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At least 235 records · Page 13

A performance model for the communication in fast multipole methods on high-performance computing platforms

Exascale systems are predicted to have approximately 1 billion cores, assuming gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. The fast multipole method (FMM) was originally developed for accelerating N-body problems in astrophysics and molecular dynamics but has recently been extended to a wider range of problems. Its high arithmetic intensity combined with its linear complexity and asynchronous communication patterns make it a promising algorithm for exascale systems. In this paper, we discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on internode communication. We focus on the communication part only; the efficiency of the computational kernels are beyond the scope of the present study. We develop a performance model that considers the communication patterns of the FMM and observe a good match between our model and the actual communication time on four high-performance computing (HPC) systems, when latency, bandwidth, network topology, and multicore penalties are all taken into account. To our knowledge, this is the first formal characterization of internode communication in FMM that validates the model against actual measurements of communication time. The ultimate communication model is predictive in an absolute sense; however, on complex systems, this objective is often out of reach or of a difficulty out of proportion to its benefit when there exists a simpler model that is inexpensive and sufficient to guide coding decisions leading to improved scaling. The current model provides such guidance.

Computer Science↗

Convective flow effects on protein crystal growth

The long-term stability of the interferometric setup for the monitoring of protein morphologies has been improved. Growth or dissolution of a crystal on a 100 A scale can now be clearly distinguished from dimensional changes occurring within the optical path of the interferometer. This capability of simultaneously monitoring the local interfacial displacement at several widely-spaced positions on the crystal surface with high local depth resolution, has already yielded novel results. We found with lysozyme that (1) the normal growth rate is oscillatory, and (2) the mean growth step density is greater at the periphery of a facet than in its center. The repartitioning of Na(+) and Cl(-) ions between lysozyme solutions and crystals was studied for a wide range of crystallization conditions. A nucleation-growth-repartitioning model was developed to interpret the large body of data in a unified way. The results strongly suggests that (1) the ion to lysozyme ratio in the crystal depends mostly on kinetic rather than crystallographic parameters, and (2) lysozyme crystals possess a salt-rich core with a diameter on the order of 10 microns. The computational model for diffusive-convective transport in protein crystallization (see the First Report) has been applied to a realistic growth cell geometry, taking into account the findings of the above repartitioning studies. These results show that some elements of a moving boundary problem must be incorporated into the model in order to obtain a more realistic description. Our experimental setup for light scattering investigations of aggregation and nucleation in protein solutions has been extensively tested. Scattering intensity measurements with a true Rayleigh scatterer produced systematically increased forward scattering, indicating problems with glare. These have been resolved. Preliminary measurements with supersaturated lysozyme solutions revealed that the scatterers grow with time. Work has begun on a computer program for the unified evaluation of simultaneously obtained, multi-angle static and dynamic light scattering data.

Rosenberger, Franz↗

An explicit, energy-conserving particle-in-cell scheme

We present an explicit temporal discretization of particle-in-cell schemes for the non-relativistic Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple, second-order explicit scheme that conserves energy exactly in the Eulerian context. We show that direct translation to particle-in-cell does not result in strict conservation, but derive a simple correction based on an analytically solvable optimization problem that recovers conservation. While this optimization problem is not guaranteed to have a real solution for every particle, we provide a correction that makes imaginary values extremely rare and still admits $\mathcal{O}$(10 –12 ) fractional errors in energy for practical simulation parameters. We present the scheme in both electrostatic – where we use the Ampère formulation – and electromagnetic contexts. With an electromagnetic field solve, the field update is most naturally linearly implicit, but the more computationally intensive particle update remains fully explicit. Here, we also show how the scheme can be extended to use the fully explicit leapfrog and pseudospectral analytic time-domain (PSATD) field solvers. The scheme is tested on standard kinetic plasma problems, confirming its conservation properties.

