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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Coupled momentum balance and phase-field solver with fenicsx module

Code solves momentum balance and phase-field equations simultaneously. The differential equations are solved on a discretized domain with appropriate boundary and initial conditions using finite element method. Primary purpose of the code is to simulate brittle fracture under dynamic loading. Constitutive equations are that of linear elasticity with degradation of stress due to fracture. Small strain formulation is used.

Zecevic, Milovan↗
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 OSTI2020

The virtual element method for linear elastodynamics models: Design, analysis, and implementation

We design the conforming virtual element method for the numerical simulation of two dimensional time-dependent elastodynamics problems. We investigate the performance of the method both theoretically and numerically. We prove the stability and the convergence of the semi-discrete approximation in the energy norm and derive optimal error estimates. We also show the convergence in the L 2 norm. The performance of the virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally seen in the p-refinement setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Modular Finite Element Methods

MFEM is a free, lightweight, scalable C++ library for finite element methods. The goal of MFEM is to enable research and development of scalable finite element discretization and solver algorithms through general finite element abstractions, accurate and flexible visualization, and tight integration with the hypre library. Conceptually, MFEM can be viewed as a finite element toolbox that provides the building blocks for developing finite element algorithms in a manner similar to that of MATLAB for linear algebra methods.

ECP↗
DOE OSTI2020

A quadratic programming flux correction method for high-order DG discretizations of S transport

In this work, we present a new flux-fixup approach for arbitrarily high-order discontinuous Galerkin (DG) discretizations of the S N transport equation, and we demonstrate the compatibility of this approach with the Variable Eddington Factor (VEF) method. The new fixup approach is sweep-compatible: during a transport sweep (block Gauss-Seidel iteration in which the scattering source is lagged), a local quadratic programming (QP) problem is solved in each spatial element to ensure that the solution satisfies certain physical constraints, including local particle balance. In this paper, we describe two choices of physical constraints, resulting in two variants of the method: QP Zero (QPZ) and QP Maximum Principle (QPMP). In QPZ, the finite element coefficients of the solution are constrained to be nonnegative. In QPMP, they are constrained to adhere to an approximate discrete maximum principle. There are two primary takeaways in this paper. First, when the positive Bernstein basis is used for DG discretization, the QPMP method eliminates negativities, preserves high-order accuracy for smooth problems, and significantly dampens unphysical oscillations in the solution. The latter feature – the dampening of unphysical oscillations – is an improvement upon standard, simpler fixup approaches such as the approach described in (denoted as the “zero and rescale” (ZR) method in this paper). This improvement comes at a moderate computational cost, but it is not prohibitive. Our results show that, even in an unrealistic worst-case scenario where 83% of the spatial elements require a fixup, the computational cost of performing a transport sweep with fixup is only ~31% greater than performing one without fixup. The second takeaway is that the VEF method can be used to accelerate the convergence of transport sweeps even when a fixup is applied. When optically thick regions are present, transport sweeps converge slowly, regardless of whether a fixup is applied, and acceleration is needed. However, attempting to apply standard diffusion synthetic acceleration (DSA) to fixed-up transport sweeps results in divergence for optically thick problems. Our results show that the same is not true for VEF. When VEF is combined with fixed-up transport sweeps, the result is a scheme that produces a nonnegative solution, converges independently of the mean free path, and, in the case of the QPMP fixup, adheres to an approximate discrete maximum principle.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Comparison of three state-of-the-art crystal plasticity based deformation twinning models for magnesium alloys

