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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

A new weak Galerkin finite element method for elliptic interface problems

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments in order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

An improved consistent, conservative, non-oscillatory and high order finite difference scheme for variable density low Mach number turbulent flow simulation

A consistent, conservative and truly high order finite difference scheme for low Mach number turbulent variable density flow simulation is presented. In the present scheme, the scalar transport equation is discretized with the explicit weighted compact nonlinear scheme (WCNS) while the continuity and momentum equations are discretized with a conservative centered high order finite difference scheme on a staggered grid. Bounded hybrid high order upwind interpolation is proposed for the evaluation of density on the cell faces of the staggered grid. The use of explicit WCNS along with the bounded density interpolation resolves the issue of degraded order of accuracy in the existing high order finite difference schemes where the centered finite difference scheme for mass and momentum conservation is combined with a total variation stable scheme for scalar transport. With the same difference operator used for the continuity and scalar transport equations, the present scheme is consistent naturally, and resolves the inconsistency problem reported in Trisjono et al. (J. Comp. Phys., 327, 612-628, 2016) without employing any modification to a scheme. Such improvements are demonstrated for several test cases.

02 PETROLEUM↗
DOE OSTI2018

Conservative fourth-order finite-volume Vlasov–Poisson solver for axisymmetric plasmas in cylindrical (r,v r ,v θ ) phase space coordinates

In this paper, a fourth-order finite-volume Vlasov–Poisson algorithm is developed for simulating axisymmetric plasma configurations in ( r , v r , v θ ) phase space coordinates. The Vlasov equation for cylindrical phase space coordinates is cast into conservation-law form and is discretized on a structured grid. The conservative finite-volume discretization is based on fifth-order upwind reconstructions of the distribution function and a fourth-order quadrature rule that accounts for transverse variations of fluxes along control volume surfaces. High-order specular reflection boundary conditions enable high-fidelity treatment of plasma distribution functions at the axis and at wall boundaries. The numerical method is applied to simulate a confined uniform neutral gas to assess convergence properties for an equilibrium system in which effects of finite-temperature and acceleration due to centrifugal and Coriolis forces are present. The discretization is also applied to a Z-pinch configuration to study electrostatic ion confinement and the dynamics of the associated breathing mode. Simulations show that the ion distribution function exhibits non-Maxwellian features and that a temperature anisotropy develops and is sustained. Finally, the finite-volume implementation is demonstrated to converge at fourth-order for both applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Accelerating high-order mesh optimization using finite element partial assembly on GPUs

In this paper we present a new GPU-oriented mesh optimization method based on high order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global nonlinear solve over the whole computational mesh, i.e., all mesh nodes are moved together. A key property of the method is that the mesh optimization process is recast in terms of finite element operations, which allows us to utilize recent advances in the field of GPU-accelerated high order finite element algorithms. For example, we reduce data motion by using tensor factorization and matrix-free methods, which have superior performance characteristics compared to traditional full finite element matrix assembly and offer advantages for GPU based HPC hardware. Furthermore, we describe the major mathematical components of the method along with their efficient GPU-oriented implementation. In addition, we propose an easily reproducible mesh optimization test that can serve as a performance benchmark for the mesh optimization community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An implementation of the phase-field model based on coupled thermomechanical finite element solvers for large-strain twinning, explicit dynamic fracture and the classical Stefan problem

The implementation of a phase-field model in finite elements usually requires significant expertise and involves the development of a user element with additional degrees of freedom. An alternative implementation of the phase-field model within a thermo-mechanical finite element simulation package was presented in (Cho et al 2012 Int. J. Solids Struct. 49 1973–1992), where the phase-field variable is treated as the temperature degree of freedom. However, this approach has only been used for small strain phase-field modelling of martensitic transformations and quasistatic phase-field modelling of fracture. Here, we present a phase-field finite element implementation via the temperature degree of freedom for several additional cases from the literature: (i) the large-strain phase-field description of deformation twinning presented in (Clayton and Knap 2011 Physica D 240 841–858), (ii) phase-field description of brittle fracture with inertial effects based on the theory from (Molnár and Gravouil 2017, Finite Elem. Anal. Des. 130 27–38) and (Miehe et al 2010 Int. J. Numer. Methods Eng. 83 1273–1311) and (iii) the classical Stefan problem of solidification presented in (Mackenzie and Robertson 2002 J. Comput. Phys. 181 526–544). The last problem involves the temperature and phase-field variables as unknowns.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Finite-frequency modeling of regional tropospheric infrasound using realistic atmospheres and terrain

