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Results for “Finite element methods”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Improving Computational Efficiency of Mechanical Finite Element Method Simulations for PV Modules: Preprint

In this work we have elucidated the trade off between structural mechanics FEM model accuracy and computation time by employing lower fidelity viscoelastic models. Results indicate that computation time can easily be cut in half while only expecting a potential maximum error of 10 % by considering lower fidelity models. A novel approach to produce the Prony Series fit for viscoelastic characterization has also been presented. Employing this approach, we were able to achieve a further 10 % reduction in computation time without further sacrificing simulation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2022

Implementation of hybrid finite element method based transport solver in GRIFFIN

A new transport solver option based on the hybrid FEM (HFEM) was implemented in GRIFFIN, the MOOSE-based reactor analysis code, as an effort to support routine core design calculations for advanced reactor applications. The HFEM formulation with P{sub N} (spherical harmonics expansion), akin to the variational nodal method, is effective for solving a spatially homogenized problem with strong transport effect. The residual and Jacobian evaluations of the HFEM weak form were derived and successfully implemented in GRIFFIN, having the diffusion and the PN options available in the new HFEM based transport solver. The performance was tested with the simplified ABTR benchmark problems. The results indicate that the HFEM-based transport solver is a feasible option for solving problems with spatially homogenized and strong streaming by providing superior accuracy with a proper p-refinement. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

42 ENGINEERING↗
DOE OSTI2021

Modeling and analyzing parasitic parameters in high frequency converters

This research focuses on electromagnetic interference (EMI) / electromagnetic compatibility (EMC) design and analysis in power electronics systems. To limit the EMI under the standards, different methods and strategies are investigated. Parasitic parameters of high frequency (HF) transformer are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements for different structures and windings arrangements. Also, the magnetic field, electric field, electric displacement, and electric potential distribution are simulated and analyzed. Moreover, a high voltage system is considered and analyzed to improve the EMC. The EMI propagation paths are analyzed. The EMI noise level of the system is obtained and compared to the IEC61800-3 standard. To improve the EMC, the parasitic parameters of the transformer, as the main path of EMI circulation, are analyzed and optimized to block the propagation. Furthermore, the geometry structure of the HF transformer is optimized to lower the parasitics in the system. Three pareto-optimal techniques are investigated for the optimization. The models and results are verified by 3D-FEM and experimental results for several given scenarios. Furthermore, the EMC modeling and conducted EMI analysis are developed for a system including an AC-DC-DC power supply (rectifier and dual active bridge (DAB) converter). Moreover, the common mode (CM) EMI noise propagation through the system is discussed and the noise sources and effect of components on the noise are analyzed. Additionally, the CM impedance of different parts of the system and the noise levels are discussed. Finally, EMI attenuation techniques were applied to the system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Improvements to a class of hybrid methods for radiation transport: Nyström reconstruction and defect correction methods

In this study, two modifications are introduced for improving the accuracy, versatility, and robustness of a class of hybrid methods for radiation transport. In general, such methods are constructed by splitting the radiative flux into collided and uncollided components to which low- and high-resolution angular approximations are applied, respectively. In this work we focus on discrete ordinates discretizations of high and low order. The first modification we introduce changes the way in which the collided component is mapped into the uncollided component at the end of each time step in a simulation. The new mapping is a Nyström-type reconstruction that is applicable to arbitrary discrete ordinates quadratures, is guaranteed to preserve positivity of the solution provided that all ordinate weights are positive, is significantly more accurate than previous methods, and can be readily extended to other discretizations such as moment methods, finite element methods, and diffusion approximations. The second modification leverages integral deferred correction (IDC) to iteratively correct for the splitting error introduced by the inconsistency in angular discretization between the collided and uncollided components, in addition to improving the accuracy of the low-order temporal error that is treated by traditional IDC methods. Numerical tests in one- and two-dimensional geometries are used to demonstrate the increased accuracy and efficiency of the proposed modifications. It is found that the two techniques combined yield methods with solution accuracy and memory requirements comparable to that of monolithic discrete ordinates methods while reducing runtime by as much as a factor of between two and ten, depending on the problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Investigation of Various Transformer Topologies for HF Isolation Applications

High-frequency (HF) transformers are an essential part of many power electronic devices. The performance and behavior of HF transformers can greatly affect the efficiency and performance of all systems, particularly, from a parasitic parameter point of view. In this article, HF transformers' parasitic parameters, such as leakage inductances and parasitic capacitances, are analyzed using a novel analytical method, finite element method (FEM), and experimental measurements of different structures and winding arrangements. Also, the magnetic field, electric field, electric displacement field, and electric potential distribution within the transformers are simulated and analyzed. Four different HF transformers with E and U cores with different windings are designed and analyzed. Investigation outcomes help to classify structures according to the trade-off between leakage inductances and series parasitic capacitances. This information can later be used for the optimal selection and design of transformers as a function of their operating frequency for any power rating and voltage level. Moreover, 3-D FEM and experimental results validate the proposed methodology to be used for designing HF transformers in high-voltage/power applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A smooth contact algorithm for the combined finite discrete element method

From its inception, the combined finite discrete element method has used a distributed potential contact force algorithm to resolve interaction between finite elements. The contact interaction algorithm relies on evaluation of the contact force potential field. The problem with existing algorithms is that the potential field introduces artificial numerical non-smoothness in the contact force. This work introduces a smooth potential field based on the finite element topology, and a generalized contact interaction law is constructed on top of the smooth potential field. Further, a number of validation cases for the proposed algorithm, considering different shapes of discrete elements, are presented, and detailed aspects of the proposed contact interaction law are tested with numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Generalized Korn’s inequalities for piecewise $H¹$ and $H²$ vector fields

The purpose of this paper is to construct a new class of discrete generalized Korn’s inequalities for piecewise $H^1$ vector fields and piecewise $H^2$ vector fields in three-dimensional space. The resulting Korn’s inequalities are different from the standard Korn’s inequalities, as they involve the trace-free symmetric gradient operator, in place of the usual symmetric gradient operator. Furthermore, it is anticipated that the new generalized Korn’s inequalities will be useful for the analysis of a broad range of finite element methods, including mixed finite element methods and discontinuous Galerkin methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Preserving Superconvergence of Spectral Elements for Curved Domains via $h$ and $p$-Geometric Refinement

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using h- and p-geometric refinement, which refines the mesh near high-curvature regions and increases the degree of geometric basis functions, respectively. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries.

97 MATHEMATICS AND COMPUTING↗