan of devices. The goal of the work described in this article was to investigate practical cooling solutions for laser diode bars. This study examined the effectiveness of a copper tungsten (CuW) microchannel heat sink paired with a dielectric coolant (FC3283) for dissipating both discrete and uniform heat fluxes up to 600 W/cm2 across a 0.25-cm2 surface area through a numerical and experimental study. CuW was chosen as the MCHS material because it is thermal expansion matched to GaAs, which is a common laser diode substrate. FC3283 serves as a dielectric coolant that is compatible with power electronics cooling. The microchannels utilized in this work were approximately $365$ $μ$ m deep and $100$ $μ$ m wide resulting in a hydraulic diameter of $160$ $μ$ m. The study investigated the cooling performance across a variety of applied power loads and flow rates to determine optimal effectiveness. The resulting thermal resistance ranged from 0.15 cm2 K/W at the highest flow rate to 0.26 cm2 K/W at the lowest flow rate. Further, the resulting thermal performance from this study demonstrates the importance of considering discrete heat sources separately from uniform heat sources and proved that the unique combination of CuW microchannels with FC3283 can be a promising cooling option toward future advancements of laser diode bars and other high-power microelectronics.

42 ENGINEERING↗
DOE OSTI2020

A Method to Represent a Well in a Three‐Dimensional Discrete Fracture Network Model

Abstract In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three‐dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high‐resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real‐world case study.

Pham, Hai (ORCID:0000000310164394)↗
DOE OSTI2020

A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems

This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation that is based on a proposed modified version of the mortar method. The well-known mortar finite element discretization method is modified to admit a local structure, providing an element-by-element or subdomain-by-subdomain assembly property. This is achieved via the introduction of additional trace finite element spaces and degrees of freedom (unknowns) associated with the interfaces between adjacent elements or subdomains. The resulting nonconforming formulation and a reduced-via-static-condensation Schur complement form on the interfaces are used in the construction of auxiliary space preconditioners for a given conforming finite element discretization problem. Overall, the properties of these preconditioners are studied and their performance is illustrated on model second order scalar elliptic problems utilizing high order elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)

This article investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin discretization of advection-dominated flows. The motivation for this study is that the time-dependent advection-diffusion equation can be seen as a “steady” advection-diffusion problem in $(d+1)$-dimensions and AIR has been shown to be a robust solver for steady advection-dominated problems. Numerical examples demonstrate the effectiveness of AIR as a preconditioner for advection-diffusion problems on fixed and time-dependent domains, using both slab-by-slab and all-at-once space-time discretizations, and in the context of uniform and space-time adaptive mesh refinement. A closer look at the geometric coarsening structure that arises in AIR also explains why AIR can provide robust, scalable, space-time convergence on advective and hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Generic Discretization Library

The GenDiL library is a collection of C++ software abstractions designed to discretize and solve partial differential equations (PDEs) for high-performance computing (HPC) applications. Its primary focus is on modern C++ generic programming, which helps ensure portability across various hardware architectures. The central idea behind the library is to provide building blocks for numerical algorithms-such as discretization methods and iteration patterns-so that domain experts can focus on the math, rather than the low-level details of hardware or implementation. By defining abstractions for data types, iteration over computational grids, and scheduling of operations, the library isolates the high-level PDE algorithms from the platform-specific optimizations needed to achieve efficient performance.

Dudouit, Yohann [Lawrence Livermore National Labor↗
DOE OSTI2023

Diagonally implicit Runge–Kutta schemes: Discrete energy-balance laws and compactness properties

Abstract We study diagonally implicit Runge–Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.

