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At least 19 records

A Block-Asynchronous Relaxation Method for Graphics Processing Units

In this paper, we analyze the potential of asynchronous relaxation methods on Graphics Processing Units (GPUs). For this purpose, we developed a set of asynchronous iteration algorithms in CUDA and compared them with a parallel implementation of synchronous relaxation methods on CPU-based systems. For a set of test matrices taken from the University of Florida Matrix Collection we monitor the convergence behavior, the average iteration time and the total time-to-solution time. Analyzing the results, we observe that even for our most basic asynchronous relaxation scheme, despite its lower convergence rate compared to the Gauss-Seidel relaxation (that we expected), the asynchronous iteration running on GPUs is still able to provide solution approximations of certain accuracy in considerably shorter time then Gauss- Seidel running on CPUs. Hence, it overcompensates for the slower convergence by exploiting the scalability and the good fit of the asynchronous schemes for the highly parallel GPU architectures. Further, enhancing the most basic asynchronous approach with hybrid schemes – using multiple iterations within the ”subdomain” handled by a GPU thread block and Jacobi-like asynchronous updates across the ”boundaries”, subject to tuning various parameters – we manage to not only recover the loss of global convergence but often accelerate convergence of up to two times (compared to the effective but difficult to parallelize Gauss-Seidel type of schemes), while keeping the execution time of a global iteration practically the same. This shows the high potential of the asynchronous methods not only as a stand alone numerical solver for linear systems of equations fulfilling certain convergence conditions but more importantly as a smoother in multigrid methods. Due to the explosion of parallelism in todays architecture designs, the significance and the need for asynchronous methods, as the ones described in this work, is expected to grow.

97 MATHEMATICS AND COMPUTING↗

Asynchronous, macrotasked relaxation strategies for the solution of viscous, hypersonic flows

A point-implicit, asynchronous macrotasked relaxation of the steady, thin-layer, Navier-Stokes equations is presented. The method employs multidirectional, single-level storage Gauss-Seidel relaxation sweeps, which effectively communicate perturbations across the entire domain in 2n sweeps, where n is the dimension of the domain. In order to enhance convergence the application of relaxation factors to specific components of the Jacobian is examined using a stability analysis of the advection and diffusion equations. Attention is also given to the complications associated with asynchronous multitasking. Solutions are generated for hypersonic flows over blunt bodies in two and three dimensions with chemical reactions, utilizing single-tasked and multitasked relaxation strategies.

Gnoffo, Peter A.↗

Asynchronous Photoexcited Electronic and Structural Relaxation in Lead-Free Perovskites

Vacancy-ordered lead free perovskites with more stable crystalline structure have been intensively explored as the alternatives for resolving the toxic and long-term stable issues of Lead halide perovskites (LHPs). The dispersive energy bands produced by the closely packed halide octahedral sublattice in these perovskites are meanwhile anticipated to facility the mobility of charge carriers. However, these perovskites suffer from unexpectedly poor charge carrier transport. To tackle this issue, we have employed the ultrafast, elemental-specific X-ray transient absorption (XTA) spectroscopy to directly probe the photoexcited electronic and structural dynamics of a prototypical vacancy-ordered lead-free perovskite (Cs 3 Bi 2 Br 9 ). We have discovered that the photogenerated holes quickly self-trapped at Br centers, simultaneously distorting the local lattice structure, likely forming small polarons in the configuration of V k center (Br 2 - dimer). More significantly, we have found a surprisingly long-lived, structural distorted state with a lifetime of ~ 59 μs, which is about three orders of magnitude slower than that of the charge carrier recombination. Such long-lived structural distortion may produce a transient “background” under continuous light illumination, influencing the charge carrier transport along the lattice framework.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Multiple grid problems on concurrent-processing computers