In magnesium alloys, deformation twinning and its interactions with dislocation slip are responsible for a sigmoidal shape stress–strain behavior and an asymmetrical tension–compression yield strength in magnesium alloys. The sensitivity of twinning to the underlying microstructure renders the crystal plasticity method the most commonly adopted modeling approach for magnesium-twinning. This paper compares three state-of-the-art crystal plasticity-based twinning models from the literature, namely the elastic-viscoplastic self-consistent twinning-detwinning (EVPSC-TDT) model, crystal plasticity finite element model based on enhanced predominate twin reorientation approach (CPFE-ePTR), and the crystal plasticity finite element model based on “discrete twinning” approach (CPFE-DT). A polycrystalline microstructure is simulated with all three methods to compare the resulting stress–strain curves and lattice strains to those from the experimentally measured data. All three methods showed the capability of capturing the experimental results with different levels of accuracy. Additionally, the EVPSC-TDT method avoids solving the finite element matrices and showed the highest computational efficiency. The CPFE-ePTR model shows a higher accuracy in capturing the lattice strain. The CPFE-DT relies on high-resolution finite element mesh and is much slower than the other two methods, but it captured the local deformation concentration and stress reversal phenomena near the twin band, which was not possible with the other two methods. Based on the comparison, guidance for the selection of the appropriate model based on the specific modeling target is provided in this paper.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient Reformulation of Linear and Nonlinear Solid-Phase Diffusion in Lithium-ion Battery Models using Symmetric Polynomials: Mass Conservation and Computational Efficiency

Lithium-ion batteries are typically modeled using porous electrode theory coupled with various transport and reaction mechanisms, along with suitable discretization or approximations for the solid-phase diffusion equation. The solid-phase diffusion equation represents the main computational burden for typical pseudo-2-dimensional (p2D) models since these equations in the pseudo r -dimension must be solved at each point in the computational grid. This substantially increases the complexity of the model as well as the computational time. Traditional approaches towards simplifying solid-phase diffusion possess certain significant limitations, especially in modeling emerging electrode materials which involve phase changes and variable diffusivities. A computationally efficient representation for solid-phase diffusion is discussed in this paper based on symmetric polynomials using Orthogonal Collocation and Galerkin formulation (weak form). A systematic approach is provided to increase the accuracy of the approximation (p form in finite element methods) to enable efficient simulation with a minimal number of semi-discretized equations, ensuring mass conservation even for non-linear diffusion problems involving variable diffusivities. These methods are then demonstrated by incorporation into the full p2D model, illustrating their advantages in simulating high C-rates and short-time dynamic operation of Lithium-ion batteries.

25 ENERGY STORAGE↗
DOE OSTI2026

A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD

Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge–Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.

Endeve, Eirik [ORNL] (ORCID:0000000312519507)↗
DOE OSTI2024

Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagrangian–Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. Here, the efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hybrid Basis and Multi-Center Grid Method for Strong-Field Processes

We present a time-dependent framework that combines a hybrid basis, consisting of Gaussian-type orbitals (GTOs) and finite-element discrete-variable representation (FEDVR) functions, with a multicenter grid to simulate strong-field and attosecond dynamics in atoms and molecules. The method incorporates the construction of the orthonormal hybrid basis, the evaluation of electronic integrals, a unitary time-propagation scheme, and the extraction of optical and photoelectron observables. Its accuracy and robustness are benchmarked on one-electron systems such as atomic hydrogen and the dihydrogen cation (H$^+_2$) through comparisons with essentially-exact reference results for bound-state energies, high-harmonic generation spectra, photoionization cross sections, and photoelectron momentum distributions. This work establishes the groundwork for its integration with quantum-chemistry methods, which is already operational but will be detailed in future work, thereby enabling ab initio simulations of correlated polyatomic systems in intense ultrafast laser fields.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

SCEPTRE 2.7 User's Guide

Sandia’s Computational Engine for Particle Transport for Radiation Effects (SCEPTRE) is a computer code that solves the linear Boltzmann transport equation, particularly targeting coupled photon-electron problems. It uses unstructured finite element meshes in space, multigroup in energy, and discrete ordinates (Sn) or other methods in angle. SCEPTRE uses an xml-based input file to specify the problem. This report documents the options and syntax of that input file.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. Finally, the simulations show that dislocations exhibit some self-organized structures as the strain is increased.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow

Here, a fast matrix-free formulation of the control volume finite element method is presented, requiring much less memory and computational work than previous efforts. The method is implemented and evaluated as a solver for low-Mach flow, including the evaluation of a preconditioning strategy for the pressure Poisson equation. The efficiency and scaling with polynomial order is evaluated on simple turbulent flows of interest, with appropriate solution quality metrics, and compared with a reference node-centered finite volume discretization. For a turbulent channel flow test, we show improvement in computational work for a given accuracy with the high-order scheme. The performance on a GPU accelerated platform is also investigated, with benefit shown for the matrix-free discretization.

42 ENGINEERING↗
DOE OSTI2023

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