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At least 1,675 records · Page 93

Systematic generation of multibody equations of motion suitable for recursive and parallel manipulation

The formulation of a method known as the joint coordinate method for automatic generation of the equations of motion for multibody systems is summarized. For systems containing open or closed kinematic loops, the equations of motion can be reduced systematically to a minimum number of second order differential equations. The application of recursive and nonrecursive algorithms to this formulation, computational considerations and the feasibility of implementing this formulation on multiprocessor computers are discussed.

Nikravesh, Parviz E.↗

A single-assignment language in a distributed memory multiprocessor

The implementation of the single-assignment programming language SISAL (McGraw et al., 1985) on a Symult 2010 parallel computer is described. The advantages of single-assignment languages over imperative languages in a multiprocessor environment are reviewed; the characteristics of SISAL are summarized; the program-graph generation and dynamic data partitioning procedures are explained; and the application of SISAL in constructing a concurrent iterative multigrid algorithm is discussed in detail and illustrated with diagrams.

Evripidou, P.↗

spammpack, Version 2013-06-18

This library is an implementation of the Sparse Approximate Matrix Multiplication (SpAMM) algorithm introduced. It provides a matrix data type, and an approximate matrix product, which exhibits linear scaling computational complexity for matrices with decay. The product error and the performance of the multiply can be tuned by choosing an appropriate tolerance. The library can be compiled for serial execution or parallel execution on shared memory systems with an OpenMP capable compiler

Source record↗

Preliminary performance evaluation of P++ single event proton scattering algorithms on GPUS - 25688

A need has been realized for fast, accurate charged particle transport in a wide variety of domains. Utilizing hardware acceleration through GPUs now common in user desktops, speedups in simulation comparable to those found with HPC systems can be realized for a fraction of the price. Preliminary results on the P++ proton transport code developed by the Rensselaer Radiation Measurement and Dosimetry Group (RRMDG) are presented. The code has been validated for the 1 GeV to 1 MeV energy regime and is targeted to benefit application areas such as proton radiography, space radiation research, and clinical accelerator therapy. The code is notable for employing a single event, 'on the fly' cross section based transport algorithm rather than the traditional condensed history or step based method seen in many production Monte Carlo codes. Performance improvements for the P++ code have been introduced through MPI parallelization as well as a CUDA version of the transport algorithm capable of running on NVidia GPUs. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Application of the TITAN Hybrid Deterministic Transport Code to Medical Physics - Paper 118

The TITAN code is a 3-dimensional parallel deterministic transport code that solves the linear Boltzmann equation. The TITAN code has hybrid algorithms that are ideal for medical physics applications: i) SN and characteristics method and ii) SN with a fictitious quadrature set and ray-tracing. These hybrid algorithms have been used in the simulation of computed tomography (CT) and single photon emission computed tomography (SPECT) In this paper, the hybrid algorithms developed for medical physics applications in the TITAN code are discussed. First, the TITAN code's block-oriented approach for utilizing SN and characteristic solvers for CT is presented and results for a simple test case are given. Second, the paper describes a hybrid formulation for SPECT with an SN solver in the phantom, a fictitious quadrature set for directions from the phantom surface passing through the collimator, and a simplified ray-tracing algorithm for particle transport to the detector. Finally, ongoing work is described and concluding remarks are given. The TITAN code's hybrid algorithms allow it to efficiently solve problems with low-scatter regions, which are frequently found in medical physics applications. The TITAN code has been used to solve a simplified CT problem and generate projection images for SPECT simulations. The WCOS technique was developed to improve the TITAN code's collimator representation. For these applications, the TITAN code was shown to require significantly less computation time than MCNP5. Work is currently underway to implement an iterative image reconstruction algorithm in the TITAN code. A script that calls the TITAN code to complete the forward projection step in SPECT has already been used to reconstruction a 2-dimensional phantom. The ability of TITAN to fully model particle transport in the patient in short computation times is expected to be a great advantage to iterative reconstruction. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