Three computer codes were studied which make use of concurrent processing computer architectures in computational fluid dynamics (CFD). The three parallel codes were tested on a two processor multiple-instruction/multiple-data (MIMD) facility at NASA Ames Research Center, and are suggested for efficient parallel computations. The first code is a well-known program which makes use of the Beam and Warming, implicit, approximate factored algorithm. This study demonstrates the parallelism found in a well-known scheme and it achieved speedups exceeding 1.9 on the two processor MIMD test facility. The second code studied made use of an embedded grid scheme which is used to solve problems having complex geometries. The particular application for this study considered an airfoil/flap geometry in an incompressible flow. The scheme eliminates some of the inherent difficulties found in adapting approximate factorization techniques onto MIMD machines and allows the use of chaotic relaxation and asynchronous iteration techniques. The third code studied is an application of overset grids to a supersonic blunt body problem. The code addresses the difficulties encountered when using embedded grids on a compressible, and therefore nonlinear, problem. The complex numerical boundary system associated with overset grids is discussed and several boundary schemes are suggested. A boundary scheme based on the method of characteristics achieved the best results.

Eberhardt, D. S.↗

High-order asynchrony-tolerant finite difference schemes for partial differential equations

Synchronizations of processing elements (PEs) in massively parallel simulations, which arise due to communication or load imbalances between PEs, significantly affect the scalability of scientific applications. We have recently proposed a method based on finite-difference schemes to solve partial differential equations in an asynchronous fashion – synchronization between PEs is relaxed at a mathematical level. While standard schemes can maintain their stability in the presence of asynchrony, their accuracy is drastically affected. In this work, we present a general methodology to derive asynchrony-tolerant (AT) finite difference schemes of arbitrary order of accuracy, which can maintain their accuracy when synchronizations are relaxed. We show that there are several choices available in selecting a stencil to derive these schemes and discuss their effect on numerical and computational performance. We provide a simple classification of schemes based on the stencil and derive schemes that are representative of different classes. Their numerical error is rigorously analyzed within a statistical framework to obtain the overall accuracy of the solution. Results from numerical experiments are used to validate the performance of the schemes.

42 ENGINEERING↗

Scalable Asynchronous Domain Decomposition Solvers

We discuss how parallel implementations of linear iterative solvers generally alternate between phases of data exchange and phases of local computation. Increasingly large problem sizes and more heterogeneous compute architectures make load balancing and the design of low latency network interconnects that are able to satisfy the communication requirements of linear solvers very challenging tasks. In particular, global communication patterns such as inner products become increasingly limiting at scale. We explore the use of asynchronous communication based on one-sided Message Passing Interface primitives in the context of domain decomposition solvers. In particular, a scalable asynchronous two-level Schwarz method is presented. We discuss practical issues encountered in the development of a scalable solver and show experimental results obtained on a state-of-the-art supercomputer system that illustrate the benefits of asynchronous solvers in load balanced as well as load imbalanced scenarios. Using the novel method, we can observe speedups of up to four times over its classical synchronous equivalent.

97 MATHEMATICS AND COMPUTING↗

LC-MEMENTO: A Memory Model for Accelerated Architectures

With the advent of heterogeneous architectures, in particular, with the ubiquity of multi-GPU systems, it is becoming increasingly important to manage device memory efficiently in order to reap the benefits of the additional core count. To date, such responsibility mainly falls on the programmer where device-to-host data communication (and vice versa), if not done properly, may incur costly memory transfer operations and synchronization. The problem may be compounded by additional requirement to maintain system-wide memory consistency that may involve expensive synchronization overhead. In this paper, we present Location Consistency Memory Model for Enhanced Transfer Operations (LC-MEMENTO). This framework considers incorporating runtime techniques for multi-GPU memory management to support relaxed synchronization semantics and memory transfer operations automatically. Specifically, we implement a relaxed form of a memory consistency model based on the Location Consistency (LC) in an Asynchronous Many-Task Runtime (ARTS) and demonstrate that, this memory model enables additional optimization opportunities for the three representative applications encompassing different computational patterns (scientific computation, graphs, data streaming, etc.).

