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Results for “Structure preserving algorithms”

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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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Los Alamos National Laboratory Computational Physics Summer Student Workshop (Final Report)

The numerical solution of highly compressible, multi-material flows is an ongoing research area. These types of flows can be solved with a Lagrangian type mesh which moves with the material in a simulation to allow precise material interface tracking. Currently, researchers at Los Alamos National Laboratory and elsewhere are investigating cell-centered Lagrangian algorithms with the aim of producing methods that have second-order accuracy, preserve symmetry, and do not generate spurious vorticity. The new cell-centered algorithms solve a Riemann-like problem at the vertex of a cell. Professor Phil Roe at the University of Michigan has proposed a new structure for Lagrangian hydrodynamic algorithms that does not rely on the solution of the Riemann problem. The new approach utilizes Flux Corrected Transport (FCT) and it implements a form of vorticity control. The first step in the development of this method has been to construct an algorithm that solves the acoustic equations on an Eulerian mesh. The algorithm, which builds on the work of Morton and Roe, calculates fluxes at cell vertices, attains second-order accuracy using FCT, and has the special property of preserving vorticity. Results are presented that confirm the second order accuracy of the scheme and the vorticity preserving properties. The results are compared to the output produced by a MUSCL-Hancock algorithm. Some discussion of limiting methods for the FCT algorithm is also given.

42 ENGINEERING↗
DOE OSTI2024

Structure preserving and energy dissipative contact approaches for implicit dynamics

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

42 ENGINEERING↗
DOE OSTI2024

AMReX v2024

The software framework, AMReX, supports the development of block-structured adaptive mesh refinement (AMR) algorithms for solving systems of partial differential equations. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving the essential local descriptions of different physical processes in complex multiphysics algorithms. AMR uses a hierarchical representation of the solution at multiple levels of resolution where the solution on each level is defined on the union of data containers at that resolution. These data containers, which represent the solution over a logically rectangular subregion of the domain, can contain field data defined on a mesh, Lagrangian particles or combinations of both. In addition to these basic data types, AMReX supports a multilevel embedded boundary representation of complex geometry; linear solvers for cell-centered and nodal data; asynchronous I/O in a native format readable by ParaView, VisIt and yt; and interfaces to hypre and PETSc solvers. AMReX enables applications to run on distributed memory architectures with multicore CPUs and with GPU accelerators. AMReX uses a lightweight abstraction layer that effectively hides the details of the architecture from the application. The framework currently supports CUDA, HIP and SYCL for GPU acceleration and OpenMP for multi-core CPU architectures.

Almgren, Ann↗
DOE OSTI2013

Block-oriented modeling of superstructure optimization problems

We present a novel software framework for modeling large-scale engineered systems as mathematical optimization problems. A key motivating feature in such systems is their hierarchical, highly structured topology. Existing mathematical optimization modeling environments do not facilitate the natural expression and manipulation of hierarchically structured systems. Rather, the modeler is forced to "flatten" the system description, hiding structure that may be exploited by solvers, and obfuscating the system that the modeling environment is attempting to represent. To correct this deficiency, we propose a Python-based "block-oriented" modeling approach for representing the discrete components within the system. Our approach is an extension of the Pyomo library for specifying mathematical optimization problems. Through the use of a modeling components library, the block-oriented approach facilitates a clean separation of system superstructure from the details of individual components. This approach also naturally lends itself to expressing design and operational decisions as disjunctive expressions over the component blocks. By expressing a mathematical optimization problem in a block-oriented manner, inherent structure (e.g., multiple scenarios) is preserved for potential exploitation by solvers. In particular, we show that block-structured mathematical optimization problems can be straightforwardly manipulated by decomposition-based multi-scenario algorithmic strategies, specifically in the context of the PySP stochastic programming library. We illustrate our block-oriented modeling approach using a case study drawn from the electricity grid operations domain: unit commitment with transmission switching and N - 1 reliability constraints. Finally, we demonstrate that the overhead associated with block-oriented modeling only minimally increases model instantiation times, and need not adversely impact solver behavior. (C) 2013 Elsevier Ltd. All rights reserved.

Friedman, Z↗
DOE OSTI2025

Spectral Clustering-Based Partitioning of Large-Scale Power Electronics-Based Power Systems for Small-Signal Stability Analysis

The nodal admittance matrix (NAM)-based approach is well-suited for small-signal stability analysis of large-scale power electronics-based power systems (PEPSs), as it preserves the system structure through its admittance matrix. Previous studies have explored partitioning such systems into subareas and interconnections to reduce computational burden; however, they lacked a formal algorithmic procedure for determining feasible partitions. While several grid partitioning methods, such as those based on graph theory or machine learning, exist in the literature, they cannot be directly applied to NAM-based analysis due to differing objectives and constraints. Here, this paper addresses this gap by presenting a systematic, step-by-step procedure for applying a spectral partitioning algorithm that yields a division of the system into subareas suitable for NAM-based analysis. The computational complexity of the proposed method is also derived to demonstrate its efficiency and justify the practicality of the resulting subarea decomposition. The performance of the partitioning method is evaluated by applying the spectral clustering-derived subareas and interconnections to the NAM-based partitioning approach on a 140-bus system. Computational times for the full-system and partitioned NAM analyses are compared using MATLAB. Additionally, PSCAD simulations of the complete system and partitioned subareas are carried out to verify the effectiveness of the proposed method.

