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At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2020

A linearity preserving nodal variation limiting algorithm for continuous Galerkin discretization of ideal MHD equations

A stabilized continuous Galerkin (CG) method for magnetohydrodynamics (MHD) is presented herein. Ideal, compressible inviscid MHD equations are discretized in space on unstructured meshes using piecewise linear or bilinear finite element bases to get a semi-discrete scheme. Stabilization is then introduced to the semi-discrete method in a strategy that follows the algebraic flux correction paradigm. This involves adding some artificial diffusion to the high order, semi-discrete method and mass lumping in the time derivative term. The result is a low order method that provides local extremum diminishing properties for hyperbolic systems. The difference between the low order method and the high order method is scaled element-wise using a limiter and added to the low order scheme. The limiter is solution dependent and computed via an iterative linearity preserving nodal variation limiting strategy. The stabilization also involves an optional consistent background high order dissipation that reduces phase errors. The resulting stabilized scheme is a semi-discrete method that can be applied to inviscid shock MHD problems and may be even extended to resistive and viscous MHD problems. To satisfy the divergence free constraint of the MHD equations, we add parabolic divergence cleaning to the system. Various time integration methods can be used to discretize the scheme in time. We demonstrate the robustness of the scheme by solving several shock MHD problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG

Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method, and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Livermore Big Artificial Neural Network Toolkit

LBANN is a toolkit that is designed to train artificial neural networks efficiently on high performance computing architectures. It is optimized to take advantages of key High Performance Computing features to accelerate neural network training. Specifically it is optimized for low-latency, high bandwidth interconnects, node-local NVRAM, node-local GPU accelerators, and high bandwidth parallel file systems. It is built on top of the open source Elemental distributed-memory dense and spars-direct linear algebra and optimization library that is released under the BSD license. The algorithms contained within LBANN are drawn from the academic literature and implemented to work within a distributed-memory framework.

Essen, BrianVan↗

DOE OSTI2017

Tempus v. 1.0

Tempus is a software framework for the time integration of ordinary differential equations (ODEs), partial differential equations (PDEs), and differential-algebraic equations (DAEs). Examples of time-integration methods available are Forward Euler, Backward Euler, Explicit Runge-Kutta and Implicit Runge-Kutta methods. Tempus can be used from small systems of equations (e.g., single ODEs for the time evolution of plasticity models) to large-scale transient simulations requiring exascale computing (e.g., flow fields around reentry vehicles and magneto-hydrodynamics). Tempus will be released as part of Trilinos under a BSD open source license.

Obert, CurtisC.↗

DOE OSTI2026

Multi-physics Preconditioning for Thermally Activated Batteries

Thermal batteries, also known as molten-salt batteries, are single-use reserve power systems activated by pyrotechnic heat generation, which transitions the solid electrolyte into a molten state. The simulation of these batteries relies on multiphysics modeling to evaluate performance and behavior under various conditions. This paper presents advancements in scalable preconditioning strategies for the Thermally Activated Battery Simulator (TABS) tool, enabling efficient solutions to the coupled electrochemical systems that dominate computational costs in thermal battery simulations. We propose a hierarchical block Gauss-Seidel preconditioner implemented through the Teko package in Trilinos, which effectively addresses the challenges posed by tightly coupled physics, including charge transport, porous flow, and species diffusion. The preconditioner leverages scalable subblock solvers, including smoothed aggregation algebraic multigrid (SA-AMG) methods and domain-decomposition techniques, to achieve robust convergence and parallel scalability. Strong and weak scaling studies demonstrate the solver’s ability to handle problem sizes up to 51.3 million degrees of freedom on 2048 processors, achieving near sub-second setup and solve times for the end-to-end electrochemical solve. These advancements significantly improve the computational efficiency and turnaround time of thermal battery simulations, paving the way for higher-resolution models and enabling the transition from 2D axisymmetric to full 3D simulations.