Reduced Free Energy Perturbation/Hamiltonian Replica Exchange Molecular Dynamics Method with Unbiased Alchemical Thermodynamic Axis

We report that replica-exchange molecular dynamics (REMD) has been proven to efficiently improve the convergence of free energy perturbation (FEP) calculations involving considerable reorganization of their surrounding. We previously introduced the FEP/(λ,H)-REMD algorithm for ligand binding, in which replicas along the alchemical thermodynamic coupling axis λ were expanded as a series of Hamiltonian boosted replicas along a second axis to form a two-dimensional (2D) replica-exchange exchange map [Jiang, W.; Roux, B., J. Chem. Theory Comput. 2010, 6 (9), 2559-2565]. Aiming to achieve a similar performance at a lower computational cost, we propose here a modified version of this algorithm in which only the end-states along the alchemical axis are augmented by boosted replicas. The reduced FEP/(λ,H)-REMD method with one-dimensional (1D) unbiased alchemical thermodynamic coupling axis λ is implemented on the basis of generic multiple copy algorithm (MCA) module of the biomolecular simulation program NAMD. The flexible MCA framework of NAMD enables a user to design customized replica-exchange patterns through Tcl scripting in the context of a highly parallelized simulation program without touching the source code. Two Hamiltonian tempering boosting scheme were examined with the new algorithm: a first one based on potential energy rescaling of a pre-identified “solute”, and a second one via the introduction of flattening torsional free energy barriers. As two illustrative examples with reliable experiment data, the absolute binding free energies of pxylene and n-butylbenzene to the nonpolar cavity of the L99A mutant of T4 lysozyme were calculated. Lastly, the tests demonstrate that the new protocol efficiently enhances the sampling of torsional motions for backbone and side chains around the binding pocket and accelerates the convergence of the free energy computations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Livermore tomography tools: Accurate, fast, and flexible software for tomographic science

Livermore Tomography Tools (LTT) is a customizable scientific software package that enables a broad range of research and development efforts into computed tomography (CT). Here, it was developed to process x-ray and neutron CT data accurately and rapidly from raw detector counts to reconstructed volumes with the flexibility to handle many special cases. LTT fulfills long-term CT software goals to provide quantitatively accurate results reported in physical units (e.g., mm -1 or cm -1 ) while exploiting all available computational advantages to maximize speed. Written in C/C++ with support for multiple CPUs and GPUs, LTT runs on many computing platforms (Linux/Unix, Windows, and Mac; laptops to supercomputers). As a result, LTT can:process data acquired from various custom-built and commercially available CT scanners, model and simulate x-ray and neutron interactions to encourage algorithm prototyping, and allow for rapid insertion of the latest algorithms.We describe LTT’s software architecture, user interfaces, and its 88 algorithms (as of this writing) for pre-processing, reconstruction, post-processing, and simulation that support many scanner geometries (parallel-, fan-, cone-beam, and custom). Several applications are presented that illustrate LTT’s accuracy, speed, and flexibility relative to other solutions.

36 MATERIALS SCIENCE↗

Multigrid Reduction in Time for Chaotic Dynamical Systems

As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes can be a significant bottleneck, as many types of simulations require large numbers of time-steps which must be computed sequentially. Parallel-in-time schemes, such as the Multigrid Reduction in Time (MGRIT) method, remedy this by parallelizing across time-steps and have shown promising results for parabolic problems. However, chaotic problems have proved more difficult, since chaotic initial value problems (IVPs) are inherently ill-conditioned. MGRIT relies on a hierarchy of successively coarser time-grids to iteratively correct the solution on the finest time-grid, but due to the nature of chaotic systems, small inaccuracies on the coarser levels can be greatly magnified and lead to poor coarse-grid corrections. Here we introduce a modified MGRIT algorithm based on an existing quadratically converging nonlinear extension to the multigrid Full Approximation Scheme (FAS), as well as a novel time-coarsening scheme. Together, these approaches better capture long-term chaotic behavior on coarse-grids and greatly improve convergence of MGRIT for chaotic IVPs. Further, we introduce a novel low-memory variant of the algorithm for solving chaotic PDEs with MGRIT which not only solves the IVP, but also provides estimates for the unstable Lyapunov vectors of the system. Finally, we provide supporting numerical results for the Lorenz system and demonstrate parallel speedup for the chaotic Kuramoto–Sivashinsky PDE over a significantly longer time-domain than in previous works.

