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At least 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. These include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

On The Computational Capabilities of Physical Systems: Relationship With Conventional Computer Science - Part 2

In the first of this pair of papers, it was proven that there cannot be a physical computer to which one can properly pose any and all computational tasks concerning the physical universe. It was then further proven that no physical computer C can correctly carry out all computational tasks that can be posed to C. As a particular example, this result means that no physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs; one cannot build a physical computer that can be assured of correctly "processing information faster than the universe does". These results do not rely on systems that are infinite, and/or non-classical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine. This generality is a direct consequence of the fact that a novel definition of computation - "physical computation" - is needed to address the issues considered in these papers, which concern real physical computers. While this novel definition does not fit into the traditional Chomsky hierarchy, the mathematical structure and impossibility results associated with it have parallels in the mathematics of the Chomsky hierarchy. This second paper of the pair presents a preliminary exploration of some of this mathematical structure. Analogues of Chomskian results concerning universal Turing Machines and the Halting theorem are derived, as are results concerning the (im)possibility of certain kinds of error-correcting codes. In addition, an analogue of algorithmic information complexity, "prediction complexity", is elaborated. A task-independent bound is derived on how much the prediction complexity of a computational task can differ for two different reference universal physical computers used to solve that task, a bound similar to the "encoding" bound governing how much the algorithm information complexity of a Turing machine calculation can differ for two reference universal Turing machines. Finally, it is proven that either the Hamiltonian of our universe proscribes a certain type of computation, or prediction complexity is unique (unlike algorithmic information complexity), in that there is one and only version of it that can be applicable throughout our universe.

Wolpert, David H.↗
DOE OSTI2015

Exploring Replica-Exchange Wang-Landau sampling in higher-dimensional parameter space

We considered a higher-dimensional extension for the replica-exchange Wang-Landau algorithm to perform a random walk in the energy and magnetization space of the two-dimensional Ising model. This hybrid scheme combines the advantages of Wang-Landau and Replica-Exchange algorithms, and the one-dimensional version of this approach has been shown to be very efficient and to scale well, up to several thousands of computing cores. This approach allows us to split the parameter space of the system to be simulated into several pieces and still perform a random walk over the entire parameter range, ensuring the ergodicity of the simulation. Previous work, in which a similar scheme of parallel simulation was implemented without using replica exchange and with a different way to combine the result from the pieces, led to discontinuities in the final density of states over the entire range of parameters. From our simulations, it appears that the replica-exchange Wang-Landau algorithm is able to overcome this diculty, allowing exploration of higher parameter phase space by keeping track of the joint density of states.

Valentim, Alexandra↗
DOE OSTI2019

A Scalable Hybrid Scheme for Ray-Casting of Unstructured Volume Data

We present an algorithm for parallel volume rendering that is a hybrid between classical object order and image order techniques. The algorithm operates on unstructured grids (and structured ones), and thus can deal with block boundaries interleaving in complex ways. It also deals effectively with cases that are prone to load imbalance, i.e., cases where cell sizes differ dramatically, either because of the nature of the input data, or because of the effects of the camera transformation. The algorithm divides work over resources such that each phase of its processing is bounded in the amount of computation it can perform. We demonstrate its efficacy through a series of studies, varying over camera position, data set size, transfer function, image size, and processor count. At its biggest, our experiments scaled up to 8,192 processors and operated on data sets with more than one billion cells. In total, we find that our hybrid algorithm performs well in all cases. This is because our algorithm naturally adapts its computation based on workload, and can operate like either an object order technique or an image order technique in scenarios where those techniques are efficient.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Improving I/O Performance for Exascale Applications through Online Data Layout Reorganization

The applications being developed within the U.S. Exascale Computing Project (ECP) to run on imminent Exascale computers will generate scientific results with unprecedented fidelity and record turn-around time. Many of these codes are based on particle-mesh methods and use advanced algorithms, especially dynamic load-balancing and mesh-refinement, to achieve high performance on Exascale machines. Yet, as such algorithms improve parallel application efficiency, they raise new challenges for I/O logic due to their irregular and dynamic data distributions. Thus, while the enormous data rates of Exascale simulations already challenge existing file system write strategies, the need for efficient read and processing of generated data introduces additional constraints on the data layout strategies that can be used when writing data to secondary storage. We review these I/O challenges and introduce two online data layout reorganization approaches for achieving good tradeoffs between read and write performance. We demonstrate the benefits of using these two approaches for the ECP particle-in-cell simulation WarpX, which serves as a motif for a large class of important Exascale applications. Here, we show that by understanding application I/O patterns and carefully designing data layouts we can increase read performance by more than 80 percent.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Towards Generic Parallel Programming in Computer Science Education with Kokkos

