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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Domain-Decomposed A-ϕ Formulation Based on Lagrange Multipliers for Low-Frequency Problems

A domain-decomposed A-ϕ formulation based on Lagrange multipliers is proposed to simulate low-frequency elec- tromagnetic problems. This method partitions the computational domain into smaller subdomains, allowing each subdomain to be independently formulated using Lagrange multipliers as Dirichlet boundary conditions, while ensuring continuity of the fields across the interfaces. A mixed finite element method, utilizing both vector and scalar basis functions, is employed to discretize the formulation, resulting in a global system to be solved. The proposed method is validated using TEAM Problem 7 at 50 Hz, demonstrating its effectiveness in handling complex geometries and addressing the low-frequency breakdown issues commonly encountered in traditional finite element methods.

Hossain, Amzad↗
DOE OSTI2024

Prediction of residual stresses in additively manufactured parts using lumped capacitance and classical lamination theory

Several industries are interested in Laser Powder Bed Fusion (L-PBF) Additively Manufactured (AM) metal parts because their designs can be made arbitrarily complex while retaining bulk-type material properties. However, the residual stresses (RS) and distortions caused by the heat gradients inherent to L-PBF processes are detrimental to the structural integrity of the parts and must be taken into consideration during the part design cycle. Predicting the state of stresses in as-built 3D printed parts is a difficult problem that is typically approached with the use of transient thermomechanical Finite Element Models (FEMs). However, the nonlinearities associated with AM processes are difficult to capture in these FEMs without increasing the computational cost of the simulation, limiting their ability to be incorporated into practical design cycles. This work presents a novel analytical framework that combines lumped capacitance nonlinear heat transfer with time dependent classical lamination theory to efficiently and accurately predict RS in as-built L-PBF parts without the need of FEMs. The simulation was compared to Neutron Diffraction (ND) residual strain measurements taken at Oak Ridge National Laboratories (ORNL) as well as Synchrotron X-ray Diffraction (XRD) strain data published by the National Institute of Standards and Technology (NIST). The simulation predictions and the experimental data showed excellent agreement for the in-plane strain directions, and general agreement for the out of plane strain component, highlighting an area where further development can be implemented.

42 ENGINEERING↗
DOE OSTI2026

Langevin and Fokker-Planck analyses for diffusion-mediated passing of circular and discorectangular species in two-dimensional channels

The propensity for pairs of diffusing species to pass each other within narrow channels or pores is of basic interest as a first-passage-type problem. It is also of relevance for solution-phase transport in nanoporous materials, and in particular for catalytic conversion reactions where high yield requires that product species can efficiently pass reactant species to exit the pores. Here, we analyze a two-dimensional model with nonoverlapping circular and discorectangular species confined to a rectangular channel, and where passing is mediated by Brownian dynamics in an implicit solvent. For narrower channels where passing is still possible, the discorectangle must align with the channel to pass the circular species. Behavior of the passing propensity, 𝑃, can be assessed by strongly damped Langevin simulations, or within an equivalent Fokker-Planck equation (FPE) formalism. The latter corresponds to a diffusion problem in a “higher-dimensional channel” with a constriction. We assess the variation of the passing propensity, 𝑃, for a broad range of channel width including its scaling just above the threshold where passing is sterically blocked. Analysis of 𝑃 versus the rotational diffusion coefficient 𝐷 𝑟 of the discorectangle reveals a significant decrease in 𝑃 for lower 𝐷 𝑟 for moderate channel width. This prompts a direct analysis of the regime where 𝐷 𝑟 → 0 , for which the FPE can be reduced to a three-dimensional diffusion problem, precise analysis of which is facilitated by adaptive-mesh finite element methods. The dependence of 𝑃 on the aspect ratio of the discorectangle is also assessed.

