SEARCH · Search NASA

Results for “parallel methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 451 records · Page 25

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Reverse-Mode Algorithmic Differentiation of an OpenMP-Parallel Compressible Flow Solver

y Reverse-mode algorithmic differentiation (AD) is an established method for obtaining adjoint derivatives of computer simulation applications. In computational fluid dynamics (CFD), adjoint derivatives of a cost function output such as drag or lift with respect to design parameters such as surface coordinates or geometry control points are a key ingredient for shape optimization, uncertainty quantification and flow control. The computational cost of CFD applications and their derivatives makes it essential to use high-performance computing hardware efficiently, including multi- and many-core architectures. Nevertheless, OpenMP is not supported in most AD tools, and previously shown methods achieve poor scalability of the derivative code. We present the AD of an OpenMP-parallelized finite volume compressible flow solver for unstructured meshes. Our approach enables us to reuse the parallelization of the original code in the computation of adjoint derivatives. The method works by identifying code segments that can be differentiated in reverse-mode without changing their memory access pattern. The OpenMP parallelization is integrated into the derivative code during the build process in a way that is robust to modifications of the original code and independent of the OpenMP support of the differentiation tool. We show the scalability of our adjoint CFD solver on test cases ranging from thousands to millions of finite volume mesh cells on CPUs with up to 16 threads as well as on an Intel XeonPhi card with 236 threads. We demonstrate that our approach is more practical to implement for production-sized CFD codes and produces more efficient adjoint derivative code than previously shown AD methods.

Huckelheim, Jan↗

DOE OSTI2021

Data processing methods and data acquisition for samples larger than the field of view in parallel-beam tomography

Parallel-beam tomography systems at synchrotron facilities have limited field of view (FOV) determined by the available beam size and detector system coverage. Scanning the full size of samples bigger than the FOV requires various data acquisition schemes such as grid scan, 360-degree scan with offset center-of-rotation (COR), helical scan, or combinations of these schemes. Though straightforward to implement, these scanning techniques have not often been used due to the lack of software and methods to process such types of data in an easy and automated fashion. The ease of use and automation is critical at synchrotron facilities where using visual inspection in data processing steps such as image stitching, COR determination, or helical data conversion is impractical due to the large size of datasets. Here, we provide methods and their implementations in a Python package, named Algotom, for not only processing such data types but also with the highest quality possible. The efficiency and ease of use of these tools can help to extend applications of parallel-beam tomography systems.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Final Scientific/Technical Report

A variety of calcifying organisms produce a transient or metastable amorphous calcium carbonate (ACC) precursor phase that is assembled and subsequently transformed into a crystalline biomineral, typically calcite or aragonite. The complex shapes, hierarchical structures, and unique physical properties of the biominerals that result from this calcification pathway have stimulated interest in adapting these concepts for the design and creation of bio-inspired functional materials in the laboratory. ACC also forms as a reactive precursor in diverse inorganic systems and is likely to play a much broader role in calcium carbonate formation. Knowledge of the structure, composition, and behavior of this metastable phase is critical for establishing a structural and mechanistic framework for calcium carbonate formation and its role in biogeochemical processes, including carbon cycling. Minor additives, such as magnesium, phosphorus, and organic macromolecules, are known to play important roles in controlling ACC stability, transformation kinetics, and selection of final crystalline polymorph. Molecular water also occurs in many types of ACC and is thought to play a structural role in its stability and transformation behavior. One of the major challenges that remain unresolved is identification of the structural basis for the role of these minor additives and molecular water. The absence of long-range order in ACC, and other amorphous phases, has posed a challenge for study by techniques commonly used for crystalline solids. Preliminary studies in our group show that the combination of two techniques, synchrotron X-ray-based pair distribution function (PDF) analysis and nuclear magnetic resonance (NMR) spectroscopy can provide entirely new insight to structural properties of synthetic ACC over length scales that are most relevant for understanding its transformation properties. Building on preliminary experiments, we propose a systematic study of synthesis, structure, and transformation behavior in abiotic systems. The work will specifically address the influence of phosphate as a minor additive. PDF analysis will utilize total X-ray scattering data collected at synchrotron facilities optimized for this method and will provide direct characterization of the short- and intermediate-range structure of ACC synthesized under controlled conditions. Parallel computational work using reverse Monte Carlo methods will allow structural models to be constructed for a more complete analysis of PDF results. NMR spectroscopy, using a variety of single- and double-resonance techniques, will provide information on H and CO3 components, including dynamical properties, and their relationship to stabilizing additives. PDF and NMR results will be complemented by parallel studies using X-ray absorption and FT-IR spectroscopy to allow direct comparison to previous studies. These techniques will be used to follow the transformation of different ACC samples, with specific additives, to crystalline phases under controlled condition (e.g., relative humidity). This work will provide the structural and mechanistic basis for understanding ACC stability, its transformation behavior, and the factors that govern polymorph selection. This new insight will directly benefit researchers in diverse fields, as well as adding to the framework of knowledge for understanding and controlling calcium carbonate formation in natural and engineered systems.