Nupur [Univ. of Tennessee, Knoxville, TN (United S↗
DOE OSTI2019

AMReX: a framework for block-structured adaptive mesh refinement

AMReX is a C++ software framework that supports the development of block-structured adaptive mesh refinement (AMR) algorithms for solving systems of partial differential equations (PDEs) with complex boundary conditions on current and emerging architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving the local descriptions of different physical processes in complex multiphysics algorithms. Current AMReX-based application codes span a number of areas, including atmospheric modeling, astrophysics, combustion, cosmology, fluctuating hydrodynamics, multiphase flows, and particle accelerators. In particular, the AMReX-Astro GitHub repository holds a number of astrophysical modeling tools based on AMReX. The origins of AMReX trace back to the BoxLib software framework. AMReX supports a number of different time-stepping strategies and spatial discretizations. Solution strategies supported by AMReX range from level-by-level approaches (with or without subcycling in time) with multilevel synchronization to full-hierarchy approaches, and any combination thereof. User-defined kernels that operate on patches of data can be written in C++ or Fortran; there is also a Fortran-interface functionality which wraps the core C++ data structures and operations in Fortran wrappers so that an application code based on AMReX can be written entirely in Fortran.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Distributed Link Removal Using Local Estimation of Network Topology

In this paper, we consider the problem of network structure manipulation in the absence of information on the global network topology. In particular, the problem of removing some of links is investigated in order to slow or stop the spread of disease in a network while preserving its connectivity. Existing methods solve this combinatorial problem in a centralized manner and they require the global information of network structure. In this paper, we propose a distributed design algorithm to compute a suboptimal solution to this problem efficiently by mimicking gradient based method, namely by iteratively removing one or multiple links at a time from the network. Specifically, using matrix perturbation analysis we formulate an optimization problem involving the eigenvector associated with the largest eigenvalue of the adjacency matrix and whose solution is equal to a suboptimal solution to the original problem. This strategy also enables us to overcome the combinatorial issue of the problem. Distributed algorithms to estimate the eigenvector and to verify network’s connectivity are then proposed which facilitate us to solve the new optimization problem. In addition, topological insights into the proposed algorithm and optimality of its solution are also discussed. Lastly, the proposed distributed design method is demonstrated and evaluated via several numerical examples.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2013

A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations

This is part II of our paper in which we propose and develop a dynamically bi-orthogonal method (DyBO) to study a class of time-dependent stochastic partial differential equations (SPDEs) whose solutions enjoy a low-dimensional structure. In part I of our paper [9], we derived the DyBO formulation and proposed numerical algorithms based on this formulation. Some important theoretical results regarding consistency and bi-orthogonality preservation were also established in the first part along with a range of numerical examples to illustrate the effectiveness of the DyBO method. In this paper, we focus on the computational complexity analysis and develop an effective adaptivity strategy to add or remove modes dynamically. Our complexity analysis shows that the ratio of computational complexities between the DyBO method and a generalized polynomial chaos method (gPC) is roughly of order O((m/N{sub p}){sup 3}) for a quadratic nonlinear SPDE, where m is the number of mode pairs used in the DyBO method and N{sub p} is the number of elements in the polynomial basis in gPC. The effective dimensions of the stochastic solutions have been found to be small in many applications, so we can expect m is much smaller than N{sub p} and computational savings of our DyBO method against gPC are dramatic. The adaptive strategy plays an essential role for the DyBO method to be effective in solving some challenging problems. Another important contribution of this paper is the generalization of the DyBO formulation for a system of time-dependent SPDEs. Several numerical examples are provided to demonstrate the effectiveness of our method, including the Navier–Stokes equations and the Boussinesq approximation with Brownian forcing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