Rahman, Md Khaledur [Ames Laboratory (AMES), Ames,↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A stable potential-based time-domain method for wideband elec- tromagnetic analysis

In previous research, the frequency-domain A-ϕ formulation has been validated using the finite element method for electromagnetic simulations of low-frequency and multi- scale problems, demonstrating excellent numerical accuracy, good matrix condition, and high computational efficiency. Time- domain simulations provide significant advantages for modeling wideband problems and are crucial for multiphysics applications. In this paper, the frequency-domain A-ϕ formulation is extended to the time domain. The central difference scheme is employed for temporal discretization to ensure both accuracy and stability. A numerical example is presented to demonstrate the capability of the proposed time-domain method in wideband electromagnetic analysis.

Mekonnen, Minyichil↗
DOE OSTI2026

Extremized nonlinear and linearized responses in soft metamaterials enabled by gradient-based design and grayscale digital light processing

In this study, we develop a gradient-based design approach that exploits grayscale digital light processing (DLP) 3D printing for extremizing the nonlinear and linearized response of soft metamaterials — materials that harness engineered geometric instabilities to undergo large and programmable changes in configuration. Grayscale DLP approaches modulate local mechanical properties at the pixel scale by tuning the light intensity within a single grayscale image, unlocking an exceptionally large design space. To effectively navigate this space, we develop smooth mappings between local light intensity values and global quantities of interest that characterize the behavior of soft metamaterials. Enabling these smooth mappings are robust and differentiable nonlinear finite element simulations powered by a trust region solver. A PDE-constrained optimization problem is then solved to invert these mappings and produce light intensity distributions that endow the printed part with varying stiffness and flexibility in distinctive regions. It is shown that optimizing the distribution of soft and stiff phases throughout a metamaterial structure results in markedly different buckling and self-contact configurations to drive extremized nonlinear compression and linearized vibration responses. Optimized light intensity distributions are translated to grayscale images and directly used to print soft metamaterial samples, showing remarkable agreement between the buckling and self-contact response in simulated and measured deformed configurations.

Additive manufacturing↗
DOE OSTI2025

A transient near to far field transformation method and verification benchmarking procedure

The numerical calculation of electromagnetic far fields in the time-domain requires a near to far field transformation (NTFF) method. While time-domain NTFF methods for popular finite-difference time-domain (FDTD) approaches are well established, there is little discourse on NTFF methods for finite-element time-domain (FETD) codes. Here, this work is concerned with the development of an NTFF method for the Empire FETD code, which utilizes curl and divergence conforming elements. This discretization presents a difficulty in obtaining the equivalent electric current for the NTFF. Straightforward finite element interpolation of the fields is shown to give poor accuracy. Alternative interpolation methods are recommended. An expanding magnetic quadrupole pulse benchmark problem, which is fully developed in the appendices, provides the basis for quantitative comparison.

FETD↗
DOE OSTI2025

Space-Time Finite Element Tensor Network Approach for the Time-Dependent Convection–Diffusion–Reaction Equation with Variable Coefficients

In this paper, we present a new space-time Galerkin-like method, where we treat the discretization of spatial and temporal domains simultaneously. This method utilizes a mixed formulation of the tensor-train (TT) and quantized tensor-train (QTT) (please see Section Tensor-Train Decomposition), designed for the finite element discretization (Q1-FEM) of the time-dependent convection–diffusion–reaction (CDR) equation. We reformulate the assembly process of the finite element discretized CDR to enhance its compatibility with tensor operations and introduce a low-rank tensor structure for the finite element operators. Recognizing the banded structure inherent in the finite element framework’s discrete operators, we further exploit the QTT format of the CDR to achieve greater speed and compression. Additionally, we present a comprehensive approach for integrating variable coefficients of CDR into the global discrete operators within the TT/QTT framework. The effectiveness of the proposed method, in terms of memory efficiency and computational complexity, is demonstrated through a series of numerical experiments, including a semi-linear example.

convection–diffusion–reaction equation↗
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 OSTI2026

HygroThermFEM v1.0

HygroThermFEM is a Finite Element Method-based numerical calculation engine for solving 2-D heat and moisture transfer problems. This numerical engine is used in the THERM software tool, and its primary purpose is for the analysis of building envelopes (e.g., windows, walls, roofs, foundations, etc.). However, the engine can also be used for any heat and moisture transfer problems that require solving fundamental 2-D energy and mass transfer equations. Fluid flow solutions (Navier-Stokes momentum equations) are not included, but the correlations for various convection heat transfer situations are provided, including the translation of complex cavity geometries into those for which correlations are applicable. The calculation engine is written in C++ and includes an API for connecting to third-party tools.