58 GEOSCIENCES↗

DOE OSTI2019

Modeling the asynchronous Jacobi method without communication delays

Asynchronous iterative methods for solving linear systems are gaining renewed interest due to the high cost of synchronization points in massively parallel codes. Historically, theory on asynchronous iterative methods has focused on asymptotic behavior, while the transient behavior remains poorly understood. In this paper, we study a model of the asynchronous Jacobi method without communication delays, which we call simplified asynchronous Jacobi. Simplified asynchronous Jacobi can be used to model asynchronous Jacobi implemented in shared memory or distributed memory with fast communication networks. Our analysis uses the idea of a propagation matrix, which is similar in concept to an iteration matrix. We show that simplified asynchronous Jacobi can continue to reduce the residual when some processes are slower than other processes. We also show that simplified asynchronous Jacobi can converge when synchronous Jacobi does not. We verify our analysis of simplified asynchronous Jacobi using results from asynchronous Jacobi implemented in shared and distributed memory.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

High Order Discontinuous Galerkin Method and Applications (Final Technical Report)

This project aims at the developments and improvements of high order accurate discontinuous Galerkin finite element methods for solving partial differential equations arising from DOE applications. Algorithm development, improvement, analysis, implementation and applications aspects are addressed. The partial differential equations under study involve solutions with shocks or other discontinuities, rapidly changing regions, or multiscale solutions. These include the so-called convection dominated cases, such as the hyperbolic equations (e.g. Euler equations of gas dynamics), parabolic equations with small viscosities (e.g. high Reynolds number Navier-Stokes equations), KdV type equations with small dispersion describing water waves (small third derivative terms), time-dependent bi-harmonic equations and equations with hyper-viscosity (small fourth or higher even derivative terms), problems with highly oscillatory coefficients, or problems for which the macro-scale PDE models may not be correct in localized regions and a micro-scale model must be used instead. Furthermore, we are interested in the long time solutions of such equations with waves traveling a long distance, such as the electromagnetic waves. The requirement on numerical methods is thus high order accuracy, low dissipation/dispersion errors over long time, and a clean and sharp discontinuity resolution. It would also be highly desirable to have the numerical methods to be flexible for complicated geometry and boundary conditions, and to be easy in an adaptive and massively parallel environment. The discontinuous Galerkin finite element method has this potential, however the design and analysis of the discontinuous Galerkin method for each specific class of partial differential equations would require detailed research.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Implementing machine learning methods on QICK hardware for qubit readout & control

Quantum readout and control is a fundamental aspect of quantum computing that requires accurate measurement of qubit states. Errors emerge in all stages, from initialization to readout, and identifying errors in post-processing necessitates resource-intensive statistical analysis. In our work, we use a lightweight fully-connected neural network (NN) to classify states of a transmon system with no prior processing. Our NN accelerator yields higher fidelities (92%) than the classical matched filter method (84%). By exploiting the natural parallelism of NNs and their placement near the source of data on field-programmable gate arrays (FPGAs), we can achieve ultra-low latency on the Quantum Instrumentation Control Kit (QICK). Integrating machine learning methods on QICK opens several pathways for efficient real-time processing of quantum circuits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Parallel Nonnegative CP Decomposition of Dense Tensors

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensors that can enforce nonnegativity of the computed low-rank factors. The principal task is to parallelize the Matricized-Tensor Times Khatri-Rao Product (MTTKRP) bottleneck subcomputation. The algorithm is computation efficient, using dimension trees to avoid redundant computation across MTTKRPs within the alternating method. Our approach is also communication efficient, using a data distribution and parallel algorithm across a multidimensional processor grid that can be tuned to minimize communication. We benchmark our software on synthetic as well as hyperspectral image and neuroscience dynamic functional connectivity data, demonstrating that our algorithm scales well to 100s of nodes (up to 4096 cores) and is faster and more general than the currently available parallel software.

