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At least 1,441 records · Page 80
All sourcesNASA NTRSDOE OSTI
DOE OSTI2011

Interlocked optimization and fast gradient algorithm for a seismic inverse problem

Highlights: {yields} A 2D extension of the 1D nonlinear inversion of well-seismic data is given. {yields} Appropriate regularization yields a well-determined large scale inverse problem. {yields} An interlocked optimization loop acts as an efficient preconditioner. {yields} The adjoint state method is used to compute the misfit function gradient. {yields} Domain decomposition method yields an efficient parallel implementation. - Abstract: We give a nonlinear inverse method for seismic data recorded in a well from sources at several offsets from the borehole in a 2D acoustic framework. Given the velocity field, approximate values of the impedance are recovered. This is a 2D extension of the 1D inversion of vertical seismic profiles . The inverse problem generates a large scale undetermined ill-conditioned problem. Appropriate regularization terms render the problem well-determined. An interlocked optimization algorithm yields an efficient preconditioning. A gradient algorithm based on the adjoint state method and domain decomposition gives a fast parallel numerical method. For a realistic test case, convergence is attained in an acceptable time with 128 processors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Massively parallel solvers for elliptic partial differential equations in numerical weather and climate prediction

The demand for substantial increases in the spatial resolution of global weather and climate prediction models makes it essential to use numerically efficient and highly scalable algorithms to solve the equations of large-scale atmospheric fluid dynamics. For stability and efficiency reasons, several of the operational forecasting centres, in particular the Met Office and the European Centre for Medium-Range Weather Forecasts (ECMWF) in the UK, use semi-implicit semi-Lagrangian time-stepping in the dynamical core of the model. The additional burden with this method is that a three-dimensional elliptic partial differential equation (PDE) for the pressure correction has to be solved at every model time step and this often constitutes a significant proportion of the time spent in the dynamical core. In global models, this PDE must be solved in a thin spherical shell. To run within tight operational time-scales, the solver has to be parallelized and there seems to be a (perceived) misconception that elliptic solvers do not scale to large processor counts and hence implicit time-stepping cannot be used in very high-resolution global models. After reviewing several methods for solving the elliptic PDE for the pressure correction and their application in atmospheric models, we demonstrate the performance and very good scalability of Krylov subspace solvers and multigrid algorithms for a representative model equation with more than 1010 unknowns on 65 536 cores on the High-End Computing Terascale Resource (HECToR), the UK's national supercomputer. Here, we tested and optimized solvers from two existing numerical libraries (the Distributed and Unified Numerics Environment (DUNE) and Parallel High Performance Preconditioners (hypre)) and implemented both a conjugate gradient solver and a geometric multigrid algorithm based on a tensor-product approach, which exploits the strong vertical anisotropy of the discretized equation. We study both weak and strong scalability and compare the absolute solution times for all methods; in contrast to one-level methods, the multigrid solver is robust with respect to parameter variations.

58 GEOSCIENCES↗
DOE OSTI2023

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

Here, we demonstrate use of a modern Fortran solver interface to manage solver algorithms for an implicit barotropic mode solver in the Model for Predictions Across Scales-Ocean (MPAS-O). ForTrilinos, a Fortran interface to Trilinos that contains a large collection of solver capabilities written in C++, has been implemented in MPAS-O to provide access to a suite of linear solver options. By virtue of the simplified wrapper and interface generator (SWIG) automation tool that generates modern Fortran interfaces to C++ code, we were able to implement the Fortran solver interface in MPAS-O using a familiar Fortran coding style while minimizing performance degradation. The ForTrilinos solver interface is written within MPAS-O’s time stepping modules as a subroutine in conjunction with MPAS-O code. Applied to an idealized ocean and a high-resolution realistic ocean test case, parallel performance of ForTrilinos solvers is examined. It is found that parallel scalability of the ForTrilinos solvers is highly dependent on the number of global synchronization points per solver iteration in each iterative solver algorithm. ForTrilinos solvers perform best compared to the Fortran hand-crafted (FHC) solver when the amount of work per processor is large enough. However, parallel scalability is better with the FHC solver and so when the work per core is modest FHC outperforms ForTrilinos. The intercomparison between the ForTrilinos and FHC solvers reveals that this performance hit in the ForTrilinos solver mostly comes from the global synchronization process, while suggesting that the matrix-vector multiplication process in the FHC solver needs to be optimized for better performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Petascale turbulence simulation using a highly parallel fast multipole method on GPUs