Parallel patterns, views, and spaces are promising abstractions to capture the programmer's intent as well as the contextual information that can be used by an underlying runtime to efficiently map software to parallel hardware. These abstractions can be valuable in cases where an algorithm must accommodate requirements of code and performance portability across hardware architectures and vendor programming models. Kokkos is a parallel programming model for host- and accelerator architectures that relies on these abstractions and targets these requirements. It consists of a pure C++ interface, a specification, and a programming library. The programming library exposes patterns and types and maps them to an underlying abstract machine model. The abstract machine model offers a generic view of parallel hardware. While Kokkos is gaining popularity in large-scale HPC applications at some DOE laboratories, we believe that the implemented concepts are of interest to a broader audience including academia as they may contribute to a generic, vendor, and architecture-independent education of parallel programming. In this work, we give an insight into the design considerations of this programming model and list important abstractions. Further, we document best practices obtained from giving virtual classes on Kokkos and give pointers to resources that the reader may consider valuable for a lecture on generic parallel programming for students with preexisting knowledge on this matter.

Ciesko, Jan↗
DOE OSTI2013

An improved iteration loop for the three dimensional quasi-static particle-in-cell algorithm: QuickPIC

We present improvements to the three-dimensional (3D) quasi-static particle-in-cell (PIC) algorithm, which is used to efficiently model short-pulse laser and particle beam–plasma interactions. In this algorithm the fields including the index of refraction created by a static particle/laser beam are calculated. These fields are then used to advance the particle/laser beam forward in time (distance). For a 3D quasi-static code, calculating the wake fields is done using a two-dimensional (2D) PIC code where the time variable is ξ=ct-z and z is the propagation direction of the particle/laser beam. When calculating the wake, the fields, particle positions and momenta are not naturally time centered so an iterative predictor corrector loop is required. In the previous iterative loop in QuickPIC (currently the only 3D quasi-static PIC code), the field equations are derived using the Lorentz gauge. Here we describe a new algorithm which uses gauge independent field equations. It is found that with this new algorithm, the results converge to the results from fully explicitly PIC codes with far fewer iterations (typically 1 iteration as compared to 2–8) for a wide range of problems. In addition, we describe a new deposition scheme for directly depositing the time derivative of the current that is needed in one of the field equations. The new deposition scheme does not require message passing for the particles inside the iteration loop, which greatly improves the speed for parallelized calculations. Comparisons of results from the new and old algorithms and to fully explicit PIC codes are also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Optimized pulsed write schemes improve linearity and write speed for low-power organic neuromorphic devices

Neuromorphic devices are becoming increasingly appealing as efficient emulators of neural networks used to model real world problems. However, no hardware to date has demonstrated the necessary high accuracy and energy efficiency gain over CMOS in both training via backpropagation and in read via vector matrix multiplication. Such shortcomings are due to device non-idealities, particularly asymmetric conductance tuning in response to uniform voltage pulse inputs. Here, by formulating a general circuit model for capacitive ion-exchange neuromorphic devices, we show that asymmetric nonlinearity in organic electrochemical neuromorphic devices (ENODes) can be suppressed by an appropriately chosen write scheme. Simulations based upon our model suggest that a nonlinear write-selector could reduce the switching voltage and energy, enabling analog tuning via a continuous set of resistance states (100 states) with extremely low switching energy (~170 fJ • µm –2 ). Furthermore, this work clarifies the pathway to neural algorithm accelerators capable of parallelism during both read and write operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