Infrasonic waves have been observed to propagate to regional (greater than 15 km) distances through the troposphere. Infrasound propagation in the geometric acoustics approximation has shown that realistic terrain can scatter acoustic energy from tropospheric ducts; however, ray methods cannot intrinsically capture finite-frequency behavior such as diffraction. A two-dimensional finite-difference time-domain (FDTD) method has been developed to solve linearized equations for infrasound propagation with realistic terrain. Acoustic wave propagation over 100 km with both flat terrain and a Gaussian hill was first simulated in order to compare finite-frequency propagation with ray predictions. The effects of realistic terrain and atmospheres on infrasound signals from a 2012 surface explosion at the Utah Testing and Training Range are then investigated. Propagation through the troposphere is suggested by array processing results, but eigenrays are not predicted due to weak to nonexistent ducting conditions. FDTD modeling suggests that the inclusion of terrain and finite frequency effects helps explain much of the observed signal in a realistic scenario. Furthermore, these results suggest that geometric acoustics may underestimate propagation through the troposphere, and that recorded waveforms at regional distances may be noticeably affected by terrain.

58 GEOSCIENCES↗
DOE OSTI2020

A Condensed Constrained Nonconforming Mortar-Based Approach for Preconditioning Finite Element Discretization Problems

This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation that is based on a proposed modified version of the mortar method. The well-known mortar finite element discretization method is modified to admit a local structure, providing an element-by-element or subdomain-by-subdomain assembly property. This is achieved via the introduction of additional trace finite element spaces and degrees of freedom (unknowns) associated with the interfaces between adjacent elements or subdomains. The resulting nonconforming formulation and a reduced-via-static-condensation Schur complement form on the interfaces are used in the construction of auxiliary space preconditioners for a given conforming finite element discretization problem. Overall, the properties of these preconditioners are studied and their performance is illustrated on model second order scalar elliptic problems utilizing high order elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Finite deformation implementation of a mixed-mode single-integral type cohesive zone with reorienting surfaces of separation

To model material ductile failure and crack propagation, cohesive zone elements can be embedded along potential fracture paths in a finite element simulation. When damage criteria are met, elements in the mesh decohere, simulating the formation and propagation of a crack. In this paper, we present a novel computational algorithm based on finite deformation theory, essential to modeling crack initiation and growth in solids undergoing large deformations. This new algorithm was formulated within a Lagrangian frame of reference to extend previous cohesive zone algorithms to include modeling crack growth in finite deformation contexts. The local coordinate system, necessary for defining an embedded cohesive zone, is constructed based upon the current configuration and is updated within the nonlinear iteration process, thereby resulting in the convergence of the solution for a growing crack in a large deformation quasi-static setting. The model’s accuracy was demonstrated by comparing finite element model simulation results with the analytic case of a constant surface separation, as shown in the verification examples. The power and efficacy of the algorithm to capture large deformations during crack growth were then demonstrated with a double cantilever beam example case. It indicates that the model can be applied to a variety of physical circumstances for predicting crack initiation and growth with delamination and fracture.

42 ENGINEERING↗
DOE OSTI2018

Quality factor assessment of finite-size all-dielectric metasurfaces at the magnetic dipole resonance

Recently there has been a large interest in achieving metasurface resonances with large quality factors. In this article, we examine metasurfaces that comprised a finite number of magnetic dipoles oriented parallel or orthogonal to the plane of the metasurface and determine analytic formulas for their resonances’ quality factors. These conditions are experimentally achievable in finite-size metasurfaces made of dielectric cubic resonators at the magnetic dipole resonance. Our results show that finite metasurfaces made of parallel (to the plane) magnetic dipoles exhibit low quality factor resonances with a quality factor that is independent of the number of resonators. More importantly, finite metasurfaces made of orthogonal (to the plane) magnetic dipoles lead to resonances with large quality factors, which ultimately depend on the number of resonators comprising the metasurface. In particular, by properly modulating the array of dipole moments by having a distribution of resonator polarizabilities, one can potentially increase the quality factor of metasurface resonances even further. These results provide design guidelines to achieve a sought quality factor applicable to any resonator geometry for the development of new devices such as photodetectors, modulators, and sensors.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2018

Progress toward a new implementation of the mortar finite element method in MOOSE