This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method to solve the Navier–Stokes equations, with a highly parallel fast multipole method (fmm) as numerical engine, and match the current record in mesh size for this application, a cube of computational points solved with a spectral method. The standard numerical approach used in this field is the pseudo-spectral method, relying on the fft algorithm as the numerical engine. The particle-based simulations presented in this paper quantitatively match the kinetic energy spectrum obtained with a pseudo-spectral method, using a trusted code. In terms of parallel performance, weak scaling results show the fmm-based vortex method achieving 74% parallel efficiency on 4096 processes (one gpu per mpi process, 3 gpus per node of the tsubame-2.0 system). The fft-based spectral method is able to achieve just 14% parallel efficiency on the same number of mpi processes (using only cpu cores), due to the all-to-all communication pattern of the fft algorithm. The calculation time for one time step was 108 s for the vortex method and 154 s for the spectral method, under these conditions. Computing with 69 billion particles, this work exceeds by an order of magnitude the largest vortex-method calculations to date.

Computer Science↗
DOE OSTI2017

Numerical approach of the quantum circuit theory

In this paper we develop a numerical method based on the quantum circuit theory to approach the coherent electronic transport in a network of quantum dots connected with arbitrary topology. The algorithm was employed in a circuit formed by quantum dots connected each other in a shape of a linear chain (associations in series), and of a ring (associations in series, and in parallel). For both systems we compute two current observables: conductance and shot noise power. We find an excellent agreement between our numerical results and the ones found in the literature. Moreover, we analyze the algorithm efficiency for a chain of quantum dots, where the mean processing time exhibits a linear dependence with the number of quantum dots in the array.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2010

A Coupling Methodology for Mesoscale-informed Nuclear Fuel Performance Codes

This study proposes an approach for capturing the effect of microstructural evolution on reactor fuel performance by coupling a mesoscale irradiated microstructure model with a finite element fuel performance code. To achieve this, the macroscale system is solved in a parallel, fully coupled, fully-implicit manner using the preconditioned Jacobian-free Newton Krylov (JFNK) method. Within the JFNK solution algorithm, microstructure-influenced material parameters are calculated by the mesoscale model and passed back to the macroscale calculation. Due to the stochastic nature of the mesoscale model, a dynamic fitting technique is implemented to smooth roughness in the calculated material parameters. The proposed methodology is demonstrated on a simple model of a reactor fuel pellet. In the model, INL’s BISON fuel performance code calculates the steady-state temperature profile in a fuel pellet and the microstructure-influenced thermal conductivity is determined with a phase field model of irradiated microstructures. This simple multiscale model demonstrates good nonlinear convergence and near ideal parallel scalability. By capturing the formation of large mesoscale voids in the pellet interior, the multiscale model predicted the irradiation-induced reduction in the thermal conductivity commonly observed in reactors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

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

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A block-tridiagonal solver with two-level parallelization for finite element-spectral codes

Two-level parallelization is introduced to solve a massive block-tridiagonal matrix system. One-level is used for distributing blocks whose size is as large as the number of block rows due to the spectral basis, and the other level is used for parallelizing in the block row dimension. The reason for the added parallelization dimension is to retard the saturation of the scaling due to communication overhead and inefficiencies in the single-level parallelization only distributing blocks. As a technique for parallelizing the tridiagonal matrix, the combined method of “Partitioned Thomas method” and “Cyclic Odd–Even Reduction” is implemented in an MPI-Fortran90 based finite element-spectral code (TORIC) that calculates the propagation of electromagnetic waves in a tokamak. The two-level parallel solver using thousands of processors shows more than 5 times improved computation speed with the optimized processor grid compared to the single-level parallel solver under the same conditions. Three-dimensional RF field reconstructions in a tokamak are reflected as examples of the physics simulations that have been enabled by this algorithmic advance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Nonlinear Fourier analysis for discontinuous conductivities: Computational results

Two reconstruction methods of Electrical Impedance Tomography (EIT) are numerically compared for nonsmooth conductivities in the plane based on the use of complex geometrical optics (CGO) solutions to D-bar equations involving the global uniqueness proofs for Calderón problem exposed in Nachman (1996) [43] and Astala and Päivärinta (2006) [6]: the Astala–Päivärinta theory-based low-pass transport matrix method implemented in Astala et al. (2011) [3] and the shortcut method which considers ingredients of both theories. The latter method is formally similar to the Nachman theory-based regularized EIT reconstruction algorithm studied in Knudsen et al. (2009) [34] and several references from there. New numerical results are presented using parallel computation with size parameters larger than ever, leading mainly to two conclusions as follows. First, both methods can approximate piecewise constant conductivities better and better as the cutoff frequency increases, and there seems to be a Gibbs-like phenomenon producing ringing artifacts. Second, the transport matrix method loses accuracy away from a (freely chosen) pivot point located outside of the object to be studied, whereas the shortcut method produces reconstructions with more uniform quality.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Scalable Nonlinear Compact Schemes

