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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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DOE OSTI2014

CSU Final Report on the Math/CS Institute CACHE: Communication-Avoiding and Communication-Hiding at the Extreme Scale

The CACHE project entails researching and developing new versions of numerical algorithms that result in data reuse that can be scheduled in a communication avoiding way. Since memory accesses take more time than any computation and require the most power, the focus on turning data reuse into data locality is critical to improving performance and reducing power usage in scientific simulations. This final report summarizes the accomplishments at Colorado State University as part of the CACHE project.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Quinoa, Version 0.1

Quinoa is a set of computational tools that enables research and numerical analysis in fluid dynamics. At this time it is a test-bed to experiment with various algorithms using fully asynchronous runtime systems.

Bakosi, Jozsef↗
DOE OSTI2017

Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods

Abstract In this paper, the numerical error of two widely used methods for remapping of discrete quantities from one computational mesh to another is investigated. We compare the intuitive, but resource intensive method utilizing intersections of computational cells with the faster and simpler swept-region-based method. Both algorithms are formally second order accurate, however, they are known to produce slightly different quantity profiles in practical applications. The second-order estimate of the error formula is constructed algebraically for both algorithms so that their local accuracy can be evaluated. This general estimate is then used to assess the dependence of the performance of both methods on parameters such as the second derivatives of the remapped distribution, mesh geometry or mesh movement. Due to the complexity of such analysis, it is performed on a set of simplified elementary mesh patterns such as cell corner expansion, rotation or shear. On selected numerical tests it is demonstrated that the swept-based method can distort a symmetric quantity distribution more substantially than the intersection-based approach when the computational mesh moves in an unsuitable direction.

Klima, Matej↗
DOE OSTI2016

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Rise of an argon bubble in liquid steel in the presence of a transverse magnetic field

The rise of gaseous bubbles in viscous liquids is a fundamental problem in fluid physics, and it is also a common phenomenon in many industrial applications such as materials processing, food processing, and fusion reactor cooling. In this work, the motion of a single argon gas bubble rising in quiescent liquid steel under an external magnetic field is studied numerically using a Volume-of-Fluid method. To mitigate spurious velocities normally generated during numerical simulation of multiphase flows with large density differences, an improved algorithm for surface tension modeling, originally proposed by Wang and Tong [“Deformation and oscillations of a single gas bubble rising in a narrow vertical tube,” Int. J. Therm. Sci. 47, 221–228 (2008)] is implemented, validated and used in the present computations. The governing equations are integrated by a second-order space and time accurate numerical scheme, and implemented on multiple Graphics Processing Units with high parallel efficiency. The motion and terminal velocities of the rising bubble under different magnetic fields are compared and a reduction in rise velocity is seen in cases with the magnetic field applied. The shape deformation and the path of the bubble are discussed. An elongation of the bubble along the field direction is seen, and the physics behind these phenomena is discussed. The wake structures behind the bubble are visualized and effects of the magnetic field on the wake structures are presented. A modified drag coefficient is obtained to include the additional resistance force caused by adding a transverse magnetic field.