Memory Models, Accelerators, Adaptive Optimization↗

Proton-detected solid-state NMR spectroscopy of spin-1/2 nuclei with large chemical shift anisotropy

Constant-time (CT) dipolar heteronuclear multiple quantum coherence (D-HMQC) has previously been demonstrated as a method for proton detection of high-resolution wideline NMR spectra of spin-1/2 nuclei with large chemical shift anisotropy (CSA). However, 1 H transverse relaxation and t 1 -noise often reduce the sensitivity of D-HMQC experiments, preventing the theoretical gains in sensitivity provided by 1 H detection from being realized. In this paper, we demonstrate a series of improved pulse sequences for 1 H detection of spin-1/2 nuclei under fast MAS, with 195 Pt SSNMR experiments on cisplatin as an example. First, a t 1 -incrementation protocol for D-HMQC dubbed Arbitrary Indirect Dwell (AID) is demonstrated. AID allows the use of arbitrary, rotor asynchronous t 1 -increments, but removes the constant time period from CT D-HMQC, resulting in improved sensitivity by reducing transverse relaxation losses. Next, we show that short high-power adiabatic pulses (SHAPs), which efficiently invert broad MAS sideband manifolds, can be effectively incorporated into 1 H detected symmetry-based resonance echo double resonance (S-REDOR) and t 1 -noise eliminated (TONE) D-HMQC experiments. The S-REDOR experiments with SHAPs provide approximately double the dipolar dephasing, as compared to experiments with rectangular inversion pulses. We lastly show that sensitivity and resolution can be further enhanced with the use of swept excitation pulses as well as adiabatic magic angle turning (aMAT).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

GPU-Accelerated Asynchronous Error Correction for Mixed Precision Iterative Refinement

In hardware-aware high performance computing, block- asynchronous iteration and mixed precision iterative refinement are two techniques that are applied to leverage the computing power of SIMD accelerators like GPUs. Although they use a very different approach for this purpose, they share the basic idea of compensating the convergence behaviour of an inferior numerical algorithm by a more efficient usage of the provided computing power. In this paper, we want to analyze the potential of combining both techniques. Therefore, we implement a mixed precision iterative refinement algorithm using a block-asynchronous iteration as an error correction solver, and compare its performance with a pure implementation of a block-asynchronous iteration and an iterative refinement method using double precision for the error correction solver. For matrices from theUniversity of FloridaMatrix collection,we report the convergence behaviour and provide the total solver runtime using different GPU architectures.

97 MATHEMATICS AND COMPUTING↗

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads

This paper considers power distribution networks with distributed energy resources and designs an incentive-based algorithm that allows the network operator and customers to pursue given operational and economic objectives while concurrently ensuring that voltages are within prescribed limits. Heterogeneous DERs with continuous and discrete control commands are considered. We address four major challenges: discrete decision variables, non-convexity due to a Stackelberg game structure, unavailability of private information from customers, and asynchronous operation. Starting from a non-convex setting, we develop a distributed stochastic dual algorithm that solves a relaxed problem, and prove that the proposed algorithm achieves the global optimal solution of the original problem on average. Feasible values for discrete decision variables are also recovered. Stability of the algorithm is analytically established and numerically corroborated.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Point-implicit relaxation strategies for viscous, hypersonic flows

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3D, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with a modified Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's symmetric total variation diminishing scheme. Newton relaxation of the fully coupled equation set is employed on a cell-to-cell basis. Under-relaxation of the inviscid and over-relaxation of the viscous contributions to the residual are implemented. Computational work is easily partitioned among many processors in an asynchronous, dynamic mode for convergence acceleration. An overview of the physical models employed herein for thermochemical nonequilibrium is included. Several test cases and comparisons with experimental data are presented involving hypersonic flow over blunt bodies which illustrate the qualitative and quantitative capabilities of this approach.