97 MATHEMATICS AND COMPUTING↗

End-to-end GPU acceleration of low-order-refined preconditioning for high-order finite element discretizations

In this article, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of effective preconditioners for high-order problems with optimal memory usage and computational complexity. The preconditioners are based on the construction of a spectrally equivalent low-order discretization on a refined mesh, which is then amenable to, for example, algebraic multigrid preconditioning. The constants of equivalence are independent of mesh size and polynomial degree. For vector finite element problems in H(curl) and H(div) (e.g., for electromagnetic or radiation diffusion problems), a specially constructed interpolation–histopolation basis is used to ensure fast convergence. Detailed performance studies are carried out to analyze the efficiency of the GPU algorithms. The kernel throughput of each of the main algorithmic components is measured, and the strong and weak parallel scalability of the methods is demonstrated. The different relative weighting and significance of the algorithmic components on GPUs and CPUs is discussed. Results on problems involving adaptively refined nonconforming meshes are shown, and the use of the preconditioners on a large-scale magnetic diffusion problem using all spaces of the finite element de Rham complex is illustrated.

97 MATHEMATICS AND COMPUTING↗

Accelerated panel methods using the fast multipole method

Panel methods are commonly used in computational fluid dynamics for the solution of potential flow problems. The methods are a numerical technique based on the surface distribution of singularity elements. The solution is the process of finding the strength of the singularity elements distributed over the body's surface. This process involves the solution of the matrix problem Pq = p' for a set of unknowns q. The Fast Multipole Method is used to directly compute q without using matrix solvers. The algorithm works in O(N) time for N points, a great improvement over standard matrix solvers. In panel methods, the surface of a body is divided into a series of quadrilateral panels. The methods involve the computation of the influence of all other panels on each individual panel. The influence is based on the surface distribution, though this can be approximated by the area for distant panels. An alternative approximation, though with arbitrary accuracy, is to develop a multipole expansion about the center of the panel to describe the effect of a given panel on distant points in space. The expansion is based on the moments of the panel, thus allow the use of various surface distributions without changing the basic algorithm, just the computation of the various moments. The expansions are then manipulated in a tree walk to develop Taylor series expansions about a point in space which describe the effect of all distant panels on any point within a volume of convergence. The effect of near panels then needs to be computed directly, but the effect of all distant panels can be computed by simply evaluating the resulting expansion. The Fast Multipole Method has been applied to panel methods for the solution of source and doublet distributions. A major feature of the algorithm is that the algorithm does not change to derive the potential and velocity for sources and doublets. The same expansions can be used for both sources and doublets. Since the velocity is related to the potential, and the doublet potential is related to the z-component of the source velocity, all values can be derived from the same expansion by taking a series of partial derivatives. This requires more expansion terms to be kept since terms are lost in the process of taking partial derivatives. Thus to maintain accuracy for the doublet computation, more terms are required than if just evaluating for sources. The resulting Fast Multipole code should then parallelize better than classical panel methods due to the locality of data dependencies found in the Fast Multipole Method. Theoretically the parallelized code should execute in O(log N) time with O(N) processors, though this is not practical. Ongoing work includes implementing the parallel accelerated panel method, including methods to improve the load balancing of the problem by taking advantage of the known geometry of panels, and to encorporate sensitivity analysis into the algorithm.