MrHyDE v.1.0

SAND2024-01324O MrHyDE, which stands for Multi-resolution Hybridized Differential Equations, is a general-purpose C++ package for the solution of coupled multiphysics and multiscale systems on massively parallel computing systems. MrHyDE is designed to enable moving beyond forward simulation for multiscale applications which includes optimization, control, uncertainty quantification, and stochastic inversion. The framework provides interfaces to several packages within the Trilinos framework and leverages automatic differentiation to enable adjoint capabilities for large-scale, gradient-based optimization. MrHyDE provides automated multiscale capabilities through a subgrid model interface and multiscale Dirichlet-to-Neumann maps. For extreme-scale applications, MrHyDE provides in situ data-compression algorithms to reduce memory requirements while maintaining performance. MrHyDE is a general-purpose, computational framework for the solution of multiscale and multiphysics applications. It uses a combination of structure-preserving, physics-compatible discretizations, fully implicit methods, multi-resolution schemes, or fully explicit methods. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

SciDAC↗
DOE OSTI2015

Identification of subsurface structures using electromagnetic data and shape priors

We consider the inverse problem of identifying large-scale subsurface structures using the controlled source electromagnetic method. To identify structures in the subsurface where the contrast in electric conductivity can be small, regularization is needed to bias the solution towards preserving structural information. We propose to combine two approaches for regularization of the inverse problem. In the first approach we utilize a model-based, reduced, composite representation of the electric conductivity that is highly flexible, even for a moderate number of degrees of freedom. With a low number of parameters, the inverse problem is efficiently solved using a standard, second-order gradient-based optimization algorithm. Further regularization is obtained using structural prior information, available, e.g., from interpreted seismic data. The reduced conductivity representation is suitable for incorporation of structural prior information. Such prior information cannot, however, be accurately modeled with a gaussian distribution. To alleviate this, we incorporate the structural information using shape priors. The shape prior technique requires the choice of kernel function, which is application dependent. We argue for using the conditionally positive definite kernel which is shown to have computational advantages over the commonly applied gaussian kernel for our problem. Numerical experiments on various test cases show that the methodology is able to identify fairly complex subsurface electric conductivity distributions while preserving structural prior information during the inversion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Noise-gating to Clean Astrophysical Image Data

I present a family of algorithms to reduce noise in astrophysical images and image sequences, preserving more information from the original data than is retained by conventional techniques. The family uses locally adaptive filters (“noise gates”) in the Fourier domain to separate coherent image structure from background noise based on the statistics of local neighborhoods in the image. Processing of solar data limited by simple shot noise or by additive noise reveals image structure not easily visible in the originals, preserves photometry of observable features, and reduces shot noise by a factor of 10 or more with little to no apparent loss of resolution. This reveals faint features that were either not directly discernible or not sufficiently strongly detected for quantitative analysis. The method works best on image sequences containing related subjects, for example movies of solar evolution, but is also applicable to single images provided that there are enough pixels. The adaptive filter uses the statistical properties of noise and of local neighborhoods in the data to discriminate between coherent features and incoherent noise without reference to the specific shape or evolution of those features. The technique can potentially be modified in a straightforward way to exploit additional a priori knowledge about the functional form of the noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

On the importance of FIB-SEM specific segmentation algorithms for porous media

A new algorithmic approach to segmentation of highly porous three dimensional image data gained by focused ion beam tomography is described which extends the key-principle of local threshold backpropagation described in Salzer et al. (2012). The technique of focused ion beam tomography has shown to be capable of imaging the microstructure of functional materials. In order to perform a quantitative analysis on the corresponding microstructure a segmentation task needs to be performed. However, algorithmic segmentation of images obtained with focused ion beam tomography is a challenging problem for highly porous materials if filling the pore phase, e.g. with epoxy resin, is difficult. The gray intensities of individual voxels are not sufficient to determine the phase represented by them and usual thresholding methods are not applicable. We thus propose a new approach to segmentation that pays respect to the specifics of the imaging process of focused ion beam tomography. As an application of our approach, the segmentation of three dimensional images for a cathode material used in polymer electrolyte membrane fuel cells is discussed. We show that our approach preserves significantly more of the original nanostructure than a thresholding approach. - Highlights: • We describe a new approach to the segmentation of FIB-SEM images of porous media. • The first and last occurrences of structures are detected by analysing the z-profiles. • The algorithm is validated by comparing it to a manual segmentation. • The new approach shows significantly less artifacts than a thresholding approach. • A structural analysis also shows improved results for the obtained microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2015

U.S. stock market interaction network as learned by the Boltzmann machine

Here, we study historical dynamics of joint equilibrium distribution of stock returns in the U.S. stock market using the Boltzmann distribution model being parametrized by external fields and pairwise couplings. Within Boltzmann learning framework for statistical inference, we analyze historical behavior of the parameters inferred using exact and approximate learning algorithms. Since the model and inference methods require use of binary variables, effect of this mapping of continuous returns to the discrete domain is studied. The presented results show that binarization preserves the correlation structure of the market. Properties of distributions of external fields and couplings as well as the market interaction network and industry sector clustering structure are studied for different historical dates and moving window sizes. We demonstrate that the observed positive heavy tail in distribution of couplings is related to the sparse clustering structure of the market. We also show that discrepancies between the model’s parameters might be used as a precursor of financial instabilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Structure- and Physics-Preserving Reductions of Power Grid Models

