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At least 127 records · Page 7

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Douglas, C. C.↗

Parallel Anisotropic Unstructured Grid Adaptation

Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation.

Tsolakis, Christos↗

Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Using Machine Learning to Discern Eruption in Noisy Environments: A Case Study Using CO2-Driven Cold-Water Geyser in Chimayó, New Mexico

In this paper, we present an approach based on machine learning (ML) to distinguish eruption and precursory signals of Chimayó geyser (New Mexico, U.S.A.) under noisy environmental conditions. This geyser can be considered a natural analog of CO 2 intrusion into shallow water aquifers. By studying this geyser, we can understand upwelling of CO 2 -rich fluids from depth, which has relevance to leak monitoring in a CO 2 sequestration project. ML methods such as random forests (RFs) are known to be robust multiclass classifiers and perform well under unfavorable, noisy conditions. However, the extent of the RF method’s accuracy is poorly understood for this CO 2 -driven geysering application. The current study aims to quantify the performance of RF classifiers to discern the geyser state. Toward this goal, we first present the data collected from the seismometer that is installed near the Chimayó geyser. The seismic signals collected at this site contain different types of noises such as daily temperature variations, animal movement near the geyser, and human activity. First, we filter the signals from these noises by combining the Butterworth high-pass (BH) filter and an autoregressive (AR) method in a multilevel fashion. We show that by combining these filtering techniques in a hierarchical fashion leads to a reduction in noise in the seismic data without removing the precursors and eruption event signals. We then use RF on the filtered data to classify the state of geyser into three classes: remnant noise, precursor, and eruption states. RF classifier is constructed based on the comprehensive features extracted using the Tsfresh Python package. We show that the classification accuracy using RF on the filtered data is greater than 90%. We also evaluate the accuracy of other classical time-series methods such as dynamic time warping (DTW) on filtered data along with RF on partially filtered data in which we remove the daily trends. Classification accuracy shows that DTW performs poorly (44%) and RF on partially filtered data performs decently (87%). Denoising seismic signals from both daily trends and human activity enhances RF classifier performance by 7%. Finally, these aspects make the proposed ML framework attractive for event discrimination and signal enhancement under noisy conditions, with strong potential for application to monitor leaks in CO 2 sequestration.

58 GEOSCIENCES↗

Integrated structure/control law design by multilevel optimization

A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.

Gilbert, Michael G.↗

Integrated structure/control law design by multilevel optimization

A new approach to integrated structure/control law design based on multilevel optimization is presented. This new approach is applicable to aircraft and spacecraft and allows for the independent design of the structure and control law. Integration of the designs is achieved through use of an upper level coordination problem formulation within the multilevel optimization framework. The method requires the use of structure and control law design sensitivity information. A general multilevel structure/control law design problem formulation is given, and the use of Linear Quadratic Gaussian (LQG) control law design and design sensitivity methods within the formulation is illustrated. Results of three simple integrated structure/control law design examples are presented. These results show the capability of structure and control law design tradeoffs to improve controlled system performance within the multilevel approach.

Gilbert, Michael G.↗

Computational and experimental characterization of high-brightness beams for femtosecond electron imaging and spectroscopy

Using a multilevel fast multipole method, coupled with the shadow imaging of femtosecond photoelectron pulses for validation, we quantitatively elucidate the photocathode, space charge, and virtual cathode physics, which fundamentally limit the spatiotemporal and spectroscopic resolution and throughput of ultrafast electron microscope (UEM) systems. We present a simple microscopic description to capture the nonlinear beam dynamics based on a two-fluid picture and elucidate an unexpected dominant role of image potential pinning in accelerating the emittance growth process. These calculations set theoretical limits on the performance of UEM systems and provide useful guides for photocathode design for high-brightness electron beam systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Wilson loops with neural networks

Wilson loops are essential objects in QCD and have been pivotal in scale setting and demonstrating confinement. Various generalizations are crucial for computations needed in effective field theories. In lattice gauge theory, Wilson loop calculations face challenges, including excited-state contamination at short times and the signal-to-noise ratio issue at longer times. To address these problems, we develop a new method by using neural networks to parametrize interpolators for the static quark-antiquark pair. We construct gauge-equivariant layers for the network and train it to find the ground state of the system. The trained network itself is then treated as our new observable for the inference. Our results demonstrate a significant improvement in the signal compared to traditional Wilson loops, performing as well as Coulomb-gauge Wilson-line correlators while maintaining gauge invariance. Additionally, we present an example where the optimized ground state is used to measure the static force directly, as well as another example combining this method with the multilevel algorithm. Finally, we extend the formalism to find excited-state interpolators for static quark-antiquark systems. To our knowledge, this work is the first study of neural networks with a physically motivated loss function for Wilson loops.

Bellscheidt, Verena [Massachusetts Inst. of Techno↗

MULTILEVEL MONTE CARLO (MLMC) SIMULATIONS: PERFORMANCE RESULTS FOR SPE10 (XY SLICES)

In this report we first describe a generic multilevel Monte Carlo method and then illustrate its superior performance over a traditional single-level Monte Carlo method for second order elliptic PDEs corresponding to two-dimensional layers in (x, y)-direction of the Tenth SPE Comparative Solution project (SPE 10) which gives high-contrast permeability coefficients. The SPE10 data set is used as a coarse level in the Monte Carlo method and the respective permeability coefficient k (provided in the SPE10 dataset) is used as a mean in the simulation. The actual coefficients are drawn based on a KL-expansion assuming that the log-mean is perturbed by a log-normal distributed samples.

