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At least 109 records · Page 6

A novel approach to quantifying the kinetics of point defect absorption at dislocations

We report that microstructure evolution under creep loading and/or irradiation is largely affected by the two-way coupling between dislocation induced plasticity and point defect diffusion as mediated by the internal elastic strain field within the medium. The magnitude of this effect has been quantified only in idealized, simplified environments such that estimates of absorption rates of point defects to dislocations ignore the collective effects on capture rates arising from particular distribution of dislocations in a given network, the interaction of point defects with the internal strain, or in many cases both. To quantify these effects, we advance a novel methodology to determine point defect capture rates locally within a spatially resolved finite difference solution to the diffusion problem for arbitrarily directed dislocations and the corresponding strain fields. In addition to examining the effects of these couplings on local and effective absorption rates of dislocation networks, the potential consequences of these interactions on other microstructure evolution phenomena are examined using void swelling under irradiation as an example. Our study indicates that local rates of defect mediated microstructural changes such as cavity growth can vary strongly as a consequence of the arrangement of the dislocation network and the corresponding strain state. Lastly, the heterogeneous aspects of the resultant defect populations are shown to provide mechanisms for microstructural evolution under irradiation that are not available in the conventional homogeneous theory.

36 MATERIALS SCIENCE↗

Spatial coupling of gyrokinetic simulations, a generalized scheme based on first-principles

In this paper, we present a scheme that spatially couples two gyrokinetic codes using first-principles. Coupled equations are presented and a necessary and sufficient condition for ensuring accuracy is derived. This new scheme couples both the field and the particle distribution function. The coupling of the distribution function is only performed once every few time-steps, using a five-dimensional (5D) grid to communicate the distribution function between the two codes. This 5D grid interface enables the coupling of different types of codes and models, such as particle and continuum codes, or delta-f and total-f models. Transferring information from the 5D grid to the marker particle weights is achieved using a new resampling technique. Demonstration of the coupling scheme is shown using two XGC gyrokinetic simulations for both the core and edge. We also apply the coupling scheme to two continuum simulations for a one-dimensional advection–diffusion problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. Here, we introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multilevel Techniques for Compression and Reduction of Scientific Data---The Multivariate Case

We develop a technique for multigrid adaptive reduction of data (MGARD). Special attention is given to the case of tensor product grids, where our approach permits the use of nonuniformly spaced grids in each direction, which can prove problematic for many types of data reduction methods. An important feature of our approach is the provision of guaranteed, computable bounds on the loss incurred by the reduction of the data. Many users are leery of lossy algorithms and will only consider using them provided that numerical bounds on the pointwise difference between the original and the reduced datasets are given. Accordingly, we develop techniques for bounding the loss measured in the $L^{\infty}(\Omega)$ norm, and we show that these bounds are realistic in the sense that they do not significantly overestimate the actual loss. Here, the resulting loss indicators are used to guide the adaptive reduction of the data so that the reduced dataset meets a user-prescribed tolerance or memory constraint. Illustrative numerical examples, including the reduction of data arising from the simulation of a nonlinear reaction-diffusion problem, a turbulent channel flow, and a climate simulation, are provided.

97 MATHEMATICS AND COMPUTING↗

Low-Order Preconditioning for the High-Order Finite Element de Rham Complex

Here, we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in H 1 , H(curl), and H(div) and is based on combining a low-order discretization posed on a refined mesh with a high-order basis for Nédélec and Raviart–Thomas elements that makes use of the concept of polynomial histopolation (polynomial fitting using prescribed mean values over certain regions). This spectral equivalence, coupled with algebraic multigrid methods constructed using the low-order discretization, results in highly scalable matrix-free preconditioners for high-order finite element problems in the full de Rham complex. Additionally, a new lowest-order (piecewise constant) preconditioner is developed for high-order interior penalty discontinuous Galerkin (DG) discretizations, for which spectral equivalence results and convergence proofs for algebraic multigrid methods are provided. In all cases, the spectral equivalence results are independent of polynomial degree and mesh size; for DG methods, they are also independent of the penalty parameter. These new solvers are flexible and easy to use; any “black-box” preconditioner for low-order problems can be used to create an effective and efficient preconditioner for the corresponding high-order problem. A number of numerical experiments are presented, based on an implementation in the finite element library MFEM. A range of challenging three-dimensional problems are used to corroborate the theoretical properties and demonstrate the flexibility and scalability of the method.

