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At least 73 records · Page 4

Parallel iterative methods for sparse linear and nonlinear equations

As three-dimensional models are gaining importance, iterative methods will become almost mandatory. Among these, preconditioned Krylov subspace methods have been viewed as the most efficient and reliable, when solving linear as well as nonlinear systems of equations. There has been several different approaches taken to adapt iterative methods for supercomputers. Some of these approaches are discussed and the methods that deal more specifically with general unstructured sparse matrices, such as those arising from finite element methods, are emphasized.

Saad, Youcef↗

Parallel inferencing method and apparatus for rule-based expert systems

The invention analyzes areas of conditions with an expert knowledge base of rules using plural separate nodes which fire respective rules of said knowledge base, each of said rules upon being fired altering certain of said conditions predicated upon the existence of other said conditions. The invention operates by constructing a P representation of all pairs of said rules which are input dependent or output dependent; constructing a C representation of all pairs of said rules which are communication dependent or input dependent; determining which of the rules are ready to fire by matching the predicate conditions of each rule with the conditions of said set; enabling said node means to simultaneously fire those of the rules ready to fire which are defined by said P representation as being free of input and output dependencies; and communicating from each node enabled by said enabling step the alteration of conditions by the corresponding rule to other nodes whose rules are defined by said C matrix means as being input or communication dependent upon the rule of said enabled node.

Schwuttke, Ursula M.↗

Applying Parallel Adaptive Methods with GeoFEST/PYRAMID to Simulate Earth Surface Crustal Dynamics

This viewgraph presentation reviews the use Adaptive Mesh Refinement (AMR) in simulating the Crustal Dynamics of Earth's Surface. AMR simultaneously improves solution quality, time to solution, and computer memory requirements when compared to generating/running on a globally fine mesh. The use of AMR in simulating the dynamics of the Earth's Surface is spurred by future proposed NASA missions, such as InSAR for Earth surface deformation and other measurements. These missions will require support for large-scale adaptive numerical methods using AMR to model observations. AMR was chosen because it has been successful in computation fluid dynamics for predictive simulation of complex flows around complex structures.

GeoFEST↗

System and method for parallel two-photon lithography using a metalens array

A metalens array is disclosed for controllably modifying a phase of a wavefront of an optical beam. The metalens array may have a substrate having at least first and second metalens unit cells, and forming a single integrated structure with no stitching being required of the first and second metalens unit cells. The first metalens unit cell has a first plurality of nanoscale features and is configured to modify a phase of a first portion of a wavefront of an optical signal incident thereon in accordance with a first predetermined phase pattern to create at least one first focal voxel within an image plane. The second metalens unit cell has a second plurality of nanoscale features configured to modify the phase of a second portion of the wavefront of the optical signal incident thereon, in accordance with a second predetermined phase pattern, to simultaneously create at least one second focal voxel within the image plane. Each metalens unit cell also has an overall diameter of no more than about 200 microns.

Xia, Xiaoxing↗

Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch

Two parallelized hybrid methods are presented for single-function optimization problems with side constraints. The optimization problems are difficult not only due to possible existence of local minima and nonsmoothness of functions, but also due to the fact that objective function and constraint values for a solution vector can only be obtained by querying a black box whose execution requires considerable computational effort. Examples are optimization problems in Engineering where objective function and constraint values are computed via complex simulation programs, and where local minima exist and smoothness of functions is not assured. The hybrid methods consist of the well-known method NOMAD and two new methods called DENCON and DENPAR that are based on the linesearch scheme CS-DFN. The hybrid methods compute for each query a set of solution vectors that are evaluated in parallel. The hybrid methods have been tested on a set of difficult optimization problems produced by a certain seeding scheme for multiobjective optimization. We compare computational results with solution by NOMAD, DENCON, and DENPAR as stand-alone methods. It turns out that among the stand-alone methods, NOMAD is significantly better than DENCON and DENPAR. However, the hybrid methods are definitely better than NOMAD.

97 MATHEMATICS AND COMPUTING↗

Advanced Computing is at the Forefront of a New “Moonshot” Revolutionizing the North American Power Grid

In the 50+ years since the first humans landed on the moon, computing has grown at breakneck speed. We are faced with another challenge that is just as daunting, and just as important to overcome-modernizing the North American electric power grid-and high-performance computing (HPC) systems with specialized software will be an important element in rising to this challenge. We describe at a high level how software developed in the ExaSGD project addresses this "moonshot" goal by utilizing exascale computing and a novel high performance solver software stack to support the mission of decarbonizing power grid operations in an environment of uncertain weather and climate. To reach the exascale benchmark the team has made a number of first-of-their-kind innovations, including novel method for stochastic optimization, fine grained parallel methods for modeling power systems, and GPU resident sparse numerical linear solvers.