Energy conservation↗

Design of the protoDUNE raw data management infrastructure

The Deep Underground Neutrino Experiment (DUNE) will employ a set of Liquid Argon Time Projection Chambers (LArTPC) with a total mass of 40 kt as the main components of its Far Detector. In order to validate this technology and characterize the detector performance at full scale, an ambitious experimental program (called “protoDUNE”) has been initiated which includes a test of the large-scale prototypes for the single-phase and dual-phase LArTPC technologies, which will run in a beam at CERN. The total raw data volume that is slated to be collected during the scheduled 3-month beam run is estimated to be in excess of 2.5 PB for each detector. This data volume will require that the protoDUNE experiment carefully design the DAQ, data handling and data quality monitoring systems to be capable of dealing with challenges inherent with peta-scale data management while simultaneously fulfilling the requirements of disseminating the data to a worldwide collaboration and DUNE associated computing sites. Here in this paper, we present our approach to solving these problems by leveraging the design, expertise and components created for the LHC and Intensity Frontier experiments into a unified architecture that is capable of meeting the needs of protoDUNE.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fan noise prediction assessment

This report is an evaluation of two techniques for predicting the fan noise radiation from engine nacelles. The first is a relatively computational intensive finite element technique. The code is named ARC, an abbreviation of Acoustic Radiation Code, and was developed by Eversman. This is actually a suite of software that first generates a grid around the nacelle, then solves for the potential flowfield, and finally solves the acoustic radiation problem. The second approach is an analytical technique requiring minimal computational effort. This is termed the cutoff ratio technique and was developed by Rice. Details of the duct geometry, such as the hub-to-tip ratio and Mach number of the flow in the duct, and modal content of the duct noise are required for proper prediction.

Bent, Paul H.↗

The Transfer of Resonance Line Polarization with Partial Frequency Redistribution in the General Hanle–Zeeman Regime

The spectral line polarization encodes a wealth of information about the thermal and magnetic properties of the solar atmosphere. Modeling the Stokes profiles of strong resonance lines is, however, a complex problem both from a theoretical and computational point of view, especially when partial frequency redistribution (PRD) effects need to be taken into account. In this work, we consider a two-level atom in the presence of magnetic fields of arbitrary intensity (Hanle–Zeeman regime) and orientation, both deterministic and micro-structured. Working within the framework of a rigorous PRD theoretical approach, we have developed a numerical code that solves the full non-LTE radiative transfer problem for polarized radiation, in one-dimensional models of the solar atmosphere, accounting for the combined action of the Hanle and Zeeman effects, as well as for PRD phenomena. After briefly discussing the relevant equations, we describe the iterative method of solution of the problem and the numerical tools that we have developed and implemented. We finally present some illustrative applications to two resonance lines that form at different heights in the solar atmosphere, and provide a detailed physical interpretation of the calculated Stokes profiles. We find that magneto-optical effects have a strong impact on the linear polarization signals that PRD effects produce in the wings of strong resonance lines. We also show that the weak-field approximation has to be used with caution when PRD effects are considered.

79 ASTRONOMY AND ASTROPHYSICS↗

On the role of topological complexity in spontaneous development of current sheets

The computations presented in this work aim to asses the importance of field line interlacing on spontaneous development of current sheets. From Parker's magnetostatic theorem, such development of current sheets is inevitable in a topologically complex magnetofluid, with infinite electrical conductivity, at equilibrium. Relevant initial value problems are constructed by superposition of two untwisted component fields, each component field being represented by a pair of global magnetic flux surface. The intensity of field line interlacing is then specified by the relative amplitude of the two superposed fields. The computations are performed by varying this relative amplitude. Also to have a direct visualization of current sheet formation, we follow the evolution of flux surfaces instead of the vector magnetic field. An important finding of this paper is in the demonstration that initial field lines having intense interlacing tend to develop current sheets which are distributed throughout the computational domain with no preference for topologically favorable sites like magnetic nulls or field reversal layers. The onsets of these current sheets are attributed to favorable contortions of magnetic flux surfaces where two oppositely directed parts of the same field line or different field lines come to close proximity. However, for less intensely interlaced field lines, the simulations indicate development of current sheets at sites only where the magnetic topology is favorable. These current sheets originate as two sets of anti-parallel complimentary field lines press onto each other.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients

This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-ρAMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the coarse basis used to define the new two-level method of our interest. We illustrate the performance of this adaptive two-level procedure with a large set of numerical experiments that demonstrate its efficiency over building the solvers from scratch.