Mathematics↗
DOE OSTI2021

PyGDH: Python Grid Discretization Helper

Mathematical models expressed in the form of discretized equations play an important role inmany scientific disciplines. In our experience, few domain scientists have sufficient backgroundin numerical computing (or the time required to acquire such a background) to use manyflexible and powerful but complex open source packages, such as FEniCS (Alnæs et al., 2015)and OpenFOAM (The OpenFOAM Foundation Ltd, n.d.). Many user-friendly open sourcepackages, such as FiPy (J. E. Guyer & Warren, 2009), and many commercial packages, suchas COMSOL Multiphysics (COMSOL AB, n.d.) and Simcenter STAR-CCM+ (Siemens DigitalIndustries Software, n.d.), provide limited flexibility in the equations that users can express.Additionally, the use of commercial packages, which by nature do not perform calculationstransparently, can hinder reproducibility, which is vital to the scientific process. PyGDH(“pigged”) is a Python 2 / Python 3 (Python Software Foundation, 1991–2020) package thatis meant to be accessible to scientists who might not be specialists in scientific computing,while approaching the level of flexibility associated with writing dedicated programs tailoredto solving specific problems. The PyGDH User’s Guide provides detailed instructions forcreating numerical models, including a brief introduction to necessary command line andPython (Python Software Foundation, 1991–2020) skills, and discussions of discretization andvalidation. Note that PyGDH emphasizes flexibility and simplicity over performance, and wasnot designed for high-performance applications or models describing complex spatial domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

High Order Implicit Residual-Based Spatial Discretization Error Estimation for S N Neutron Transport

This work demonstrates our novel residual source spatial discretization error estimator (LeR/TEAD) for a DGFEM-1 discretization and assesses it along with two contemporary estimators, Ragusa and Wang's h -refinement estimator (RW) and Duo, Azmy, and Zikatanov's explicit residual-based estimator (DAZ), on a suite of Method of Manufactured Solutions (MMS) 2D problems and three realistic problem geometries. LeR/TE-AD is attractive because it directly estimates the local error in the angular flux, as opposed to a mere indicator of the error's behavior, on the same mesh and method order as the original numerical solution, thus typically being less computationally intensive than a refinement-based method. On the MMS suite, LeR/TE-AD consistently displayed a reduced performance versus its DGFEM-0 results in terms of accuracy and precision metrics, though it was not typically grossly inaccurate. This is attributed to the irregularities in the true solution across singular characteristics limiting the local accuracy of the numerical flux solution, leading to poor derivative approximations used in the residual approximations. The error transport problem then spreads the error in the residual to nearby cells, causing a greater degree of imprecision that did not afflict DAZ or RW. In testing the estimators on realistic problem geometries, however, LeR/TE-AD fared better. In practice, the true error is much larger in non-idealized geometries like in MMS, and a superlinear true solution means that RW and DAZ are not beneficially biased for DGFEM-1 error estimation. LeR/TE-AD was typically first or second in accuracy, primarily competing with RW, but the latter usually consumed 2-4 times the computational time as LeR/TE-AD, and requires a solution with four times as many unknowns. Furthermore, RW and LeR/TE-AD can be used to compute direct estimates of the error in any quantity of interest that is based on the angular ux solution, such as the fission rate density in a fuel pin, whereas DAZ requires a heuristic extension due to its norm-based nature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Statistical Hauser-Feshbach model calculation for (α, n) reaction cross section and discrete level population

We calculate the α-particle induced reactions on 17,18 O, 19 F, and 23 Na, in the energy range 0 ≤ E α ≤ 10 MeV, with a particular attention to the branching ratios of populated discrete levels in the (α,n) channels. Since there are too many open channels to employ the R-matrix theory, we apply the statistical Hauser-Feshbach model to calculate these reaction cross sections and branching ratios. The branching ratio is defined as b n = $\frac{σ_n}{Σ_iσ_i + σ_c}$ , where σ n is the n-th level production cross section after the neutron emission, and σ c is the production of the continuum state. In the cases of our target nuclei and the energy range of interest, the residual nuclei of the neutron emission channel are always in their discrete states, so that σ c can be negligible.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Effects of finite element discretization and model simplification on calculations of ductile failure initiation

The finite element method is a scheme to discretize the infinite number of degrees of freedom in continuum-level problems down to a finite number of degrees of freedom. This discretization is done in conjunction with methods that also reduce the field differential equations to sets of algebraic ones that can be solved by arithmetical operations. Therefore, solutions attained by finite element models are approximations to the exact solutions of the field equations.

97 MATHEMATICS AND COMPUTING↗