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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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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Towards improved speed and accuracy of laser powder bed fusion simulations via representation of multiple time scales

Here, we report the result of investigations into alternative representations of the temporal evolution of the laser powder bed fusion (LPBF) process. In order to provide the reader with sufficient context for the following discussion, the modeling challenge and its underlying cause, as well as current attempts to provide a satisfactory solution, will be discussed. Next, the author will describe two numerical methods (multirate time integration and parallel-in-time) to better represent the temporal scales of the problem. Finally, the results of applying these methods to a two-dimensional version of the heat transfer portion of the LPBF problem will be presented, reporting on both convergence and performance behavior, which indicate the possibility of significant speedup of solution calculations (40–100 times), along with well-characterized effects on solution accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Impact of plasma density/collisionality on divertor heat flux width

Both ASDEX-Upgrade (AUG) data and the generalized HD (GHD) model showed that the scrape-off width broadens as the density/collisionality increases [1, 2]. A series of BOUT++ transport simulations are performed to study the physics of the scaling characteristics of the divertor heat flux width vs density/collisionality via a plasma density scan with either fixed pressure profile or fixed temperature profile inside separatrix. Additionally, the simulations show that even in the drift dominated regime, the divertor heat flux width can be broadened due to the transition of the SOL residence time from the parallel particle flow time to the enhanced parallel conduction time as the collisionality/density increases as posited in the GHD model. In addition, the heat flux width is found to be proportional to the square root of ion mass for low collisionality while it has a weakly dependence on ion mass for high collisionality. Furthermore, our simulations show that as the density increases, the radial electric field (E r ) well shallows, which potentially weakens E r × B flow shear stabilization of turbulence at high density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

This paper presents some recent advances for parallel-in-time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction in time (MGRIT) for an important application area, linear elasticity. Previously, efforts at parallel-in-time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel-in-time algorithms for this application area currently do not exist. This paper proposes some solutions made possible by MGRIT (e.g., slow temporal coarsening and FCF-relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel-in-time methods. Using a recently developed convergence theory for MGRIT and Parareal, we show that the changed formulation of the problem avoids the instability issues and allows the reduction of the error using two temporal grids. We then extend our approach to the multilevel case, where we demonstrate how slow temporal coarsening improves convergence. Finally, the paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Long-time molecular dynamics simulations on massively parallel platforms: A comparison of parallel replica dynamics and parallel trajectory splicing

Molecular dynamics (MD) is one of the most widely used techniques in computational materials science. By providing fully resolved trajectories, it allows for a natural description of static, thermodynamic, and kinetic properties. A major hurdle that has hampered the use of MD is the fact that the timescales that can be directly simulated are very limited, even when using massively parallel computers. We compare two time-parallelization approaches, parallel replica dynamics (ParRep) and parallel trajectory splicing (ParSplice), that were specifically designed to address this issue for rare event systems by leveraging parallel computing resources. Using simulations of the relaxation of small disordered platinum nanoparticles, a comparative performance analysis of the two methods is presented. Finally, the results show that ParSplice can significantly outperform ParRep in the common case where the trajectory remains trapped for a long time within a region of configuration space but makes rapid structural transitions within this region.

36 MATERIALS SCIENCE↗
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 OSTI2016

Multigrid Reduction in Time for Nonlinear Parabolic Problems

The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Two-Level Convergence Theory for Multigrid Reduction in Time (MGRIT)

Here we develop a two-grid convergence theory for the parallel-in-time scheme known as multigrid reduction in time (MGRIT), as it is implemented in the open-source package [XBraid: Parallel Multigrid in Time, http://llnl.gov/casc/xbraid]. MGRIT is a scalable and multilevel approach to parallel-in-time simulations that nonintrusively uses existing time-stepping schemes, and in a specific two-level setting it is equivalent to the widely known parareal algorithm. The goal of this paper is twofold. First, we present a two-level MGRIT convergence analysis for linear problems where the spatial discretization matrix can be diagonalized, and then apply this analysis to our two basic model problems, the heat equation and the advection equation. One important assumption is that the coarse and fine time-grid propagators can be diagaonalized by the same set of eigenvectors, which is often the case when the same spatial discretization operator is used on the coarse and fine time grids. In many cases, the MGRIT algorithm is guaranteed to converge, and we demonstrate numerically that the theoretically predicted convergence rates are sharp in practice for our model problems. Second, we explore how the convergence of MGRIT compares to the stability of the chosen time-stepping scheme. In particular, we demonstrate that a stable time-stepping scheme does not necessarily imply convergence of MGRIT, although MGRIT with FCF-relaxation always converges for the diffusion dominated problems considered here.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient Multigrid Reduction-in-Time for Method-of-Lines Discretizations of Linear Advection