In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Embedding spatial decomposition in parareal in time power system simulation

We propose an approach for combining two decompositions in power system simulation, temporal and spatial, with a goal to achieve faster simulation time than utilizing either one of them alone. The proposed approach builds upon the structure of the Parareal algorithm for temporal decomposition and explores an efficient way of embedding the spatial decomposition into its coarse and fine solutions. This introduces two types of simultaneous parallelism in power system simulations - parallelism between system areas and between coarse integration intervals for time integration. The results from the application of the proposed approach are shown on a two-area system comprised of the IEEE 16-machine, 68-bus, and the IEEE 50-machine, 145-bus system.

Duan, Nan↗
DOE OSTI2016

Optical CT imaging of solid radiochromic dosimeters in mismatched refractive index solutions using a scanning laser and large area detector

Purpose: The practical use of the PRESAGE® solid plastic dosimeter is limited by the inconvenience of immersing it in high-viscosity oils to achieve refractive index matching for optical computed tomography (CT) scanning. The oils are slow to mix and difficult to clean from surfaces, and the dosimeter rotation can generate dynamic Schlieren inhomogeneity patterns in the reference liquid, limiting the rotational and overall scan speed. Therefore, it would be beneficial if lower-viscosity, water-based solutions with slightly unmatched refractive index could be used instead. The purpose of this work is to demonstrate the feasibility of allowing mismatched conditions when using a scanning laser system with a large acceptance angle detector. A fiducial-based ray path measurement technique is combined with an iterative CT reconstruction algorithm to reconstruct images. Methods: A water based surrounding liquid with a low viscosity was selected for imaging PRESAGE® solid dosimeters. Liquid selection was optimized to achieve as high a refractive index as possible while avoiding rotation-induced Schlieren effects. This led to a refractive index mismatch of 6% between liquid and dosimeters. Optical CT scans were performed with a fan-beam scanning-laser optical CT system with a large area detector to capture most of the refracted rays. A fiducial marker placed on the wall of a cylindrical sample occludes a given light ray twice. With knowledge of the rotation angle and the radius of the cylindrical object, the actual internal path of each ray through the dosimeter can be calculated. Scans were performed with 1024 projections of 512 data samples each, and rays were rebinned to form 512 parallel-beam projections. Reconstructions were performed on a 512 × 512 grid using 100 iterations of the SIRT iterative CT algorithm. Proof of concept was demonstrated with a uniformly attenuating solution phantom. PRESAGE® dosimeters (11 cm diameter) were irradiated with Cobalt-60 irradiator to achieve either a uniform dose or a 2-level “step-dose” pattern. Results: With 6% refractive index mismatching, a circular field of view of 85% of the diameter of a cylindrical sample can be reconstructed accurately. Reconstructed images of the test solution phantom were uniform (within 3%) inside this radius. However, the dose responses of the PRESAGE® samples were not spatially uniform, with variations of at least 5% in sensitivity. The variation appears as a “cupping” artifact with less sensitivity in the middle than at the periphery of the PRESAGE® cylinder. Polarization effects were also detected for these samples. Conclusions: The fiducial-based ray path measurement scheme, coupled with an iterative reconstruction algorithm, enabled optical CT scanning of PRESAGE® dosimeters immersed in mismatched refractive index solutions. However, improvements to PRESAGE® dose response uniformity are required.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2011

Performance study of GPUs in real-time trigger applications for HEP experiments

Graphical Processing Units (GPUs) have evolved into highly parallel, multi-threaded, multicore powerful processors with high memory bandwidth. GPUs are used in a variety of intensive computing applications. The combination of highly parallel architecture and high memory bandwidth makes GPUs a potentially promising technology for effective real-time processing for High Energy Physics (HEP) experiments. However, not much is known of their performance in real-time applications that require low latency, such as the trigger for HEP experiments. We describe an R and D project with the goal to study the performance of GPU technology for possible low latency applications, performing basic operations as well as some more advanced HEP lower-level trigger algorithms (such as fast tracking or jet finding). We present some preliminary results on timing measurements, comparing the performance of a CPU versus a GPU with NVIDIA's CUDA general-purpose parallel computing architecture, carried out at CDF's Level-2 trigger test stand. These studies will provide performance benchmarks for future studies to investigate the potential and limitations of GPUs for real-time applications in HEP experiments.