25 ENERGY STORAGE↗

DOE OSTI2016

Livermore Big Artificial Neural Network Toolkit

Essen, Brian Van↗

DOE OSTI2020

ROM-Based Surrogate Systems Modeling of EBR-II

We report the System Analysis Module (SAM), developed and maintained by Argonne National Laboratory, is designed to provide whole-plant transient safety analysis capabilities for a number of advanced non-light water reactors, including sodium-cooled fast reactor (SFR), lead-cooled fast reactor (LFR), and molten salt reactor (MSR)/fluoride-salt-cooled high-temperature reactor (FHR) designs. SAM is primarily constructed as a systems-level analysis tool, with the potential to incorporate reduced order models from three-dimensional computational fluid dynamics (CFD) simulations to improve characterization of complex, multidimensional physics. It is recognized that the computational expense associated with CFD can be intractable for various engineering analyses, such as uncertainty quantification, inference, and design optimization. This paper explores the reducibility of a SAM model using recent advances in randomized linear algebra techniques, which attempt to find recurring patterns in the various realizations generated by a model after randomly perturbing all its input parameters. The reduction is described in terms of fewer degrees of freedom (DOFs), referred to as the active DOFs, for the model variables such as input model parameters and model responses. The results indicate that there is significant room for additional reduction that may be leveraged for additional computational gains when employing SAM for engineering-intensive analyses that require repeated model executions. Different from physics-based reduction approaches, the proposed approach allows one to estimate upper bounds on the reduction errors, which are rigorously developed in this work. Finally, different methods for surrogate model construction, such as regression and neural network-based training, are employed to correlate the input and output active DOFs, which are related back to the original variables using matrix-based linear transformations.

42 ENGINEERING↗

DOE OSTI2022

Performance and power modeling and prediction using MuMMI and 10 machine learning methods

Energy-efficient scientific applications require insight into how high performance computing system features impact the applications' power and performance. This insight can result from the development of performance and power models. Here, in this article, we use the modeling and prediction tool MuMMI (Multiple Metrics Modeling Infrastructure) and 10 machine learning methods to model and predict performance and power consumption and compare their prediction error rates. We use an algorithm-based fault-tolerant linear algebra code and a multilevel checkpointing fault-tolerant heat distribution code to conduct our modeling and prediction study on the Cray XC40 Theta and IBM BG/Q Mira at Argonne National Laboratory and the Intel Haswell cluster Shepard at Sandia National Laboratories. Our experimental results show that the prediction error rates in performance and power using MuMMI are less than 10% for most cases. By utilizing the models for runtime, node power, CPU power, and memory power, we identify the most significant performance counters for potential application optimizations, and we predict theoretical outcomes of the optimizations. Based on two collected datasets, we analyze and compare the prediction accuracy in performance and power consumption using MuMMI and 10 machine learning methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

The influence of interval arithmetic on the shape of uncertainly defined domains modelled by closed curves

The paper presents an unambiguous modelling of imprecisely defined shapes of closed curves using classical and directed interval arithmetic. The authors focus on the development of an effective strategy of modelling interval smooth closed curves (which enforce C{sup 2} continuity in points at which adjacent interval segments join) using interval cubic Bézier segments. For this purpose, algebraic relationships between Bézier and de Boor control points, formerly known for precisely defined curves, are generalized. We obtain interval control points that define interval closed curves. Additionally, the reliability of such way of modelling of closed curves is examined. We directly apply classical and directed interval arithmetic to mentioned relationships and try to solve obtained interval systems of algebraic equations. However, we obtain ambiguous solutions. Therefore, we propose our new strategy of modification of directed interval arithmetic to obtain reliable and unambiguous shapes of interval closed curves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Derivation of K-matrix reaction theory in a discrete basis formalism

The usual derivations of the S and K matrices for two-particle reactions proceed through the Lippmann–Schwinger equation with formal definitions of the incoming and outgoing scattering states. Here we present a simpler alternative derivation that is carried out completely in the Hamiltonian representation, using a discrete basis of configurations for the scattering channels as well as the quasi-bound configurations of the combined fragments. We use matrix algebra to derive an explicit expression for the K matrix in terms of the Hamiltonian of the internal states of the compound system and the coupling between the channels and the internal states. The formula for the K matrix includes explicitly a real dispersive shift matrix to the internal Hamiltonian that is easily computed in the formalism. That expression is applied to derive the usual form of the S matrix as a sum over poles in the complex energy plane. Some extensions and limitations of the discrete-basis Hamiltonian formalism are discussed in the concluding remarks and in the Appendix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

Attacking the Opioid Epidemic: Determining the Epistatic and Pleiotropic Genetic Architectures for Chronic Pain and Opioid Addiction

We describe the CoMet application for large-scale epistatic Genome-Wide Association Studies (eGWAS) and pleiotropy studies. High performance is attained by transforming the underlying vector comparison methods into highly performant generalized distributed dense linear algebra operations. The 2-way and 3-way Proportional Similarity metric and Custom Correlation Coefficient are implemented using native or adapted GEMM kernels optimized for GPU architectures. By aggressive overlapping of communications, transfers and computations, high efficiency with respect to single GPU kernel performance is maintained up to the full Titan and Summit systems. Nearly 300 quadrillion element comparisons per second and over 2.3 mixed precision ExaOps are reached on Summit by use of Tensor Core hardware on the Nvidia Volta GPUs. Performance is four to five orders of magnitude beyond comparable state of the art. CoMet is currently being used in projects ranging from bioenergy to clinical genomics, including for the genetics of chronic pain and opioid addiction.