Leathrum, James F., Jr.↗

Epidemic failure detection and consensus for extreme parallelism

Future extreme-scale high-performance computing systems will be required to work under frequent component failures. The MPI Forum s User Level Failure Mitigation proposal has introduced an operation, MPI Comm shrink, to synchronize the alive processes on the list of failed processes, so that applications can continue to execute even in the presence of failures by adopting algorithm-based fault tolerance techniques. This MPI Comm shrink operation requires a failure detection and consensus algorithm. This paper presents three novel failure detection and consensus algorithms using Gossiping. The proposed algorithms were implemented and tested using the Extreme-scale Simulator. The results show that in all algorithms the number of Gossip cycles to achieve global consensus scales logarithmically with system size. The second algorithm also shows better scalability in terms of memory and network bandwidth usage and a perfect synchronization in achieving global consensus. The third approach is a three-phase distributed failure detection and consensus algorithm and provides consistency guarantees even in very large and extreme-scale systems while at the same time being memory and bandwidth efficient.

97 MATHEMATICS AND COMPUTING↗

Mahakala: A Python-based Modular Ray-tracing and Radiative Transfer Algorithm for Curved Spacetimes

We introduce Mahakala, a Python-based, modular, radiative ray-tracing code for curved spacetimes. We employ Google's JAX framework for accelerated automatic differentiation, which can efficiently compute Christoffel symbols directly from the metric, allowing the user to easily and quickly simulate photon trajectories through non-Kerr spacetimes. JAX also enables Mahakala to run in parallel on both CPUs and GPUs. Mahakala natively uses the Cartesian Kerr–Schild coordinate system, which avoids numerical issues caused by the pole in spherical coordinate systems. We demonstrate Mahakala's capabilities by simulating 1.3 mm wavelength images (the wavelength of Event Horizon Telescope observations) of general relativistic magnetohydrodynamic simulations of low-accretion rate supermassive black holes. The modular nature of Mahakala allows us to quantitatively explore how different regions of the flow influence different image features. We show that most of the emission seen in 1.3 mm images originates close to the black hole and peaks near the photon orbit. We also quantify the relative contribution of the disk, forward jet, and counterjet to 1.3 mm images.

79 ASTRONOMY AND ASTROPHYSICS↗

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

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

42 ENGINEERING↗

An Artificial Retina Processor for Track Reconstruction at the LHC Crossing Rate

The goal of the INFN-RETINA R&D project is to develop and implement a computational methodology that allows to reconstruct events with a large number (> 100) of charged-particle tracks in pixel and silicon strip detectors at 40 MHz, thus matching the requirements for processing LHC events at the full bunch-crossing frequency. Our approach relies on a parallel pattern-recognition algorithm, dubbed artificial retina, inspired by the early stages of image processing by the brain. In order to demonstrate that a track-processing system based on this algorithm is feasible, we built a sizable prototype of a tracking processor tuned to 3 000 patterns, based on already existing readout boards equipped with Altera Stratix III FPGAs. The detailed geometry and charged-particle activity of a large tracking detector currently in operation are used to assess its performances. We report on the test results with such a prototype.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