Ballard, Grey↗

DOE OSTI2017

The Parareal Method for Solving Space-Dependent Neutron Kinetics Equations in Hexagonal-z Geometry

Neutron kinetics plays an important role in reactor safety and analysis. The backward Euler method is the most widely used time integration method in the calculation of space-dependent nuclear reactor kinetics. Xia (2006) used this method to discretize the derivative of flux, and adopted the analytic integration to discretize the delayed neutron precursor concentrations. Diagonally Implicit Runge-Kutta (DIRK) method owns high accuracy and excellent stability, and it was applied in the rectangle core for calculating core the nuclear reactor kinetics by Wenbo Zhao (2013). Recently, DIRK was applied to the neutron kinetics for hexagonal-z geometry application (CAI, 2016). As solving the neutron kinetics equations is very time-consuming and the number of available cores continues to increase with parallel architectures evolving, parallel algorithms need to be designed in order to effectively utilize the available resources. However, it is difficult to parallel in time axis because the later moment is strongly dependent on the previous moment. Some methods have been proposed to parallel in time algorithm over the last decades. One of the famous methods to realize time parallelism is the Parareal algorithm (Lions, 2001), which offers a promising approach to increase the degree of concurrency. More than one decade from this method first proposed, this method has been studied and applied in the many fields of applied mathematics, physics, chemistry, parallel computing, etc. Fischer (2014 applied the Parareal method in the field of the Navier-Stokes Equations. Baudron (2014) combined the Parareal method with finite element method to solve the neutron kinetics equations, where the Parareal method was implemented based on the implicit Euler method or method. In this paper, the Parareal method is studied in the hexagonal-z geometry with the help of DIRK developed for neutron kinetics equations (CAI, 2016)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

A non-intrusive parallel-in-time approach for simultaneous optimization with unsteady PDEs

This paper presents a non-intrusive framework for integrating existing unsteady partial differential equation (PDE) solvers into a parallel-in-time simultaneous optimization algorithm. The time-parallelization is provided by the non-intrusive software library XBraid [Parallel multigrid in time, software available at http://llnl.gov/casc/xbraid], which applies an iterative multigrid reduction technique to the time domain of existing time-marching schemes for solving unsteady PDEs. Its general user-interface has been extended in [S. Günther, N.R. Gauger, and J.B. Schroder, A non-intrusive parallel-in-time adjoint solver with the XBraid library, Comput. Vis. Sci. 19 (2018), pp. 85–95. Available at arXiv, math.OC/1705.00663] for computing adjoint sensitivities such that gradients of output quantities with respect to design changes can be computed parallel-in-time alongside with the primal PDE solution. In this paper, the primal and adjoint XBraid iterations are embedded into a simultaneous optimization framework, namely the One-shot method. In this method, design updates towards optimality are employed after each state and adjoint update such that optimality and feasibility of the design and the PDE solution are reached simultaneously. Finally, the time-parallel optimization method is validated on an advection-dominated flow control problem which shows significant speedup over a classical time-serial optimization algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Numerical analyses of exponential time-differencing schemes for the solution of atmospheric models

In high-resolution numerical weather prediction models, fast-moving acoustic waves must be treated in a stable manner. Among the implicit–explicit (IMEX) schemes used for the solution of these models, horizontally explicit, vertically implicit (HEVI) methods show good stability and scalability on massively parallel machines. In this work, we present two classes of exponential time-differencing (ETD) methods for atmospheric models that use a HEVI splitting strategy, one being a three-stage method with the addition of artificial diffusion, the second based on a Strang splitting approach. Overall, the stability properties of the methods are analyzed and numerical examples are provided, which compare time-step restrictions and cost-to-accuracy ratios of the new methods with those for existing approaches.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

A memory-distributed quasi-Newton solver for nonlinear programming problems with a small number of general constraints

We approach the problem of parallelizing state-of-the-art nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasi-Newton interior-point methods that use limited-memory secant Hessian approximations. Such interior-point methods are known to have better convergence properties and to be more effective on large-scale problems than gradient-based and derivative-free optimization algorithms. We target nonlinear and potentially nonconvex optimization problems with an arbitrary number of bound constraints and a small number of general equality and inequality constraints on the optimization variables. These problems occur for example in the form of optimal control, optimal design, and inverse problems governed by ordinary or partial differential equations, whenever they are expressed in a “reduced-space” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasi-Newton linear systems that leverages the fact that the quasi-Newton Hessian matrix has a small number of dense blocks that border a low-rank update of a diagonal matrix. This enables an efficient parallelization on memory-distributed computers of the iterations of the optimization algorithm, a state-of-the-art filter line-search interior-point algorithm by Wächter et. al. We illustrate the efficiency of the proposed method by solving structural topology optimization problems on up to 4608 cores on a parallel machine.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Surrogate Hessian accelerated structural optimization for stochastic electronic structure theories