Joubert, Wayne↗

DOE OSTI2015

Simulation Speed Analysis and Improvements of Modelica Models for Building Energy Simulation

This paper presents an approach for speeding up Modelica models. Insight is provided into how Modelica models are solved and what determines the tool’s computational speed. Aspects such as algebraic loops, code efficiency and integrator choice are discussed. This is illustrated using simple building simulation examples and Dymola. The generality of the work is in some cases verified using OpenModelica. Using this approach, a medium sized office building including building envelope, heating ventilation and air conditioning (HVAC) systems and control strategy can be simulated at a speed five hundred times faster than real time.

Jorissen, Filip↗

DOE OSTI2015

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, large conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.

58 GEOSCIENCES↗

DOE OSTI2021

Improving scalability of electronic structure code for molecular simulations in the presence of environment

A scalable density functional electronic code with Gaussian basis set, called UTEP-NRLMOL, is developed to perform simulations of molecular systems in the presence of the environment with particular attention to the memory requirements. In the electronic structure calculations, the memory and computation time are proportional to the number of atoms. Memory requirements for density functional calculations scale as N*N, where N is the number of atoms. While the recent advances in HPC offer platforms with large numbers of cores, the limited amount of memory available on a given node and poor scalability of the electronic structure codes hinder their efficient usage of these platforms. We have introduced new scaling and parallelization paradigms using MPI-3 shared-memory functionality combined with usage of sparse algebra and storage of matrices in sparse format. This extends the range of applicability of the UTEP-NRLMOL code to large systems over 10,000 atoms, or using up to 67,000 basis functions, and making use of HPC architectures using over 6,000 processors utilizing all available cores. We have also interfaced code with effective fragment potential and polarizable continuum model libraries. The code was used in simulations of several applications which are published in reputed scientific journals.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2017

Computing the non-Markovian coarse-grained interactions derived from the Mori–Zwanzig formalism in molecular systems: Application to polymer melts

Memory effects are often presented during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori–Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. In particular, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. Yet, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

One dimensional staggered bosons, clock models, and their noninvertible symmetries

We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete Z N symmetry predict that these are critical points with a U ( 1 ) current algebra at c = 1 and radius 2 N whenever N > 4 . We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2018

Divisible Rigid Groups. II. Stability, Saturation, and Elementary Submodels

A group G is said to be rigid if it contains a normal series G = G{sub 1} > G{sub 2} > . . . > G{sub m} > G{sub m+1} = 1, whose quotients G{sub i}/G{sub i+1} are Abelian and, treated as right ℤ[G/G{sub i}]- modules, are torsion-free. A rigid group G is divisible if elements of the quotient G{sub i}/G{sub i+1} are divisible by nonzero elements of the ring ℤ[G/G{sub i}]. Every rigid group is embedded in a divisible one. Previously, it was stated that the theory 𝔗{sub m} of divisible m-rigid groups is complete. Here, it is proved that this theory is ω-stable. Furthermore, we describe saturated models, study elementary submodels of an arbitrary model, and find a representation for a countable saturated model in the form of a limit group in the Fraïssé system of all finitely generated m-rigid groups. Also, it is proved that the theory 𝔗{sub m} admits quantifier elimination down to a Boolean combination of ∀∃-formulas.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Numerical solution of systems of fractional delay differential equations using a new kind of wavelet basis

In the present paper, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet basis and their properties are utilized to obtain their operational matrix of fractional integration in the Riemann–Liouville sense and delay operational matrix. Convergence and error bound of the expansion by this kind of wavelet functions are investigated. Then, these operational matrices along with the Galerkin approach have been implemented to solve systems of fractional delay differential equations (SFDDEs). The main superiority of the proposed technique is that it reduces SFDDEs to a system of algebraic equations. Moreover, accuracy and efficiency of the suggested Chelyshkov wavelet approach are verified through some linear and nonlinear SFDDEs. Finally, the obtained numerical results are compared with those previously reported in the literature.

97 MATHEMATICS AND COMPUTING↗