Vidanovic, Dragan [Lawrence Berkeley National Labo↗
DOE OSTI2025

On optimal control of hybrid dynamical systems using complementarity constraints

Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate them using non-smooth and non-convex complementarity constraints as a mathematical program with complementarity constraints (MPCC). We utilize a moving finite element based strategy to discretize the differential equation system to accurately locate the unknown switching points at the finite element boundary and achieve high-order accuracy at intermediate non-collocation points. We propose a globalization approach to solve the discretized MPCC problem using a mixed NLP/MILP-based strategy to converge to a non-spurious first-order optimal solution. The method is tested on three dynamic optimization examples, including a gas–liquid tank model and an optimal control problem with a sliding mode solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

PDE-constrained high-order mesh optimization

Here, we present a novel framework for PDE-constrained r-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regularization. We adopt the Target-Matrix Optimization Paradigm to control geometric properties across the mesh, independent of the PDE of interest. To incorporate the accuracy of the PDE solution, we introduce error measures that control the finite element discretization error. The implicit dependence of these error measures on the mesh nodal positions is accurately captured by adjoint sensitivity analysis. Additionally, a convolution-based gradient regularization strategy is used to ensure stable and effective adaptation of high-order meshes. We demonstrate that the proposed framework can improve mesh quality and reduce the error by up to 10 times for the solution of Poisson and linear elasto-static problems. The approach is general with respect to the dimensionality, the order of the mesh, the types of mesh elements, and can be applied to any PDE that admits well-defined adjoint operators.

Computer science↗
DOE OSTI2024

Poromechanical cohesive interface element with combined Mode I-II cohesive zone elastoplasticity for simulating fracture in fluid-saturated porous media

A combined Mode I-II cohesive zone (CZ) elasto-plastic constitutive model, and a two-dimensional (2D) cohesive interface element (CIE) are formulated and implemented at small strain within an ABAQUS User Element (UEL) for simulating 2D crack nucleation and propagation in fluid-saturated porous media. Here, the CZ model mitigates problems of convergence for the global Newton-Raphson solver within ABAQUS, which when combined with a viscous stabilization procedure allows for simulation of post-peak response under load control for coupled poromechanical finite element analysis, such as concrete gravity dam stability analysis. Verification examples are presented, along with a more complex ambient limestone-concrete wedge fracture experiment, water-pressurized concrete wedge experiment, and concrete gravity dam stability analyses. A calibration procedure for estimating the CZ parameters is demonstrated with the limestone-concrete wedge fracture process. For the water-pressurized concrete wedge fracture experiment it is shown that the inherent time-dependence of the poromechanical CIE analysis provides a good match with experimental force versus displacement results at various crack mouth opening rates, yet misses the pore water pressure evolution ahead of the crack tip propagation. This is likely a result of the concrete being partially-saturated in the experiment, whereas the finite element analysis assumes fully water saturated concrete. For the concrete gravity dam analysis, it is shown that base crack opening and associated water uplift pressure leads to a reduced Factor of Safety, which is confirmed by separate analytical calculations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Inverse problem in the large momentum effective theory framework