TH-E-18A-01: Developments in Monte Carlo Methods for Medical Imaging

Monte Carlo simulation methods are widely used in medical physics research and are starting to be implemented in clinical applications such as radiation therapy planning systems. Monte Carlo simulations offer the capability to accurately estimate quantities of interest that are challenging to measure experimentally while taking into account the realistic anatomy of an individual patient. Traditionally, practical application of Monte Carlo simulation codes in diagnostic imaging was limited by the need for large computational resources or long execution times. However, recent advancements in high-performance computing hardware, combined with a new generation of Monte Carlo simulation algorithms and novel postprocessing methods, are allowing for the computation of relevant imaging parameters of interest such as patient organ doses and scatter-to-primaryratios in radiographic projections in just a few seconds using affordable computational resources. Programmable Graphics Processing Units (GPUs), for example, provide a convenient, affordable platform for parallelized Monte Carlo executions that yield simulation times on the order of 10{sup 7} xray/ s. Even with GPU acceleration, however, Monte Carlo simulation times can be prohibitive for routine clinical practice. To reduce simulation times further, variance reduction techniques can be used to alter the probabilistic models underlying the x-ray tracking process, resulting in lower variance in the results without biasing the estimates. Other complementary strategies for further reductions in computation time are denoising of the Monte Carlo estimates and estimating (scoring) the quantity of interest at a sparse set of sampling locations (e.g. at a small number of detector pixels in a scatter simulation) followed by interpolation. Beyond reduction of the computational resources required for performing Monte Carlo simulations in medical imaging, the use of accurate representations of patient anatomy is crucial to the virtual generation of medical images and accurate estimation of radiation dose and other imaging parameters. For this, detailed computational phantoms of the patient anatomy must be utilized and implemented within the radiation transport code. Computational phantoms presently come in one of three format types, and in one of four morphometric categories. Format types include stylized (mathematical equation-based), voxel (segmented CT/MR images), and hybrid (NURBS and polygon mesh surfaces). Morphometric categories include reference (small library of phantoms by age at 50th height/weight percentile), patient-dependent (larger library of phantoms at various combinations of height/weight percentiles), patient-sculpted (phantoms altered to match the patient's unique outer body contour), and finally, patient-specific (an exact representation of the patient with respect to both body contour and internal anatomy). The existence and availability of these phantoms represents a very important advance for the simulation of realistic medical imaging applications using Monte Carlo methods. New Monte Carlo simulation codes need to be thoroughly validated before they can be used to perform novel research. Ideally, the validation process would involve comparison of results with those of an experimental measurement, but accurate replication of experimental conditions can be very challenging. It is very common to validate new Monte Carlo simulations by replicating previously published simulation results of similar experiments. This process, however, is commonly problematic due to the lack of sufficient information in the published reports of previous work so as to be able to replicate the simulation in detail. To aid in this process, the AAPM Task Group 195 prepared a report in which six different imaging research experiments commonly performed using Monte Carlo simulations are described and their results provided. The simulation conditions of all six cases are provided in full detail, with all necessary data on material composition, source, geometry, scoring and other parameters provided. The results of these simulations when performed with the four most common publicly available Monte Carlo packages are also provided in tabular form. The Task Group 195 Report will be useful for researchers needing to validate their Monte Carlo work, and for trainees needing to learn Monte Carlo simulation methods. In this symposium we will review the recent advancements in highperformance computing hardware enabling the reduction in computational resources needed for Monte Carlo simulations in medical imaging. We will review variance reduction techniques commonly applied in Monte Carlo simulations of medical imaging systems and present implementation strategies for efficient combination of these techniques with GPU acceleration. Trade-offs involved in Monte Carlo acceleration by means of denoising and “sparse sampling” will be discussed. A method for rapid scatter correction in cone-beam CT (<5 min/scan) will be presented as an illustration of the simulation speeds achievable with optimized Monte Carlo simulations. We will also discuss the development, availability, and capability of the various combinations of computational phantoms for Monte Carlo simulation of medical imaging systems. Finally, we will review some examples of experimental validation of Monte Carlo simulations and will present the AAPM Task Group 195 Report. Learning Objectives: Describe the advances in hardware available for performing Monte Carlo simulations in high performance computing environments. Explain variance reduction, denoising and sparse sampling techniques available for reduction of computational time needed for Monte Carlo simulations of medical imaging. List and compare the computational anthropomorphic phantoms currently available for more accurate assessment of medical imaging parameters in Monte Carlo simulations. Describe experimental methods used for validation of Monte Carlo simulations in medical imaging. Describe the AAPM Task Group 195 Report and its use for validation and teaching of Monte Carlo simulations in medical imaging.

60 APPLIED LIFE SCIENCES↗

CGYRO

CGYRO is a multi-species spectral gyrokinetic solver with sonic rotation capability. It is an Eulerian GK solver specifically designed and optimized for collisional, electromagnetic, multiscale simulation. A key algorithmic aspect of CGYRO is the radially spectral formulation used to reduce the complicated integral gyroaveraging kernel into a multiplication in wavenumber space, but retaining the ability to treat profile variation important for edge plasmas. This makes it suitable for next-generation computational systems that require high levels of parallel concurrency.

Belli, EmilyA↗

Theory, computation, and application of exponential splines

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.

Mccartin, B. J.↗