17 WIND ENERGY↗

Hybrid massively parallel fast sweeping method for static Hamilton–Jacobi equations

The fast sweeping method is a popular algorithm for solving a variety of static Hamilton–Jacobi equations. Fast sweeping algorithms for parallel computing have been developed, but are severely limited. In this work, we present a multilevel, hybrid parallel algorithm that combines the desirable traits of two distinct parallel methods. The fine and coarse grained components of the algorithm take advantage of heterogeneous computer architecture common in high performance computing facilities. We present the algorithm and demonstrate its effectiveness on a set of example problems including optimal control, dynamic games, and seismic wave propagation. We give results for convergence, parallel scaling, and show state-of-the-art speedup values for the fast sweeping method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

1st Computational Physics School for Fusion Research (2019 CPS-FR)

The rising number of applications of machine learning and computational statistics in fusion energy research requires flexibility in adopting a growing variety of tools. The Computational Physics School for Fusion Research (CPS-FR) aims at providing young researchers with critical skill sets to deal with modern fusion energy research challenges. The School aims at covering essentials of: Computational Statistics, Machine Learning, Deep Learning and optimization methods, Parallel Programming and HPC. As the first edition of the CPS-FR just concluded, this report highlights its main results and summarizes its contents.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Scalable Adaptive Multilevel Solvers for Multiphysics Problems

In this project, we carried out many studies on adaptive and parallel multilevel methods for numerical modeling for various applications, including Magnetohydrodynamics (MHD) and complex fluids. We have made significant efforts and advances in adaptive multilevel methods of the multiphysics problems: multigrid methods, adaptive finite element methods, and applications.

97 MATHEMATICS AND COMPUTING↗

Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed

97 MATHEMATICS AND COMPUTING↗

Multiply accelerated ReaxFF molecular dynamics: coupling parallel replica dynamics with collective variable hyper dynamics

To address the time scales required to study complex chemical reactions, methods performing accelerated molecular dynamics are necessary even with the recent advancement in high-performance computing. A number of different acceleration techniques are available. Here we explore potential synergies between two popular acceleration methods – Parallel Replica Dynamics (PRD) and Collective Variable Hyperdynamics (CVHD), by analysing the speedup obtained for the pyrolysis of n-dodecane. We determine that PRD + CVHD provides additional speedup to CVHD by reaching the required time scales for the reaction at an earlier wall-clock time. Although some speedup is obtained with the additional replicas, we found that the effectiveness of the inclusion of PRD is depreciated for systems where there is a dramatic increase in reaction rates induced by CVHD. Similar observations were made in the simulation of ethylene-carbonate/Li system, which is inherently more reactive than pyrolysis, suggest that the speedup obtained via the combination of the two acceleration methods can be generalised to most practical chemical systems.

42 ENGINEERING↗

DyG-DPCD: A Distributed Parallel Community Detection Algorithm for Large-Scale Dynamic Graphs

Dynamic (Temporal) graphs capture the valuable evolution of real-world systems, from the continuously evolving patterns of social interactions and genetic pathways to the dynamic fluctuations of economic forces. Detecting communities for such evolving networks poses unique challenges. Detecting and analyzing the evolution of communities within dynamic graphs unlocks valuable insights into the underlying structural and temporal patterns of real-world systems. However, the sheer volume of modern graph data and the inherent complexity of the temporal dimension pose significant challenges to scalable community detection algorithms. Addressing this gap, our work explores the limited landscape of scalable distributed-memory parallel methods specifically designed for dynamic network community detection. We propose a novel parallel algorithm, DyG-DPCD (Dynamic Graph Distributed Parallel Community Detection), to detect communities in dynamic networks using the Message Passing Interface (MPI) framework. We present a vertex-centric approach, allowing us to detect communities through local optimization. Furthermore, we enhance our baseline algorithm by incorporating three heuristics, which improve the algorithm’s performance significantly while maintaining the quality of the solutions. We demonstrate the efficiency of our algorithm by experimenting on several real-world large-scale networks with hundreds of millions of edges spanning diverse domains. Notably, DyG-DPCD achieves speedups between 25× and 30× for large networks that we experimented on using NERSC compute nodes. In conclusion, our algorithm outperforms the STINGER parallel re-agglomeration algorithm by 30×.

97 MATHEMATICS AND COMPUTING↗