43 PARTICLE ACCELERATORS↗
DOE OSTI2014

Petascale Hierarchical Modeling VIA Parallel Execution

The research allows more effective model building. By allowing researchers to fit complex models to large datasets in a scalable manner, our algorithms and software enable more effective scientific research. In the new area of “big data,” it is often necessary to fit “big models” to adjust for systematic differences between sample and population. For this task, scalable and efficient model-fitting tools are needed, and these have been achieved with our new Hamiltonian Monte Carlo algorithm, the no-U-turn sampler, and our new C++ program, Stan. In layman’s terms, our research enables researchers to create improved mathematical modes for large and complex systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A communication-avoiding 3D sparse triangular solver

We present a novel distributed memory algorithm to improve the strong scalability of the solution of a sparse triangular system. This operation appears in the solve phase of direct methods for solving general sparse linear systems, Ax = b. Our 3D sparse triangular solver employs several techniques, including a 3D MPI process grid, elimination tree parallelism, and data replication, all of which reduce the per-process communication when combined. We present analytical models to understand the communication cost of our algorithm and show that our 3D sparse triangular solver can reduce the per-process communication volume asymptotically by a factor of O(n1/4) and O(n1/6) for problems arising from the finite element discretizations of 2D "planar" and 3D "non-planar" PDEs, respectively. We implement our algorithm for use in SuperLU_DIST3D, using a hybrid MPI+OpenMP programming model. Our 3D triangular solve algorithm, when run on 12k cores of Cray XC30, outperforms the current state-of-the-art 2D algorithm by 7.2x for planar and 2.7x for the non-planar sparse matrices, respectively.

Sao, Piyush↗
DOE OSTI2013

Many-core applications to online track reconstruction in HEP experiments

Interest in parallel architectures applied to real time selections is growing in High Energy Physics (HEP) experiments. In this paper we describe performance measurements of Graphic Processing Units (GPUs) and Intel Many Integrated Core architecture (MIC) when applied to a typical HEP online task: the selection of events based on the trajectories of charged particles. We use as benchmark a scaled-up version of the algorithm used at CDF experiment at Tevatron for online track reconstruction – the SVT algorithm – as a realistic test-case for low-latency trigger systems using new computing architectures for LHC experiment. We examine the complexity/performance trade-off in porting existing serial algorithms to many-core devices. Measurements of both data processing and data transfer latency are shown, considering different I/O strategies to/from the parallel devices.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Numerically stable, scalable formulas for parallel and online computation of higher-order multivariate central moments with arbitrary weights

Formulas for incremental or parallel computation of second order central moments have long been known, and recent extensions of these formulas to univariate and multivariate moments of arbitrary order have been developed. Such formulas are of key importance in scenarios where incremental results are required and in parallel and distributed systems where communication costs are high. We survey these recent results, and improve them with arbitrary-order, numerically stable one-pass formulas which we further extend with weighted and compound variants. We also develop a generalized correction factor for standard two-pass algorithms that enables the maintenance of accuracy over nearly the full representable range of the input, avoiding the need for extended-precision arithmetic. We then empirically examine algorithm correctness for pairwise update formulas up to order four as well as condition number and relative error bounds for eight different central moment formulas, each up to degree six, to address the trade-offs between numerical accuracy and speed of the various algorithms. Finally, we demonstrate the use of the most elaborate among the above mentioned formulas, with the utilization of the compound moments for a practical large-scale scientific application.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Stochastic density functional theory

Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn–Sham density matrix (DM). This causes a problem since many types of large systems of interest have a rather broad DM range and are therefore not amenable to analysis using DFT methods. For this reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM evaluations, is emerging as an attractive alternative linear-scaling approach. This review develops a general formulation of sDFT in terms of a (non)orthogonal basis representation and offers an analysis of the statistical errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set implementation of sDFT, applied to water clusters and silicon nanocrystals, it demonstrates and explains how the standard deviation and the bias depend on the sampling rate and the system size in various types of calculations. We also develop a basis-set embedded-fragments theory, demonstrating its utility for reducing the SEs for energy, density of states and nuclear force calculations. Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU wall-time linear-scaling. Lastly, the method parallelizes well over distributed processors with good scalability and therefore may find use in the upcoming exascale computing architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