The mortar finite element method has been used for many years in a variety of applications, including the enforcement of continuity conditions across decomposed domains, the implementation of Dirichlet boundary conditions, obtaining improved estimates of surface fluxes, and for solving large deformation contact mechanics problems. There is a currently great deal of interest in developing more robust mechanical and thermal contact solution strategies in the MOOSE framework and physics modules, and schemes based on the mortar finite element approach appear to be a promising avenue of development. There are a number of challenges associated with the development of a robust Lagrange multiplier based formulation of the mortar finite element method which can be tackled using the relatively simple framework of thermal contact problems, before tackling more complicated applications such as thermomechanical contact. In this report, we describe several aspects of our mortar finite element method implementation for solving thermal contact problems. The approach and notation used are based primarily based on the work of Bin Yang et al. ("Two dimensional mortar contact methods for large deformation frictional sliding," International Journal for Numerical Methods in Engineering 62(9), 2005).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Finite Volume Discretization of the Euler Equations in Pronghorn

Modeling flow and heat transfer in high temperature gas reactors (HTGR) requires the ability to model a wide range of flow speeds from slow (natural convection), to intermediate (forced-flow conditions), to supersonic regimes (depressurization) for a wide range of geometries including the pebble bed, upper and lower plenum, and risers. In previous work, Pronghorn has effectively modeled low-to-medium speed flows in scenarios such as the one described in the two-dimensional PBMR-400 benchmark, using its finite-element-based streamline-upwind Petrov-Galerkin (SUPG) stabilized implementation of the Euler equations. However, limitations of this method become apparent when dealing with more complicated geometries (e.g. imposing slip boundary conditions at nodes belonging to two different boundaries) and when gas speeds are fast enough for shocks and supersonic flow to occur. For these problems, the finite-element-based solver lacks robustness and is plagued by slow iterative convergence or even divergence. In order to address these challenges, the Pronghorn code at INL has been updated with new, modified versions of its original equations. The new Pronghorn models are built on the finite volume method with a Harten-Lax-van Leer-Contact (HLLC) Riemann solver based numerical flux method, which (1) allows imposing slip boundary conditions much more robustly and (2) performs well for a wide range of flow speeds. The finite-volume-based flow solver will form the basis for a robust coarse-mesh thermal-hydraulics capability in Pronghorn.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2016

Pellet Cladding Mechanical Interaction Modeling Using the Extended Finite Element Method

As a brittle material, the ceramic UO2 used as light water reactor fuel experiences significant fracturing throughout its life, beginning with the first rise to power of fresh fuel. This has multiple effects on the thermal and mechanical response of the fuel/cladding system. One such effect that is particularly important is that when there is mechanical contact between the fuel and cladding, cracks that extending from the outer surface of the fuel into the volume of the fuel cause elevated stresses in the adjacent cladding, which can potentially lead to cladding failure. Modeling the thermal and mechanical response of the cladding in the vicinity of these surface-breaking cracks in the fuel can provide important insights into this behavior to help avoid operating conditions that could lead to cladding failure. Such modeling has traditionally been done in the context of finite-element-based fuel performance analysis by modifying the fuel mesh to introduce discrete cracks. While this approach is effective in capturing the important behavior at the fuel/cladding interface, there are multiple drawbacks to explicitly incorporating the cracks in the finite element mesh. Because the cracks are incorporated in the original mesh, the mesh must be modified for cracks of specified location and depth, so it is difficult to account for crack propagation and the formation of new cracks at other locations. The extended finite element method (XFEM) has emerged in recent years as a powerful method to represent arbitrary, evolving, discrete discontinuities within the context of the finite element method. Development work is underway by the authors to implement XFEM in the BISON fuel performance code, and this capability has previously been demonstrated in simulations of fracture propagation in ceramic nuclear fuel. These preliminary demonstrations have included only the fuel, and excluded the cladding for simplicity. This paper presents initial results of efforts to apply XFEM to model stress concentrations induced by fuel fractures at the fuel/cladding interface during pellet cladding mechanical interaction (PCMI). This is accomplished by enhancing the thermal and mechanical contact enforcement algorithms employed by BISON to permit their use in conjunction with XFEM. The results from this methodology are demonstrated to be equivalent to those from using meshed discrete cracks. While the results of the two methods are equivalent for the case of a stationary crack, it is demonstrated that XFEM provides the additional flexibility of allowing arbitrary crack initiation and propagation during the analysis, and minimizes model setup effort for cases with stationary cracks.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

High Order Finite Elements S{sub N} Transport in X-Y Geometry on Meshes with Curved Surfaces