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that many of these methods perform quite poorly for advection-dominated problems. In this report we analyze the particular iterative parallel-in-time algorithm of multigrid reduction-in-time (MGRIT) for discretizations of constant-wave-speed linear advection problems. We focus on common method-of-lines discretizations that employ upwind finite differences in space and Runge-Kutta methods in time. Using a convergence framework we developed in previous work, we prove for a subclass of these discretizations that, if using the standard approach of rediscretizing the fine-grid problem on the coarse grid, robust MGRIT convergence with respect to CFL number and coarsening factor is not possible. This poor convergence and non-robustness is caused, at least in part, by an inadequate coarse-grid correction for smooth Fourier modes in space-time known as characteristic components. We propose an alternative coarse-grid operator that provides a better correction of these modes. This coarse-grid operator is related to previous work and uses a semi-Lagrangian discretization combined with an implicitly treated truncation error correction. Theory and numerical experiments show the proposed coarse-grid operator yields fast MGRIT convergence for many of the method-of-lines discretizations considered, including for both implicit and explicit discretizations of high order. Parallel results demonstrate speed-up over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Photon counting imaging with an electron-bombarded CCD: Towards a parallel-processing photoelectronic time-to-amplitude converter

We have used an electron-bombarded CCD for optical photon counting imaging. The photon event pulse height distribution was found to be linearly dependent on the gain voltage. We propose on this basis that a gain voltage sweep during exposure in an electron-bombarded sensor would allow photon arrival time determination with sub-frame exposure time resolution. This effectively uses an electron-bombarded sensor as a parallel-processing photoelectronic time-to-amplitude converter, or a two-dimensional photon counting streak camera. Several applications that require timing of photon arrival, including Fluorescence Lifetime Imaging Microscopy, may benefit from such an approach. A simulation of a voltage sweep performed with experimental data collected with different acceleration voltages validates the principle of this approach. Moreover, photon event centroiding was performed and a hybrid 50% Gaussian/Centre of Gravity + 50% Hyperbolic cosine centroiding algorithm was found to yield the lowest fixed pattern noise. Finally, the camera was mounted on a fluorescence microscope to image F-actin filaments stained with the fluorescent dye Alexa 488 in fixed cells.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2013

Characterizing and Mitigating Work Time Inflation in Task Parallel Programs

Task parallelism raises the level of abstraction in shared memory parallel programming to simplify the development of complex applications. However, task parallel applications can exhibit poor performance due to thread idleness, scheduling overheads, and work time inflation – additional time spent by threads in a multithreaded computation beyond the time required to perform the same work in a sequential computation. We identify the contributions of each factor to lost efficiency in various task parallel OpenMP applications and diagnose the causes of work time inflation in those applications. Increased data access latency can cause significant work time inflation in NUMA systems. Our locality framework for task parallel OpenMP programs mitigates this cause of work time inflation. Our extensions to the Qthreads library demonstrate that locality-aware scheduling can improve performance up to 3X compared to the Intel OpenMP task scheduler.

Olivier, Stephen L.↗
DOE OSTI2023

Exponential Runge-Kutta Parareal for non-diffusive equations

Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial time-stepping methods. However, like many parallel-in-time methods it can fail to converge when applied to non-diffusive equations such as hyperbolic systems or dispersive nonlinear wave equations. Here, this paper explores the use of exponential integrators within the Parareal iteration. Exponential integrators are particularly interesting candidates for Parareal because of their ability to resolve fast-moving waves, even at the large stepsizes used by coarse propagators. This work begins with an introduction to exponential Parareal integrators followed by several motivating numerical experiments involving the nonlinear Schrödinger equation. These experiments are then analyzed using linear analysis that approximates the stability and convergence properties of the exponential Parareal iteration on nonlinear problems. The paper concludes with two additional numerical experiments involving the dispersive Kadomtsev-Petviashvili equation and the hyperbolic Vlasov-Poisson equation. These experiments demonstrate that exponential Parareal methods offer improved time-to-solution compared to serial exponential integrators when solving certain non-diffusive equations.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2021