42 ENGINEERING↗
DOE OSTI2015

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

58 GEOSCIENCES↗
DOE OSTI2021

Machine Learning Assisted Safety Modeling and Analysis of Advanced Reactors

With the advances in computational power and numerical methods, analysts can now rely on first-principle simulations to predict ultra-fine details in a variety of applications. Advances in machine learning (ML) have produced algorithms that can now learn high-level abstractions via hierarchical models. This project aims to leverage advances in ML techniques and the available high-resolution simulation data to develop a novel modeling and simulation (M\&S) methodology for reactor safety analysis. While application-agnostic ML techniques are available, complex physics constraints need to be incorporated into ML techniques to build ML-based closures for computationally efficient predictive simulations. This project intends to develop a physics-guided data-driven multi-scale methodology for M\&S of advanced reactors. The project focuses on thermal fluid (T/F) phenomena, which play major roles in advanced reactor safety. Specifically, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor (SFR). The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data with Reynolds-averaged Navier-Stokes (RANS) turbulence model to ensure accuracy. Three different neural networks are developed and tested for loss-of-flow transients in the hot pool of SFR, i.e. the densely connected convolutional neural network (DCNN), long-short-term-memory network based on proper orthogonal decomposition (POD-LSTM), and the DCNN informed by LSTM (DCNN-LSTM). The performances of these three neural networks are evaluated based on baseline models. The DCNN-LSTM model has been chosen for further hyperparameter optimization. Furthermore, based on a simplified two-dimensional case, uncertainty quantification (UQ) of the developed ML-based closure are investigated with three methods, i.e. Monte Carlo dropout, deep ensemble, and Bayesian neural network. The developed ML-based turbulent viscosity closure relation based on deep ensemble is then integrated into the system analysis module SAM and serves as a term in the conservation equations. Such a SAM-ML based procedure guarantees that the obtained results are consistent with the physical constraints of the thermal-fluid system. The SAM-ML simulation on the same loss-of-flow transient showed comparable accuracy with the CFD simulation but with a much coarser mesh setup. Last but not least, the ML-based closure improvement with the support of higher-fidelity data from large eddy simulation (LES) is discussed. As a first step towards this direction, a baseline LES simulation is performed to obtain comparable data with RANS results. Based on the early results, future investigation on further improving the ML-based closure is discussed. We believe the developed approach that combines scientific machine learning with nuclear system analysis code can benefit the advanced reactor community as more accurate safety analyses will better characterize reactor safety margins and reduce licensing efforts.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Conservative tightly-coupled simulations of stochastic multiscale systems

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employing either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum dynamics simulation of the advection-diffusion equation

The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.

Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗
DOE OSTI2015

Batched matrix computations on hardware accelerators based on GPUs

Scientific applications require solvers that work on many small size problems that are independent from each other. At the same time, the high-end hardware evolves rapidly and becomes ever more throughput-oriented and thus there is an increasing need for an effective approach to develop energy-efficient, high-performance codes for these small matrix problems that we call batched factorizations. The many applications that need this functionality could especially benefit from the use of GPUs, which currently are four to five times more energy efficient than multicore CPUs on important scientific workloads. This study, consequently, describes the development of the most common, one-sided factorizations, Cholesky, LU, and QR, for a set of small dense matrices. The algorithms we present together with their implementations are, by design, inherently parallel. In particular, our approach is based on representing the process as a sequence of batched BLAS routines that are executed entirely on a GPU. Importantly, this is unlike the LAPACK and the hybrid MAGMA factorization algorithms that work under drastically different assumptions of hardware design and efficiency of execution of the various computational kernels involved in the implementation. Thus, our approach is more efficient than what works for a combination of multicore CPUs and GPUs for the problems sizes of interest of the application use cases. The paradigm where upon a single chip (a GPU or a CPU) factorizes a single problem at a time is not at all efficient in our applications’ context. We illustrate all of these claims through a detailed performance analysis. With the help of profiling and tracing tools, we guide our development of batched factorizations to achieve up to two-fold speedup and three-fold better energy efficiency as compared against our highly optimized batched CPU implementations based on MKL library. Finally, the tested system featured two sockets of Intel Sandy Bridge CPUs and we compared with a batched LU factorizations featured in the CUBLAS library for GPUs, we achieve as high as 2.5× speedup on the NVIDIA K40 GPU.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Modeling and simulation challenges pursued by the Consortium for Advanced Simulation of Light Water Reactors (CASL)

The Consortium for the Advanced Simulation of Light Water Reactors (CASL), the first Energy Innovation Hub of the Department of Energy, was established in 2010 with the goal of providing modeling and simulation (M&S) capabilities that support and accelerate the improvement of nuclear energy's economic competitiveness and the reduction of spent nuclear fuel volume per unit energy, and all while assuring nuclear safety. To accomplish this requires advances in M&S capabilities in radiation transport, thermal-hydraulics, fuel performance and corrosion chemistry. To focus CASL's R&D, industry challenge problems have been defined, which equate with long standing issues of the nuclear power industry that M&S can assist in addressing. To date CASL has developed a multi-physics “core simulator” based upon pin-resolved radiation transport and subchannel (within fuel assembly) thermal-hydraulics, capitalizing on the capabilities of high performance computing. CASL's fuel performance M&S capability can also be optionally integrated into the core simulator, yielding a coupled multi-physics capability with untapped predictive potential. Material models have been developed to enhance predictive capabilities of fuel clad creep and growth, along with deeper understanding of zirconium alloy clad oxidation and hydrogen pickup. Understanding of corrosion chemistry (e.g., CRUD formation) has evolved at all scales: micro, meso and macro. CFD R&D has focused on improvement in closure models for subcooled boiling and bubbly flow, and the formulation of robust numerical solution algorithms. For multiphysics integration, several iterative acceleration methods have been assessed, illuminating areas where further research is needed. Finally, uncertainty quantification and data assimilation techniques, based upon sampling approaches, have been made more feasible for practicing nuclear engineers via R&D on dimensional reduction and biased sampling. Industry adoption of CASL's evolving M&S capabilities, which is in progress, will assist in addressing long-standing and future operational and safety challenges of the nuclear industry. - Highlights: • Complexity of physics based modeling of light water reactor cores being addressed. • Capability developed to help address problems that have challenged the nuclear power industry. • Simulation capabilities that take advantage of high performance computing developed.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