97 MATHEMATICS AND COMPUTING↗

Polypole Program For The Calculation Of Intra-granular Fission Gas Release

PolyPole is a numerical algorithm for the calculation of intra-granular fission gas release. In particular, the algorithm solves the gas diffusion problem in a fuel grain in time-varying conditions. The program has been extensively tested. PolyPole combines a high accuracy with a high computational efficiency and is ideally suited for application in fuel performance codes.

Pastore, Giovanni↗

AMG2023

The AMG2023 benchmark solves two diffusion problems with a linear solver preconditioned with algebraic multigrid. The code only contains a driver, a Makefile, and a documentation file. It requires an installation of the open source software library hypre that needs to be downloaded elsewhere and is not included here. Its purpose is to benchmark linear solver performance on high performance computers.

Li, Ruipeng↗

A two-level GPU-accelerated incomplete LU preconditioner for general sparse linear systems

This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures, specifically, those that are equipped with graphic processing units (GPUs). In addition to block-Jacobi, we present general purpose two-level ILU Schur complement-based approaches, where different strategies are presented to solve the coarse-level reduced system. These strategies are combined with modified ILU methods in the construction of the coarse-level operator, in order to effectively remove smooth errors by targeting an algebraically smooth vector. We leverage available GPU-based sparse matrix kernels to accelerate the setup and the solve phases of the proposed ILU preconditioner. We evaluate the efficiency of the proposed methods as a smoother for algebraic multigrid (AMG) and as a preconditioner for Krylov subspace methods on challenging anisotropic diffusion problems and a collection of general sparse matrices.

97 MATHEMATICS AND COMPUTING↗

Efficient quadrature rules for finite element discretizations of nonlocal equations

In this paper we design efficient quadrature rules for finite element discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first showthat the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient finite element assembly.

97 MATHEMATICS AND COMPUTING↗

Report on hypre performance on AMD GPUs

In this report, the performance of the algebraic multigrid solver used as a preconditioner for conjugate gradient is investigated on 2 nodes of Spock, an early access system at ORNL with 4 MI-100 GPUs and a 64-core Rome CPU per node. We compare GPU and CPU performance for three different diffusion problems using increasing problem sizes.

97 MATHEMATICS AND COMPUTING↗

Polypole Program For The Calculation Of Intra-granular Fission Gas Release

PolyPole is a numerical algorithm for the calculation of intra-granular fission gas release. In particular, the algorithm solves the gas diffusion problem in a fuel grain in time-varying conditions. The program has been extensively tested. PolyPole combines a high accuracy with a high computational efficiency and is ideally suited for application in fuel performance codes.

Pastore, Giovanni↗

Some New Verification Test Problems for Multimaterial Diffusion on Meshes that are Non-Aligned with Material Boundaries

In this report a number of new verification test problems for multimaterial diffusion will be shown. Using them we will show that homogenization of multimaterial cells in either Arbitrary Lagrangian Eulerian (ALE) or Eulerian simulations can lead to errors in the energy flow at the interfaces. Results will be presented that show that significant improvements and predictive capability can be gained by using either a surrogate supermesh, such as Thin Mesh in FLAG, or the emerging method based on Static Condensation.

36 MATERIALS SCIENCE↗

Error analysis of numerical methods for thick diffusive neutron transport problems on Shishkin mesh

A thin layer will develop at the boundary if the incoming angular flux is anisotropic in thick diffusive neutron transport problems. Solving such singularly perturbed problems, which have non-smooth solutions with singularity near the boundary, is computationally challenging. Standard finite difference schemes on a uniform mesh cannot yield ε-uniform convergence, where ε is a small parameter, while it can be achieved on a suitable piecewise-uniform Shishkin mesh. We present a formal error analysis of the diamond difference (DD) method and step difference (SD) method for solving the S{sub N} neutron transport equation. The analysis can be extended to other finite difference methods. Numerical results are presented to confirm the error estimates and the advantages of the Shishkin mesh. (author)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A dynamic likelihood approach to filtering transport processes: advection-diffusion dynamics