Gnoffo, P. A.↗

Online Stochastic Optimization of Networked Distributed Energy Resources

Our work investigates distributed control and incentive mechanisms to coordinate distributed energy resources (DERs) with both continuous and discrete decision variables as well as device dynamics in distribution grids. We formulate a multi-period social welfare maximization problem, and based on its convex relaxation propose a distributed stochastic dual gradient algorithm for managing DERs. Moreover, we extend it to an online realtime setting with time-varying operating conditions, asynchronous updates by devices, and feedback being leveraged to account for nonlinear power flows as well as reduce communication overhead. The resulting algorithm provides a general online stochastic optimization algorithm for coordinating networked DERs with discrete power setpoints and dynamics to meet operational and economic objectives and constraints. We characterize the convergence of the algorithm analytically and evaluate its performance numerically.

24 POWER TRANSMISSION AND DISTRIBUTION↗

A Surrogate-Based Asynchronous Decomposition Technique for Realistic Security-Constrained Optimal Power Flow Problems

Here we present a decomposition approach for obtaining good feasible solutions for the security-constrained, alternating-current, optimal power flow (SC-AC-OPF) problem at an industrial scale and under real-world time and computational limits. The approach was designed while preparing and participating in ARPA-E’s Grid Optimization Competition (GOC) Challenge 1. The challenge focused on a near-real-time version of the SC-AC-OPF problem, where a base operating point is optimized, taking into account possible single-element contingencies, after which the system adapts its operating point following the response of automatic frequency droop controllers and voltage regulators. Our solution approach for this problem relies on state-of-the-art nonlinear programming algorithms, and it employs nonconvex relaxations for complementarity constraints, a specialized two-stage decomposition technique with sparse approximations of recourse terms and contingency ranking and prescreening. The paper describes and justifies our approach and outlines the features of its implementation, including functions and derivatives evaluation, warm-starting strategies, and asynchronous parallelism. We discuss the results of the independent benchmark of our approach by ARPA-E’s GOC team in Challenge 1, where it was found to consistently produce high-quality solutions across a wide range of network sizes and difficulty, and conclude by outlining future extensions of the approach.

97 MATHEMATICS AND COMPUTING↗

Photovoltaic Inverter Controllers Seeking AC Optimal Power Flow Solutions

This paper considers future distribution networks featuring inverter-interfaced photovoltaic (PV) systems, and addresses the synthesis of feedback controllers that seek real- and reactive-power inverter setpoints corresponding to AC optimal power flow (OPF) solutions. The objective is to bridge the temporal gap between long-term system optimization and real-time inverter control, and enable seamless PV-owner participation without compromising system efficiency and stability. The design of the controllers is grounded on a dual ..epsilon..-subgradient method, while semidefinite programming relaxations are advocated to bypass the non-convexity of AC OPF formulations. Global convergence of inverter output powers is analytically established for diminishing stepsize rules for cases where: i) computational limits dictate asynchronous updates of the controller signals, and ii) inverter reference inputs may be updated at a faster rate than the power-output settling time.

14 SOLAR ENERGY↗

A Methodology for the Design and Verification of Globally Asynchronous/Locally Synchronous Architectures

Recent advanced in model-checking have made it practical to formally verify the correctness of many complex synchronous systems (i.e., systems driven by a single clock). However, many computer systems are implemented by asynchronously composing several synchronous components, where each component has its own clock and these clocks are not synchronized. Formal verification of such Globally Asynchronous/Locally Synchronous (GA/LS) architectures is a much more difficult task. In this report, we describe a methodology for developing and reasoning about such systems. This approach allows a developer to start from an ideal system specification and refine it along two axes. Along one axis, the system can be refined one component at a time towards an implementation. Along the other axis, the behavior of the system can be relaxed to produce a more cost effective but still acceptable solution. We illustrate this process by applying it to the synchronization logic of a Dual Fight Guidance System, evolving the system from an ideal case in which the components do not fail and communicate synchronously to one in which the components can fail and communicate asynchronously. For each step, we show how the system requirements have to change if the system is to be implemented and prove that each implementation meets the revised system requirements through modelchecking.