Radiation hydrodynamics is useful to model astrophysics, ICF, and glass manufacturing. A large amount of research has been conducted to understand how to solve hydrodynamics equations using high-order finite elements. Researchers at LLNL have developed a general high-order FEM library, Modular Finite Element Methods (MFEM), to enable this research. The BLAST code uses MFEM to evolve the Lagrangian hydrodynamics equations, resulting in meshes with higher order curved surfaces. Our research focuses on the requirements for high order finite element solutions of the radiation transport equation with the eventual goal of studying the complete high-order radiation hydrodynamics solution methodology. For this research we used MFEM to develop a proof-of-concept code that solves the high order finite element transport equations in Cartesian coordinates on meshes with curved surfaces. We have solved several test problems to assess the behavior of our method. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

A Continuous-Discontinuous Hybrid Finite Element Method for S{sub N} Transport

Particle transport phenomenon for neutral particles, such as neutrons and photons, is governed by the linear Boltzmann equation, which is a first-order partial differential equation (PDE). In order to solve the transport equation, discontinuous finite element method (DFEM) is heavily developed. However, the large memory consumption due to the extra degrees of freedom is problematic in multi-D calculations. Another path is to recast the transport equation to a second-order form, such as the well-known self-adjoint angular flux equation (SAAF) and the even parity equations, and spatially discretize the equation using continuous finite element method (CFEM). Yet, such forms generally have problems in void situation as the streaming operator contains a 1/σ{sub t} term and becomes singular in void, which draws numerous efforts on developing void-treatment methods. An intuition to mitigate the shortcomings of both methods is then to develop a method that utilizes DFEM in part of the problem where CFEM has issues while in the other part, CFEM is employed to avoid DFEM's high cost. In this work, we present a novel continuous-discontinuous finite element method (CDFEM) for solving the discrete-ordinates (S{sub N}) transport equations. We perform the hybridization between 1/σ{sub t}-weighted least-squares finite element methods (1/σ{sub t}-LSFEM), with continuous basis functions, and first-order solver. Different solvers are defined in different regions, or subdomains, of the problem. The resulting scheme is such that CFEM-SAAF is performed in subdomains with continuous basis functions while upwinding based DFEM solver is utilized in subdomains with discontinuous basis functions. The connection between subdomains is through an upwinding operation on the interface, which can be performed via the sweep procedure. A foreseeable benefit is such a scheme is compatible with void as first-order DFEM solver can be used in void. On the other hand, as DFEM is only used in part of the problem, CDFEM can effectively avoid the notorious memory consumption of DFEM in multi-D calculation for the future work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

On the validation of seismic imaging methods: Finite frequency or ray theory?

Abstract We investigate the merits of the more recently developed finite‐frequency approach to tomography against the more traditional and approximate ray theoretical approach for state of the art seismic models developed for western North America. To this end, we employ the spectral element method to assess the agreement between observations on real data and measurements made on synthetic seismograms predicted by the models under consideration. We check for phase delay agreement as well as waveform cross‐correlation values. Based on statistical analyses on S wave phase delay measurements, finite frequency shows an improvement over ray theory. Random sampling using cross‐correlation values identifies regions where synthetic seismograms computed with ray theory and finite‐frequency models differ the most. Our study suggests that finite‐frequency approaches to seismic imaging exhibit measurable improvement for pronounced low‐velocity anomalies such as mantle plumes.

58 GEOSCIENCES↗
DOE OSTI2024

Generalized boost transformations in finite volumes and application to Hamiltonian methods

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Embedded symmetric positive semi-definite machine-learned elements for reduced-order modeling in finite-element simulations with application to threaded fasteners

Here, we present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain into an “outer” coarse-scale domain that we resolve using a finite element method (FEM) and an “inner” fine-scale domain. We then develop a machine-learned (ML) model for the impact of the inner domain on the outer domain. In essence, for solid mechanics, our machine-learned surrogate performs static condensation of the inner domain degrees of freedom. This is achieved by learning the map from displacements on the inner-outer domain interface boundary to forces contributed by the inner domain to the outer domain on the same interface boundary. We consider two such mappings, one that directly maps from displacements to forces without constraints, and one that maps from displacements to forces by virtue of learning a symmetric positive semi-definite (SPSD) stiffness matrix. We demonstrate, in a simplified setting, that learning an SPSD stiffness matrix results in a coarse-scale problem that is well-posed with a unique solution. We present numerical experiments on several exemplars, ranging from finite deformations of a cube to finite deformations with contact of a fastener-bushing geometry. We demonstrate that enforcing an SPSD stiffness matrix drastically improves the robustness and accuracy of FEM–ML coupled simulations, and that the resulting methods can accurately characterize out-of-sample loading configurations with significant speedups over the standard FEM simulations.

97 MATHEMATICS AND COMPUTING↗