The large size of multiscale, distribution and transmission, power grids hinders fast systemwide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable for fast simulations and follow-up applications. While the classical Kron reduction has been successful in reduced order modeling of power grids with traditional, hierarchical design, the selection of reference nodes for the reduced model in a multiscale, distribution and transmission, network becomes ambiguous. In this work we extend the use of the iterative Kron reduction by utilizing the electric grid's graph topology for the selection of reference nodes, consistent with the design features of multiscale networks. Additionally, we propose further reductions by aggregation of coherent subnetworks of triangular meshes, based on the graph topology and network characteristics, in order to preserve currents and build another power-flow equivalent network. Our reductions are achieved through the use of iterative aggregation of subgraphs that include general tree structures, lines, and triangles. Important features of our reduction algorithms include that (i) the reductions are either equivalent to the Kron reduction or otherwise produce a power-flow equivalent network; (ii) due to the mentioned power-flow equivalence, the reduced network can model the dynamic of the swing equations for a lossless, inductive, steady state network; (iii) the algorithms efficiently utilize hash tables to store the sequential reduction steps. The third feature allows for easy reintroduction of detailed models into the reduced, conceptual network and makes the final reduced order model backward compatible with a sequence of intermediate, partially reduced networks with varying resolution---the ordered sequence of iterative reductions corresponds to a sequence of reduced order models. The performance of our graph reduction algorithms and features of the reduced grids are discussed on a real-word transmission and distribution grid. We produce visualizations of the reduced models through open source libraries and release our reduction algorithms with example code and toy data.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Local rewiring algorithms to increase clustering and grow a small world

Abstract Many real-world networks have high clustering among vertices: vertices that share neighbours are often also directly connected to each other. A network’s clustering can be a useful indicator of its connectedness and community structure. Algorithms for generating networks with high clustering have been developed, but typically rely on adding or removing edges and nodes, sometimes from a completely empty network. Here, we introduce algorithms that create a highly clustered network by starting with an existing network and rearranging edges, without adding or removing them; these algorithms can preserve other network properties even as the clustering increases. They rely on local rewiring rules, in which a single edge changes one of its vertices in a way that is guaranteed to increase clustering. This greedy step can be applied iteratively to transform a random network into a form with much higher clustering. Additionally, the algorithms presented grow a network’s clustering faster than they increase its path length, meaning that network enters a regime of comparatively high clustering and low path length: a small world. These algorithms may be a basis for how real-world networks rearrange themselves organically to achieve or maintain high clustering and small-world structure.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Automatic Differentiation for Adjoint Stencil Loops

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is aided by compilers, libraries, and domain-specific languages. Reverse-mode automatic differentiation, also known as algorithmic differentiation, autodiff, adjoint differentiation, or back-propagation, is sometimes used to obtain gradients of programs that contain stencil loops. Unfortunately, conventional automatic differentiation results in a memory access pattern that is not stencil-like and not easily parallelisable. In this paper we present a novel combination of automatic differentiation and loop transformations that preserves the structure and memory access pattern of stencil loops, while computing fully consistent derivatives. The generated loops can be parallelised and optimised for performance in the same way and using the same tools as the original computation. We have implemented this new technique in the Python tool PerforAD, which we release with this paper along with test cases derived from seismic imaging and computational fluid dynamics applications.

Automatic Differentiation↗
DOE OSTI2023

Small-Signal Angle Stability-Oriented False Data Injection Cyber-Attacks on Power Systems

The small-signal angle stability (SSAS) of a power system is determined by the property of operation points. The widely applied false data injection (FDI) cyber-attack, however, is able to stealthily mislead the optimal power flow (OPF) and thus compromise operation points, leading to damages to the SSAS margin. Here, to provide insights for cyber defenders, this paper proposes and investigates a stealthy SSAS-oriented FDI cyber-attack focusing on two attacking purposes, i.e., the SSAS margin and operation cost, with higher priority on the former one. First, this paper establishes a novel bi-level model with an implicit SSAS constraint based on a structure preserving model to compromise operation points. Then, for the SSAS interarea mode in a typical two-area system, this paper formulates closed-form expressions of how the SSAS margin and operation cost behave with respect to stealthy injections. By comparison, for the SSAS local mode in general power systems, this paper proposes a moving target cyber-attack-based hierarchical solution algorithm. Simulation results on a two-area system, a Kundur 11 bus system, and a modified IEEE 14 bus system demonstrate the significant damaging effects of the proposed SSAS-oriented FDI cyber-attack and the conflict between the two attacking purposes.

Benders decomposition↗