97 MATHEMATICS AND COMPUTING↗

TIME-DEPENDENT PHOTOIONIZATION OF GASEOUS NEBULAE: THE PURE HYDROGEN CASE

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full time-dependent energy balance, ionization balance, and radiation transfer equations in a self-consistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionization/thermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and nonlinearly from the illuminated face of the cloud to the ionization front (IF). IF/thermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud. Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solution. Moreover, even the time average of ionization and temperature is different from any steady-state case. This time average is characterized by overionization and a broader IF with respect to the steady-state solution for a mean value of the radiation flux. Around the time average of physical conditions there is a large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations. Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of nonlinear propagation times for thermal fronts/IFs and equilibration times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

TIME-DEPENDENT MULTI-GROUP MULTI-DIMENSIONAL RELATIVISTIC RADIATIVE TRANSFER CODE BASED ON SPHERICAL HARMONIC DISCRETE ORDINATE METHOD

We develop a time-dependent, multi-group, multi-dimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids that are involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) which evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed-frame approach; the source function is evaluated in the comoving frame, whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated using various test problems and comparisons with the results from a relativistic Monte Carlo code. These validations confirm that the code correctly calculates the intensity and its evolution in the computational domain. The code enables us to obtain an Eddington tensor that relates the first and third moments of intensity (energy density and radiation pressure) and is frequently used as a closure relation in radiation hydrodynamics calculations.

79 ASTRONOMY AND ASTROPHYSICS↗

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

Ambur, Damodar R.↗

Time-Dependent Photoionization of Gaseous Nebulae: The Pure Hydrogen Case

We study the problem of time-dependent photoionization of low density gaseous nebulae subjected to sudden changes in the intensity of ionizing radiation. To this end, we write a computer code that solves the full timedependent energy balance, ionization balance, and radiation transfer equations in a self-consistent fashion for a simplified pure hydrogen case. It is shown that changes in the ionizing radiation yield ionizationthermal fronts that propagate through the cloud, but the propagation times and response times to such fronts vary widely and nonlinearly from the illuminated face of the cloud to the ionization front (IF). IFthermal fronts are often supersonic, and in slabs initially in pressure equilibrium such fronts yield large pressure imbalances that are likely to produce important dynamical effects in the cloud. Further, we studied the case of periodic variations in the ionizing flux. It is found that the physical conditions of the plasma have complex behaviors that differ from any steady-state solution. Moreover, even the time average of ionization and temperature is different from any steady-state case. This time average is characterized by overionization and a broader IF with respect to the steady-state solution for a mean value of the radiation flux. Around the time average of physical conditions there is a large dispersion in instantaneous conditions, particularly across the IF, which increases with the period of radiation flux variations. Moreover, the variations in physical conditions are asynchronous along the slab due to the combination of nonlinear propagation times for thermal frontsIFs and equilibration times.

Seyfert↗

Exploring the Performance of Spark for a Scientific Use Case

We present an evaluation of the performance of a Spark implementation of a classification algorithm in the domain of High Energy Physics (HEP). Spark is a general engine for in-memory, large-scale data processing, and is designed for applications where similar repeated analysis is performed on the same large data sets. Classification problems are one of the most common and critical data processing tasks across many domains. Many of these data processing tasks are both computation- and data-intensive, involving complex numerical computations employing extremely large data sets. We evaluated the performance of the Spark implementation on Cori, a NERSC resource, and compared the results to an untuned MPI implementation of the same algorithm. While the Spark implementation scaled well, it is not competitive in speed to our MPI implementation, even when using significantly greater computational resources.