A Bayesian data assimilation scheme is formulated for advection-dominated advective and diffusive evolutionary problems, based upon the Dynamic Likelihood (DLF) approach to filtering. The DLF was developed specifically for hyperbolic problems –waves–, and in this paper, it is extended via a split step formulation, to handle advection-diffusion problems. In the dynamic likelihood approach, observations and their statistics are used to propagate probabilities along characteristics, evolving the likelihood in time. The estimate posterior thus inherits phase information. For advection-diffusion the advective part of the time evolution is handled on the basis of observations alone, while the diffusive part is informed through the model as well as observations. We expect, and indeed show here, that in advection-dominated problems, the DLF approach produces better estimates than other assimilation approaches, particularly when the observations are sparse and have low uncertainty. The added computational expense of the method is cubic in the total number of observations over time, which is on the same order of magnitude as a standard Kalman filter and can be mitigated by bounding the number of forward propagated observations, discarding the least informative data.

97 MATHEMATICS AND COMPUTING↗

Reduced-order modeling of parameterized multi-group diffusion k-eigenvalue problems

In this paper, a group-wise Reduced-Order Model, based on a Proper Orthogonal Decomposition (POD) technique, is presented for parameterized multi-group diffusion k-eigenvalue problems. The group-wise approach is shown to be more robust than model-order reduction based on monolithic multi-group POD modes. In addition, fewer POD modes are required. The method of snapshots is employed to generate the offline training set. Two Naïve and a Greedy snapshot-generation strategies are compared. The input parameter space is surveyed using Latin Hypercube Sampling techniques. The effectiveness of the group-wise model-order reduction method is demonstrated on two reactor-physics benchmarks, a two-group 3D Pressurized Water Reactor problem with 26 uncertain input parameters and a seven-group UO 2 -MOX fuel 3D mini-core with 287 uncertain input parameters. In both examples the Reduced-Order Models built using the snapshots generated by the Greedy algorithm proved to be slightly better. Model-order reduction yields results that are within 1 pcm of the full-order model, with speed-up factors of about 1000–3000, depending upon the test case.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Phase field benchmark problems targeting fluid flow and electrochemistry

Here, we continue our development of phase field model benchmark problems with the addition of a third set, complimenting our previously developed problems for diffusion, precipitation, dendritic growth and linear elasticity. These benchmark problems are being jointly developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST) along with input from the phase field community. The first problem in this third set targets Stokes flow, with a particular emphasis on flow around an obstruction placed asymmetrically in the domain. While Stokes flow is not traditionally in the canon of phase field problems, it is a class of problems gaining importance in areas such as filtration and water purification. The second problem deals with coupled Cahn-Hilliard diffusion and electrostatic forces, which is an important area in energy storage and battery sciences. We present our own solutions and discuss sources of numerical errors for the Stokes problem as well as simple checks to avoid fundamental issues in the coupled diffusion-electrostatics problem. The latter problem contains some subtleties that we expand on in an Appendix.

36 MATERIALS SCIENCE↗

Application of the theory of open quantum systems to nuclear physics problems

Quantum diffusion equations with transport coefficients explicitly depending on time are derived from the generalized non-Markovian Langevin equations. The asymptotic behavior of the friction and diffusion coefficients is investigated in the case of the FC and RWA couplings between the collective and internal subsystems. An asymptotic expression is obtained for the propagator of the density matrix of the open quantum system with the general quadratic Hamiltonian, linearly coupled (in coordinate and momentum) to internal degrees of freedom. The effect of different sets of transport coefficients on the decoherence and decay rate of the metastable state is investigated using the master equation for the reduced density matrix of open quantum systems. The developed approach is used to study the capture of the projectile nucleus by the target nucleus at energies near the Coulomb barrier. Capture cross sections in asymmetric reactions are well described with allowance for the calculated capture probabilities. Particular cases where dissipation favors penetration through the potential barrier are found. The generalized Kramers formula for the quasi-stationary decay rate of the quantum metastable systems is analytically derived.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