97 MATHEMATICS AND COMPUTING↗

Improved calculation of optimum design sensitivity

Optimum design parameter sensitivity analysis has become an important topic in recent years. The principal reasons for obtaining optimum design sensitivity information with respect to various problem parameters are (l) to predict revised optimum designs, associated with specified perturbations of the problem parameters, without re-optimizing the problem and, (2) to provide sensitivity information in multilevel optimization strategies. Methods for calculating these derivatives were proposed by several authors. The most important drawback in estimating parameter sensitivities by the current methods is that they do not allow for changes in the active constraint set. Changes in the active constraint set produce discontinuities in the optimum design sensitivities, and therefore, a correct formulation has to be cast in terms of directional derivatives. Optimum design parameter sensitivity analysis is addressed in terms of directional derivatives so as to include possible discontinuities and it also presents a method for estimating optimum design sensitivities using finite differences.

Sepulveda, Abdon E.↗

Electromagnetic Launch Vehicle Fairing and Acoustic Blanket Model of Received Power Using FEKO

Evaluating the impact of radio frequency transmission in vehicle fairings is important to sensitive spacecraft. This paper employees the Multilevel Fast Multipole Method (MLFMM) feature of a commercial electromagnetic tool to model the fairing electromagnetic environment in the presence of an internal transmitter. This work is an extension of the perfect electric conductor model that was used to represent the bare aluminum internal fairing cavity. This fairing model includes typical acoustic blanketing commonly used in vehicle fairings. Representative material models within FEKO were successfully used to simulate the test case.

Trout, Dawn H.↗

Electromagnetic Launch Vehicle Fairing and Acoustic Blanket Model of Received Power Using FEKO

Evaluating the impact of radio frequency transmission in vehicle fairings is important to electromagnetically sensitive spacecraft. This study employs the multilevel fast multipole method (MLFMM) from a commercial electromagnetic tool, FEKO, to model the fairing electromagnetic environment in the presence of an internal transmitter with improved accuracy over industry applied techniques. This fairing model includes material properties representative of acoustic blanketing commonly used in vehicles. Equivalent surface material models within FEKO were successfully applied to simulate the test case. Finally, a simplified model is presented using Nicholson Ross Weir derived blanket material properties. These properties are implemented with the coated metal option to reduce the model to one layer within the accuracy of the original three layer simulation.

Trout, Dawn H.↗

Multilevel Monte Carlo Estimation of Unbiased Expectation via Sample Reuse and the Low Variance Estimation of Asymptotic Rates

A new variant of the multilevel Monte Carlo estimator [5, 3, 9, 12] is presented for the estimation of expectation statistics that utilizes sample reuse in specified levels, explicitly removes approximation error bias associated with numerically computed output quantities of interest that have an asymptotic limit behavior, and permits a low variance estimate of the asymptotic rate of convergence to that limit. In addition, it is shown that this new multilevel Monte Carlo variant can yield a computational cost savings. A review of Monte Carlo and multilevel Monte Carlo estimators is presented that includes analysis of expected value, expected mean squared error, and the calculation of optimized multilevel sample size parameters. The multilevel Monte Carlo estimator produces estimates of expectation for numerically approximated output quantities of interest that are biased by approximation error. When the quantity of interest can be modeled as the asymptotic limit of numerically approximated output quantities of interest, it is theoretically possible to remove this approximation error bias in the multilevel Monte Carlo estimator. In actual implementations, however, this procedure is unreliable due to statistical variability and inaccuracy in estimating the needed asymptotic limit. Analysis and numerical experiment show that the proposed variant of the multilevel Monte Carlo method greatly reduces (in some cases eliminates) the statistical variability in this limit estimation.

Barth, Timothy↗

Smoothed aggregation adaptive spectral element-based algebraic multigrid

SAAMGE provides parallel methods for building multilevel hierarchies and solvers that can be used for elliptic equations with highly heterogeneous coefficients. Additionally, hierarchy adaptation is implemented allowing solving multiple problems with close coefficients without rebuilding the hierarchy.

Source record↗

HAZARD ANALYSIS OF DIGITAL ENGINEERED SAFETY FEATURES ACTUATION SYSTEM IN ADVANCED NUCLEAR POWER PLANTS USING A REDUNDANCY-GUIDED APPROACH

Replacing the existing aging analog instrumentation and control (I&C) systems with modern safety control and protection digital technology offers one of the foremost means of performance improvements and cost reductions for the existing nuclear power plants (NPPs). However, the qualification of digital I&C systems remains a challenge, especially considering the issue of software common-cause failures (CCFs), which are difficult to address. With the application and upgrades of advanced digital I&C systems, software CCFs have become a potential threat to plant safety because most redundant designs use similar digital platforms or software in the operating and application systems. With complex designs of multilayer redundancy to meet the single-failure criterion, digital I&C safety systems (e.g., engineered safety-features actuation system [ESFAS]) are of a particular concern in the U.S. Nuclear Regulatory Commission (NRC) licensing procedures. This paper applies a modularized approach to conduct redundancy-guided systems-theoretic hazard analysis for an advanced digital ESFAS with multilevel redundancy designs. Systematic methods and risk-informed tools are incorporated to address both hardware and software CCFs, which provide guidance to eliminate the triggers of potential single points of failure in the design of digital safety systems in advanced plant designs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Partial secular Bloch-Redfield master equation for incoherent excitation of multilevel quantum systems

We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Using a derivative-free optimization method for multiple solutions of inverse transport problems

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a mesh adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.

42 ENGINEERING↗

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility of the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.

97 MATHEMATICS AND COMPUTING↗