Sehrish, Saba↗

Reactor Pressure Vessel Fracture Analysis Capabilities in Grizzly

Efforts have been underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). Development in prior years has resulted a capability to calculate -integrals. For this application, these are used to calculate stress intensity factors for cracks to be used in deterministic linear elastic fracture mechanics (LEFM) assessments of fracture in degraded RPVs. The -integral can only be used to evaluate stress intensity factors for axis-aligned flaws because it can only be used to obtain the stress intensity factor for pure Mode I loading. Off-axis flaws will be subjected to mixed-mode loading. For this reason, work has continued to expand the set of fracture mechanics capabilities to permit it to evaluate off-axis flaws. This report documents the following work to enhance Grizzly’s engineering fracture mechanics capabilities for RPVs: • Interaction Integral and -stress: To obtain mixed-mode stress intensity factors, a capability to evaluate interaction integrals for 2D or 3D flaws has been developed. A -stress evaluation capability has been developed to evaluate the constraint at crack tips in 2D or 3D. Initial verification testing of these capabilities is documented here. • Benchmarking for axis-aligned flaws: Grizzly’s capabilities to evaluate stress intensity factors for axis-aligned flaws have been benchmarked against calculations for the same conditions in FAVOR. • Off-axis flaw demonstration: The newly-developed interaction integral capabilities are demon- strated in an application to calculate the mixed-mode stress intensity factors for off-axis flaws. • Other code enhancements: Other enhancements to the thermomechanics capabilities that relate to the solution of the engineering RPV fracture problem are documented here.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Adaptive Sequential Monte Carlo for Multiple Changepoint Analysis

Process monitoring and control requires detection of structural changes in a data stream in real time. This paper introduces an efficient sequential Monte Carlo algorithm designed for learning unknown changepoints in continuous time. The method is intuitively simple: new changepoints for the latest window of data are proposed by conditioning only on data observed since the most recent estimated changepoint, as these observations carry most of the information about the current state of the process. The proposed method shows improved performance over the current state of the art. Another advantage of the proposed algorithm is that it can be made adaptive, varying the number of particles according to the apparent local complexity of the target changepoint probability distribution. This saves valuable computing time when changes in the changepoint distribution are negligible, and enables re-balancing of the importance weights of existing particles when a significant change in the target distribution is encountered. The plain and adaptive versions of the method are illustrated using the canonical continuous time changepoint problem of inferring the intensity of an inhomogeneous Poisson process, although the method is generally applicable to any changepoint problem. Performance is demonstrated using both conjugate and non-conjugate Bayesian models for the intensity. Lastly, appendices to the article are available online, illustrating the method on other models and applications.

97 MATHEMATICS AND COMPUTING↗

Breaking Down the Computational Barriers to Real-Time Urban Flood Forecasting

Flooding impacts are on the rise globally, and concentrated in urban areas. Currently, there are no operational systems to forecast flooding at spatial resolutions that can facilitate emergency preparedness and response actions mitigating flood impacts. We present a framework for real-time flood modeling and uncertainty quantification that combines the physics of fluid motion with advances in probabilistic methods. The framework overcomes the prohibitive computational demands of high-fidelity modeling in real-time by using a probabilistic learning method relying on surrogate models that are trained prior to a flood event. This shifts the overwhelming burden of computation to the trivial problem of data storage, and enables forecasting of both flood hazard and its uncertainty at scales that are vital for time-critical decision-making before and during extreme events. The framework has the potential to improve flood prediction and analysis and can be extended to other hazard assessments requiring intense high-fidelity computations in real-time.

54 ENVIRONMENTAL SCIENCES↗

Can shock waves on helicopter rotors generate noise? - A study of the quadrupole source

An analysis has previously established that local shock surfaces attached to helicopter rotor blades moving at high subsonic speeds are potent noise generators; in pursuit of this insight, a novel formulation is presented for the prediction of the noise of a deformable shock, whose area changes as a function of the azimuthal position of the blade. The derivation of this formulation has its basis in a mapping of the moving shock to a time-independent region. In virtue of this mapping, the implementation of the main result on a computer becomes straightforward enough for incorporation into the available rotor-noise prediction code. A problem illustrating the importance of rotor shocks in the generation of high-intensity noise is presented.

Farassat, F.↗