In this work, we present an efficient energy-based method for structural optimization with stochastic electronic structure theories, such as diffusion quantum Monte Carlo (DMC). This method is based on robust line-search energy minimization in reduced parameter space, exploiting approximate but accurate Hessian information from a surrogate theory, such as density functional theory. The surrogate theory is also used to characterize the potential energy surface, allowing for simple but reliable ways to maximize statistical efficiency while retaining controllable accuracy. We demonstrate the method by finding the minimum DMC energy structures of the selected flake-like aromatic molecules, such as benzene, coronene, and ovalene, represented by 2, 6, and 19 structural parameters, respectively. In each case, the energy minimum is found within two parallel line-search iterations. The method is near-optimal for a line-search technique and suitable for a broad range of applications. It is easily generalized to any electronic structure method where forces and stresses are still under active development and implementation, such as diffusion Monte Carlo, auxiliary-field Monte Carlo, and stochastic configuration interaction, as well as deterministic approaches such as the random-phase approximation. Accurate and efficient means of geometry optimization could shed light on a broad class of materials and molecules, showing high sensitivity of induced properties to structural variables.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Weighted relaxation for multigrid reduction in time

Current trends in computer architectures now mean that faster computation speed must come primarily from increased concurrency, not faster clock speeds, which are stagnating. Thus, this situation creates bottlenecks for serial algorithms, including the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. Here, in this work, we consider multigrid-reduction-in-time (MGRIT), a multilevel method applied to the time dimension that computes multiple time-steps in parallel. Like all multigrid methods, MGRIT relies on the complementary relationship between relaxation on a fine-grid and a correction from the coarse grid to solve the problem. All current MGRIT implementations are based on unweighted-Jacobi relaxation; here we introduce the concept of weighted relaxation to MGRIT. We derive new convergence bounds for weighted relaxation, and use this analysis to guide the selection of relaxation weights. Numerical results then demonstrate that by choosing appropriate non-unitary relaxation weights, one can achieve faster convergence rates and lower iteration counts for MGRIT when compared with unweighted relaxation. In most cases, weighted relaxation yields a 10%–20% saving in iterations, which is significant when using large high-performance computers. For A-stable integration schemes, results also illustrate that under-relaxation can restore convergence in some cases where unweighted relaxation is not convergent.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Determination of battery stability with advanced diagnostics.

Lithium ion batteries for use in battery electric vehicles (BEVs) has seen considerable expansion over the last several years. It is expected that market share and the total number of BEVs will continue to increase over coming years and that there will be changes in the environmental and use conditions for BEV batteries. Specifically aging of the batteries and exposure to an increased number of crash conditions presents a distinct possibility that batteries may be in an unknown state posing danger to the operator, emergency response personnel and other support personnel. The present work expands on earlier efforts to explore the ability to rapidly monitor using impedance spectroscopy techniques and characterize the state of different battery systems during both typical operations and under abusive conditions. The work has found that it is possible to detect key changes in performance for strings of up to four cells in both series and parallel configurations for both typical and abusive response. As a method the sensitivity for detecting change is enhanced for series configurations. For parallel configurations distinct changes are more difficult to ascertain, but under abusive conditions and for key frequencies it is feasible to use current rapid impedance techniques to identify change. The work has also found it feasible to use rapid impedance as an evaluation method for underload conditions, especially for series strings of cells.