HPC4Mobilty w/ UCB

The purpose of this project is to examine the energy impact of urban-scale traffic for the Los Angeles Basin by developing and implementing a scalable traffic assignment model. An energy optimization function will be posed and when integrated into the optimization code for travel assignment it can be mathematically proven to converge. The energy optimization function can then be compared to the typical travel time optimization that is traditionally used in traffic assignment models. The analysis will begin with static traffic assignment models with the routing for all origin and destinations computed in parallel on high performance computing facilities. Convergence of the numerical methods rely on the solution of convex programs (or extensions of these). This step will mostly consist of demonstrating the ability to parallelize the Frank Wolfe algorithm on various platforms. This work will contribute to LBNL’s efforts to develop new processes, analytical tools, program designs, and business models to advance the state of the art in next-generation sustainable transportation solutions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2017

An Augmented Lagrangian Filter Method for Real-Time Embedded Optimization

We present a filter line-search algorithm for nonconvex continuous optimization that combines an augmented Lagrangian function and a constraint violation metric to accept and reject steps. The approach is motivated by real-time optimization applications that need to be executed on embedded computing platforms with limited memory and processor speeds. The proposed method enables primal–dual regularization of the linear algebra system that in turn permits the use of solution strategies with lower computing overheads. We prove that the proposed algorithm is globally convergent and we demonstrate the developments using a nonconvex real-time optimization application for a building heating, ventilation, and air conditioning system. Our numerical tests are performed on a standard processor and on an embedded platform. Lastly, we demonstrate that the approach reduces solution times by a factor of over 1000.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Least-squares solutions of generalized inverse eigenvalue problem over Hermitian–Hamiltonian matrices with a submatrix constraint

In this paper, a gradient-based iterative algorithm is proposed for finding the least-squares solutions of the following constrained generalized inverse eigenvalue problem: given X∈C{sup n×m}, Λ=diag(λ{sub 1},λ{sub 2},…,λ{sub m})∈C{sup m×m}, find A{sup ∗},B{sup ∗}∈C{sup n×n}, such that ∥AX−BXΛ∥ is minimized, where A{sup ∗},B{sup ∗} are Hermitian–Hamiltonian except for a special submatrix. For any initial constrained matrices, a solution pair (A{sup ∗},B{sup ∗}) can be obtained in finite iteration steps by this iterative algorithm in the absence of roundoff errors. The least-norm solution can be obtained by choosing a special kind of initial matrix pencil. In addition, the unique optimal approximation solution to a given matrix pencil in the solution set of the above problem can also be obtained. A numerical example is given to show the efficiency of the proposed algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Parallel iterative methods for a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces

In this paper, we propose some new parallel iterative methods by the hybrid and shrinking projection to find a common fixed point of a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces when the domain C satisfies diam(C) < ∞. We also give some applications of our main results for the problem of finding a common fixed point of nonexpansive mappings, nonexpansive semi-groups, the problem of finding a common zero point of monotone operators, the system of generalized mixed equilibrium problems and the system of variational inequalities without the condition diam(C) < ∞. Three numerical examples also are given to illustrate the effectiveness of the proposed algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Well-balanced Component-wise Scheme for Shallow Water System

This paper presents a well-balanced numerical scheme for solving free surface flows involving wetting and drying. The proposed algorithm combines a component-wise approach with hydrostatic reconstruction strategy to compute flows over wet or dry surfaces and to satisfy the steady state condition of still water. The robustness of the proposed scheme is verified under several benchmark hydraulic tests.

42 ENGINEERING↗
DOE OSTI2015

Modeling of fracture of protective concrete structures under impact loads

This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.

36 MATERIALS SCIENCE↗