GSoFa: Scalable Sparse Symbolic LU Factorization on GPUs

Decomposing a matrix $\mathbf {A}$ into a lower matrix $\mathbf {L}$ and an upper matrix $\mathbf {U}$, which is also known as LU decomposition, is an essential operation in numerical linear algebra. For a sparse matrix, LU decomposition often introduces more nonzero entries in the $\mathbf {L}$ and $\mathbf {U}$ factors than in the original matrix. A symbolic factorization step is needed to identify the nonzero structures of $\mathbf {L}$ and $\mathbf {U}$ matrices. Attracted by the enormous potentials of the Graphics Processing Units (GPUs), an array of efforts have surged to deploy various LU factorization steps except for the symbolic factorization, to the best of our knowledge, on GPUs. This article introduces gSoFa, the first GPU-based symbolic factorization design with the following three optimizations to enable scalable LU symbolic factorization for nonsymmetric pattern sparse matrices on GPUs. First, here we introduce a novel fine-grained parallel symbolic factorization algorithm that is well suited for the Single Instruction Multiple Thread (SIMT) architecture of GPUs. Second, we tailor supernode detection into a SIMT friendly process and strive to balance the workload, minimize the communication and saturate the GPU computing resources during supernode detection. Third, we introduce a three-pronged optimization to reduce the excessive space consumption problem faced by multi-source concurrent symbolic factorization. Taken together, gSoFa achieves up to 31× speedup from 1 to 44 Summit nodes (6 to 264 GPUs) and outperforms the state-of-the-art CPU project, on average, by 5×. Notably, gSoFa also achieves up to 47 percent of the peak memory throughput of a V100 GPU in the Summit Supercomputer.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

Flight data processing with the F-8 adaptive algorithm

An explicit adaptive control algorithm based on maximum likelihood estimation of parameters has been designed for NASA's DFBW F-8 aircraft. To avoid iterative calculations, the algorithm uses parallel channels of Kalman filters operating at fixed locations in parameter space. This algorithm has been implemented in NASA/DFRC's Remotely Augmented Vehicle (RAV) facility. Real-time sensor outputs (rate gyro, accelerometer and surface position) are telemetered to a ground computer which sends new gain values to an on-board system. Ground test data and flight records were used to establish design values of noise statistics and to verify the ground-based adaptive software. The software and its performance evaluation based on flight data are described

Hartmann, G.↗
NASA NTRS1983

Potential of minicomputer/array-processor system for nonlinear finite-element analysis

The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.

Strohkorb, G. A.↗
NASA NTRS1987

Performance prediction of concurrent systems

Concurrent systems are computers that use multiple processors to solve a single problem. A means to predict the application performance on these systems is a useful tool in many areas of concurrent system research. A computationally efficient and accurate method to predict performance for a class of parallel computations on concurrent systems is described. A parallel computation is modeled as a task system with precedence relationships expressed as a series parallel directed acyclic graph. Resources in concurrent systems are modeled as service centers in queueing network models. Using these two models as inputs, the method outputs predictions of both the time to complete the computation and the concurrent system utilization. The algorithm used is based on the approximate Mean Value Analysis in queueing network modeling with extensions to model concurrency in the computation. The new algorithm was validated against both detailed simulation and actual execution on a commercial multiprocessor.

Mak, Victor W. K.↗
NASA NTRS1991

Multiphase complete exchange on a circuit switched hypercube

On a distributed memory parallel computer, the complete exchange (all-to-all personalized) communication pattern requires each of n processors to send a different block of data to each of the remaining n - 1 processors. This pattern is at the heart of many important algorithms, most notably the matrix transpose. For a circuit switched hypercube of dimension d(n = 2(sup d)), two algorithms for achieving complete exchange are known. These are (1) the Standard Exchange approach that employs d transmissions of size 2(sup d-1) blocks each and is useful for small block sizes, and (2) the Optimal Circuit Switched algorithm that employs 2(sup d) - 1 transmissions of 1 block each and is best for large block sizes. A unified multiphase algorithm is described that includes these two algorithms as special cases. The complete exchange on a hypercube of dimension d and block size m is achieved by carrying out k partial exchange on subcubes of dimension d(sub i) Sigma(sup k)(sub i=1) d(sub i) = d and effective block size m(sub i) = m2(sup d-di). When k = d and all d(sub i) = 1, this corresponds to algorithm (1) above. For the case of k = 1 and d(sub i) = d, this becomes the circuit switched algorithm (2). Changing the subcube dimensions d, varies the effective block size and permits a compromise between the data permutation and block transmission overhead of (1) and the startup overhead of (2). For a hypercube of dimension d, the number of possible combinations of subcubes is p(d), the number of partitions of the integer d. This is an exponential but very slowly growing function and it is feasible over these partitions to discover the best combination for a given message size. The approach was analyzed for, and implemented on, the Intel iPSC-860 circuit switched hypercube. Measurements show good agreement with predictions and demonstrate that the multiphase approach can substantially improve performance for block sizes in the 0 to 160 byte range. This range, which corresponds to 0 to 40 floating point numbers per processor, is commonly encountered in practical numeric applications. The multiphase technique is applicable to all circuit-switched hypercubes that use the common e-cube routing strategy.