25 ENERGY STORAGE↗

DOE OSTI2024

Multigrid Reduction in Time for Chaotic and Hyperbolic Problems (Final Report)

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations (PDEs), which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic and chaotic problems of interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic and chaotic problems on future architectures. The chosen methodology for solving these problems parallel-in-time is multigrid, because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. Multigrid is already commonly used in many DOE simulations for scalably and optimally solving space-only PDE problems. The areas of hyperbolic and chaotic problems are chosen because of their relevance to problems of programmatic interest to DOE. However, these problems are also well-known to be difficult for parallel-in-time methods, with the most common method, parareal, diverging in many cases. The current state of-the-art for parallel-in-time at LLNL is the multigrid reduction in time (MGRIT) XBraid package, which also struggles for such problems, while still showing some improvement over parareal. In summary, new methods are needed for an efficient parallel-in-time scheme for hyperbolic and chaotic problems, and this work shall research promising new multigrid methods in this area. In particular, this work shall continue researching the directions from the current collaboration with Dr. Falgout, which are laid out in the work Toward Parallel in Time for Chaotic Dynamical Systems and showed the first known results of a parallel-in-time speedup for a chaotic problem. This work outlines two key improvements to XBraid for chaotic problems, the so-called “theta” and “delta-correction” methods. Here, these two improvements will be further researched and improved (including with a new relaxation method inspired by on Least Squares Shadowing (LSS)) and explored for more complicated problems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs

Quantum chemistry is a discipline which relies heavily on very expensive numerical computations. The scaling of correlated wave function methods lies, in their standard implementation, between O(N-5) and O(e(N)), where N is proportional to the system size. Therefore, performing accurate calculations on chemically meaningful systems requires (i) approximations that can lower the computational scaling and (ii) efficient implementations that take advantage of modern massively parallel architectures. QUANTUM PACKAGE is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multireference second-order perturbation theory (PT2). The determinant-driven framework allows the programmer to include any arbitrary set of determinants in the reference space, hence providing greater methodological freedom. The sCI method implemented in QUANTUM PACKAGE is based on the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm which complements the variational sCI energy with a PT2 correction. Additional external plugins have been recently added to perform calculations with multireference coupled cluster theory and range-separated density-functional theory. All the programs are developed with the IRPF90 code generator, which simplifies collaborative work and the development of new features. QUANTUM PACKAGE strives to allow easy implementation and experimentation of new methods, while making parallel computation as simple and efficient as possible on modern supercomputer architectures. Currently, the code enables, routinely, to realize runs on roughly 2 000 CPU cores, with tens of millions of determinants in the reference space. Moreover, we have been able to push up to 12 288 cores in order to test its parallel efficiency. In the present manuscript, we also introduce some key new developments: (i) a renormalized second-order perturbative correction for efficient extrapolation to the full CI limit and (ii) a stochastic version of the CIPSI selection performed simultaneously to the PT2 calculation at no extra cost.

Garniron, Yann↗

DOE OSTI2019

Immersed Boundary Method Halo Exchange in a Hemodynamics Application

In recent years, highly parallelized simulations of blood flow resolving individual blood cells have been demonstrated. Simulating such dense suspensions of deformable particles in flow often involves a partitioned fluid-structure interaction (FSI) algorithm, with separate solvers for Eulerian fluid and Lagrangian cell grids, plus a solver - e.g., immersed boundary method - for their interaction. Managing data motion in parallel FSI implementations is increasingly important, particularly for inhomogeneous systems like vascular geometries. In this study, we evaluate the influence of Eulerian and Lagrangian halo exchanges on efficiency and scalability of a partitioned FSI algorithm for blood flow. We describe an MPI+OpenMP implementation of the immersed boundary method coupled with lattice Boltzmann and finite element methods. We consider how communication and recomputation costs influence the optimization of halo exchanges with respect to three factors: immersed boundary interaction distance, cell suspension density, and relative fluid/cell solver costs.

Gounley, John↗

DOE OSTI2021

Planetary normal mode computation: Parallel algorithms, performance and reproducibility

This report is an extension of work entitled “Computing planetary interior normal modes with a highly parallel polynomial filtering eigensolver.” by Shi et al., [1] originally presented at the SC18 conference. A highly parallel polynomial filtered eigensolver was developed and exploited to calculate the planetary normal modes. The proposed method is ideally suited for computing interior eigenpairs for large-scale eigenvalue problems as it greatly enhances memory and computational efficiency. In this article, the second-order finite element method is used to further improve the accuracy as only the first-order finite element method was deployed in the previous work. The parallel algorithm, its parallel performance up to 20k processors, and the great computational accuracy are illustrated. The reproducibility of the previous work was successfully performed on the Student Cluster Competition at the SC19 conference by several participant teams using a completely different Mars-model dataset on different clusters. Both weak and strong scaling performances of the reproducibility by the participant teams were impressive and encouraging. The analysis and reflection of their results are demonstrated and future direction is discussed.

97 MATHEMATICS AND COMPUTING↗