Miller, Steven P.↗

EMAPS: An Efficient Multiscale Approach to Plasma Systems with Non-MHD Scale Effects

Using Discrete-Event Simulation (DES) as a novel paradigm for time integration of large-scale physics-driven systems, we have achieved significant breakthroughs in simulations of multi-dimensional magnetized plasmas where ion kinetic and finite Larmor radius (FLR) and Hall effects play a crucial role. For these purposes we apply a unique asynchronous simulation tool: a parallel, electromagnetic Particle-in-Cell (PIC) code, HYPERS (Hybrid Particle Event-Resolved Simulator), which treats plasma electrons as a charge neutralizing fluid and solves a self-consistent set of non-radiative Maxwell, electron fluid equations and ion particle equations on a structured computational grid. HYPERS enables adaptive local time steps for particles, fluid elements and electromagnetic fields. This ensures robustness (stability) and efficiency (speed) of highly dynamic and nonlinear simulations of compact plasma systems such spheromaks, FRCs, ion beams and edge plasmas. HYPERS is a unique asynchronous code that has been designed to serve as a test bed for developing multi-physics applications not only for laboratory plasma devices but generally across a number of plasma physics fields, including astrophysics, space physics and electronic devices. We have made significant improvements to the HYPERS core: (1) implemented a new asynchronous magnetic field integration scheme that preserves local divB=0 to within round-off errors; (2) Improved staggered-grid discretizations of electric and magnetic fields. These modifications have significantly enhanced the accuracy and robustness of 3D simulations. We have conducted first-ever end-to-end 3D simulations of merging spheromak plasmas. The preliminary results show: (1) tilt-driven relaxation of a freely expanding spheromak to an m=1 Taylor helix configuration and (2) possibility of formation of a tilt-stable field-reversed configuration via merging and magnetic reconnection of two double-sided spheromaks with opposite helicities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Resistive Network Optimal Power Flow: Uniqueness and Algorithms

The optimal power flow (OPF) problem minimizes the power loss in an electrical network by optimizing the voltage and power delivered at the network buses, and is a nonconvex problem that is generally hard to solve. By leveraging a recent development on the zero duality gap of OPF, we propose a second-order cone programming convex relaxation of the resistive network OPF, and study the uniqueness of the optimal solution using differential topology, especially the Poincare-Hopf Index Theorem. We characterize the global uniqueness for different network topologies, e.g., line, radial, and mesh networks. This serves as a starting point to design distributed local algorithms with global behaviors that have low complexity, are computationally fast, and can run under synchronous and asynchronous settings in practical power grids.

Tan, CW↗

Asymmetric Lithium Extraction and Insertion in High Voltage Spinel at Fast Rate

Spinel-structured ordered-LiNi 0.5 Mn 1.5 O 4 (o-LNMO) has experienced a resurgence of interest in the context of reducing scarce elements such as cobalt from lithium-ion battery. O-LNMO undergoes two two-phase reaction at slow rates. However, it is not known if such phenomenon also applies at fast rates. Herein, we investigate the rate-dependent phase transition behavior of o-LNMO through in operando time-resolved X-ray diffraction. The results indicate that a narrow region of solid solution reaction exists for charge and discharge at both slow and fast rate. The overall phase transition is highly asymmetric at fast rates. During fast charge, it is a particle-by-particle mechanism resulting from asynchronized reaction among the particles. Finally, during fast discharge, it is likely a core-shell mechanism involving transition from Li 0+x Ni 0.5 Mn 1.5 O 4 to Li 1+x Ni 0.5 Mn 1.5 O 4 in the outer layer of particles. The Li 0.5 Ni 0.5 Mn 1.5 O 4 phase is suppressed during fast discharge and only appears through Li redistribution upon relaxation.

25 ENERGY STORAGE↗