Bokhari, Shahid H.↗
NASA NTRS1992

High-performance computing for flight vehicles; Proceedings of the Symposium, Washington, Dec. 7-9, 1992

The present conference discusses high-performance computing systems for flight vehicles, large-scale simulations on high-performance flight computers and software, multidisciplinary and design/optimization applications of computers, computational electromagnetics and acoustics, the simulation of aircraft powerplant turbomachinery and reacting flows, and flow calculations on parallel machines. Also discussed are direct flow simulation Monte Carlo methods, structural mechanics sensitivity and fracture calculations on parallel machines, grid-generation and advanced algorithms for CFD, advanced solid-mechanics and structures applications, and advancements in flow visualization technology and neural networks.

Noor, Ahmed K.↗
NASA NTRS1993

Simulations of particle acceleration in parallel shocks: Direct comparison between Monte Carlo and one-dimensional hybrid codes

We have made a direct comparison between two different computer simulations of a plane, parallel, collisionless shock including particle acceleration to energies typical of those of diffuse ions observed at the earth bow shock. Despite the fact that the one-dimensional hybrid and Monte Carlo techniques employ entirely different algorithms, they give surprisingly close agreement in the overall shapes of the complete distribution functions for protons as well as heavier ions. Both methods show that energetic ions emerge smoothly from the background thermal plasma with approximately the same relative injection rate and that the fraction of the incoming plasma's energy flux that is converted into downstream enthalpy flux of the accelerated population (i.e., the acceleration efficiency) is similar in the two cases. The fraction of the downstream proton distribution made up of superthermal particles is quite large, with at least 10% of the energy flux going into protons with energies above 10 keV. In addition, an upstream precursor, produced by backstreaming energetic particles, is present in both shocks, although the Monte Carlo precursor is considerably longer than that produced in the hybrid shock. These results offer convincing evidence that, at least in these ways, the two simulations are consistent in their description of parallel shock structure and particle acceleration, and they lay the groundwork for development of shock models employing a combination of both methods.

Ellison, Donald C.↗
NASA NTRS1997

Parallel Multiscale Algorithms for Astrophysical Fluid Dynamics Simulations

Our goal is to develop software libraries and applications for astrophysical fluid dynamics simulations in multidimensions that will enable us to resolve the large spatial and temporal variations that inevitably arise due to gravity, fronts and microphysical phenomena. The software must run efficiently on parallel computers and be general enough to allow the incorporation of a wide variety of physics. Cosmological structure formation with realistic gas physics is the primary application driver in this work. Accurate simulations of e.g. galaxy formation require a spatial dynamic range (i.e., ratio of system scale to smallest resolved feature) of 104 or more in three dimensions in arbitrary topologies. We take this as our technical requirement. We have achieved, and in fact, surpassed these goals.

Norman, Michael L.↗
NASA NTRS2007

Optimizations of a Hardware Decoder for Deep-Space Optical Communications

The National Aeronautics and Space Administration has developed a capacity approaching modulation and coding scheme that comprises a serial concatenation of an inner accumulate pulse-position modulation (PPM) and an outer convolutional code [or serially concatenated PPM (SCPPM)] for deep-space optical communications. Decoding of this code uses the turbo principle. However, due to the nonbinary property of SCPPM, a straightforward application of classical turbo decoding is very inefficient. Here, we present various optimizations applicable in hardware implementation of the SCPPM decoder. More specifically, we feature a Super Gamma computation to efficiently handle parallel trellis edges, a pipeline-friendly 'maxstar top-2' circuit that reduces the max-only approximation penalty, a low-latency cyclic redundancy check circuit for window-based decoders, and a high-speed algorithmic polynomial interleaver that leads to memory savings. Using the featured optimizations, we implement a 6.72 megabits-per-second (Mbps) SCPPM decoder on a single field-programmable gate array (FPGA). Compared to the current data rate of 256 kilobits per second from Mars, the SCPPM coded scheme represents a throughput increase of more than twenty-six fold. Extension to a 50-Mbps decoder on a board with multiple FPGAs follows naturally. We show through hardware simulations that the SCPPM coded system can operate within 1 dB of the Shannon capacity at nominal operating conditions.

quadratic polynomial interleaver↗