One proposal to compute parton distributions from first principles is the large momentum effective theory (LaMET), which requires the Fourier transform of matrix elements computed nonperturbatively. Lattice quantum chromodynamics (QCD) provides calculations of these matrix elements over a finite range of Fourier harmonics that are often noisy or unreliable in the largest computed harmonics. It has been suggested that enforcing an exponential decay of the missing harmonics helps alleviate this issue. Using nonperturbative data, we show that the uncertainty introduced by this inverse problem in a realistic setup remains significant without very restrictive assumptions, and that the importance of the exact asymptotic behavior is minimal for values of 𝑥 where the framework is currently applicable. We show that the crux of the inverse problem lies in harmonics of the order of 𝜆 = 𝑧⁢𝑃 𝑧 ∼ 5–15, where the signal in the lattice data is often barely existent in current studies, and the asymptotic behavior is not firmly established. We stress the need for more sophisticated techniques to account for this inverse problem, whether in the LaMET or related frameworks like the short-distance factorization. We also address a misconception that, with available lattice methods, the LaMET framework allows a “direct” computation of the 𝑥-dependence, whereas the alternative short-distance factorization only gives access to moments or fits of the 𝑥-dependence.

Dutrieux, Hervé [Aix-Marseille Université, Marseil↗
DOE OSTI2025

OpenSn: A massively parallel, open-source simulation environment for discrete ordinates radiation transport

OpenSn is an open-source, massively parallel deterministic radiation transport code for solving the discrete-ordinates ( S N ) form of the Boltzmann transport equation on unstructured, arbitrary polyhedral meshes. It supports high-fidelity simulations involving steady-state, eigenvalue, and adjoint problems for neutral particles (e.g., neutrons, photons, multi-particles), using the multigroup approximation in energy. OpenSn combines angular discretization via discrete ordinates with a discontinuous Galerkin finite element method (DGFEM) in space, enabling accurate resolution of transport physics on arbitrary polyhedral cells, included locally refined spatial grids. It includes multiple angular quadrature types, including locally refined angular quadratures. Written in modern C++ with a Python API, OpenSn runs efficiently on platforms ranging from laptops to supercomputers. The transport sweep algorithm is implemented using a task-based, directed-acyclic-graph (DAG) approach for each angle and supports asynchronous parallelism across thousands of MPI ranks. Group-set aggregation improves compute intensity, and synthetic acceleration techniques (e.g., diffusion synthetic acceleration, second-moment method) enhance solver convergence. OpenSn has been verified on reactor physics problems and demonstrated excellent weak and strong scaling performance on more than 32,768 processes, making it a versatile and robust platform for large-scale transport simulations in complex geometries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

MAPS: the MFEM Anisotropic Plasma Solver

Simulating magnetically confined fusion plasmas presents a uniquely challenging problem due to the nonlinear anisotropic heat conduction. We introduce the MAPS (MFEM Anisotropic Plasma Solver) tool, which uses a high-order finite element method to compute transport solutions on unstructured meshes. We show results for a set of three 2-D verification tests, two of which demonstrate the expected convergence properties for various mesh resolutions and polynomial degrees. We then discuss the convergence rate for the third test.

Barnett, Rhea [ORNL] (ORCID:0000000317527979)↗
DOE OSTI2024

Kinetic Plasma Simulation in the MOOSE Framework: Verification of Electrostatic Particle In Cell Capabilities

In magnetic confinement nuclear fusion reactors, the interaction between the plasma edge and plasma facing components is extremely important. At the plasma edge, a kinetic representation such as particle-in-cell (rather than a fluid representation) is required to accurately capture the plasma behavior. General purpose particle-in-cell plasma simulation capabilities have been developed in the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework. This new capability is a part of the development of a new MOOSE-based framework for modeling plasma facing components, the Fusion ENergy Integrated multiphys-X (FENIX) framework. In this work, the verification of foundational particle-in-cell capabilities in FENIX is presented. This new plasma simulation capability has three main components: moving particles in discrete steps on the finite element mesh, mapping charge density from the particle's location to the finite element mesh, and solving for the electrostatic potential based on the charge density mapped from particles to the mesh. In this paper, simple verification problems demonstrating each of these new capabilities are presented, and future work includes electromagnetic capabilities and Monte Carlo collisions with neutral gas particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