Time-periodic steady-state solution of fluid-structure interaction and cardiac flow problems through multigrid-reduction-in-time

In this study, a time-periodic MGRIT algorithm is proposed as a means to reduce the time-to-solution of numerical algorithms by exploiting the time periodicity inherent to many applications in science and engineering. The time-periodic MGRIT algorithm is applied to a variety of linear and nonlinear single- and multiphysics problems that are periodic-in-time. It is demonstrated that the proposed parallel-in-time algorithm can obtain the same time-periodic steady-state solution as sequential time-stepping. It is shown that the required number of MGRIT iterations can be estimated a priori and that the new MGRIT variant can significantly and consistently reduce the time-to-solution compared to sequential time-stepping, irrespective of the number of dimensions, linear or nonlinear PDE models, single-physics or coupled problems and the employed computing resources. The numerical experiments demonstrate that the time-periodic MGRIT algorithm enables a greater level of parallelism yielding faster turnaround, and thus, facilitating more complex and more realistic problems to be solved.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

PFLOTRAN-E4D: A parallel open source PFLOTRAN module for simulating time-lapse electrical resistivity data

Time-lapse electrical resistivity tomography (ERT) is finding increased application for remotely monitoring processes occurring in the near subsurface in three-dimensions (i.e. 4D monitoring). However, there are few codes capable of simulating the evolution of subsurface resistivity and corresponding tomographic measurements arising from a particular process, particularly in parallel and with an open source license. Herein we describe and demonstrate an electrical resistivity tomography module for the PFLOTRAN subsurface simulation code, named PFLOTRAN-E4D. The PFLOTRAN-E4D module operates in parallel using a dedicated set of compute cores in a master-slave configuration. At each time step, the master processes receives subsurface states from PFLOTRAN, converts those states to bulk electrical conductivity, and instructs the slave processes to simulate a tomographic data set. The resulting multi-physics simulation capability enables accurate feasibility studies for ERT imaging, the identification of the ERT signatures that are unique to a given process, and facilitates the joint inversion of ERT data with hydrogeological data for subsurface characterization. PFLOTRAN-E4D is demonstrated herein using a field study of stage-driven groundwater/river water interaction ERT monitoring along the Columbia River, Washington, USA. Results demonstrate the complex nature of changes subsurface electrical conductivity, in both the saturated and unsaturated zones, arising from water table changes and from river water intrusion into the aquifer. The results also demonstrate the sensitivity of surface based ERT measurements to those changes over time. PFLOTRAN-E4D is available with the PFLOTRAN development version with an open-source license at https://bitbucket.org/pflotran/pflotran-dev .

Environmental Molecular Sciences Laboratory↗
DOE OSTI2021

Optimizing multigrid reduction-in-time and Parareal coarse-grid operators for linear advection

Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent partial differential equations (PDEs) in modern high-performance computing environments. While these techniques have been very successful for parabolic equations, it has often been observed that their performance suffers dramatically when applied to advection-dominated problems or purely hyperbolic PDEs using standard rediscretization approaches on coarse grids. In this paper, we apply MGRIT or Parareal to the constant-coefficient linear advection equation, appealing to existing convergence theory to provide insight into the typically nonscalable or even divergent behavior of these solvers for this problem. To overcome these failings, we replace rediscretization on coarse grids with improved coarse-grid operators that are computed by applying optimization techniques to approximately minimize error estimates from the convergence theory. Therefore, one of our main findings is that, in order to obtain fast convergence as for parabolic problems, coarse-grid operators should take into account the behavior of the hyperbolic problem by tracking the characteristic curves. Our approach is tested for schemes of various orders using explicit or implicit Runge–Kutta methods combined with upwind-finite-difference spatial discretizations. In all cases, we obtain scalable convergence in just a handful of iterations, with parallel tests also showing significant speed-ups over sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An experimental comparison of a space-time multigrid method with PFASST for a reaction-diffusion problem

We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multigrid strategies. For both approaches, we start from an integral formulation of the continuous time dependent problem. Then, a collocation form for PFASST and a discontinuous Galerkin discretization in time for the space-time multi-grid are employed, resulting in the same discrete solution at the time nodes. Strong and weak scaling of both multilevel strategies are compared for varying orders of the temporal discretization. Moreover, we investigate the respective convergence behavior for non-linear problems and highlight quantitative differences in execution times

97 MATHEMATICS AND COMPUTING↗