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At least 163 records · Page 9

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.

TRT-THEORETICAL↗

Parallel performance optimizations on unstructured mesh-based simulations

This paper addresses two key parallelization challenges the unstructured mesh-based ocean modeling code, MPAS-Ocean, which uses a mesh based on Voronoi tessellations: (1) load imbalance across processes, and (2) unstructured data access patterns, that inhibit intra- and inter-node performance. Our work analyzes the load imbalance due to naive partitioning of the mesh, and develops methods to generate mesh partitioning with better load balance and reduced communication. Furthermore, we present methods that minimize both inter- and intranode data movement and maximize data reuse. Our techniques include predictive ordering of data elements for higher cache efficiency, as well as communication reduction approaches. We present detailed performance data when running on thousands of cores using the Cray XC30 supercomputer and show that our optimization strategies can exceed the original performance by over 2×. Additionally, many of these solutions can be broadly applied to a wide variety of unstructured grid-based computations.

97 MATHEMATICS AND COMPUTING↗

Performance of a Heterogeneous Grid Partitioner for N-body Applications

An important characteristic of distributed grids is that they allow geographically separated multicomputers to be tied together in a transparent virtual environment to solve large-scale computational problems. However, many of these applications require effective runtime load balancing for the resulting solutions to be viable. Recently, we developed a latency tolerant partitioner, called MinEX, specifically for use in distributed grid environments. This paper compares the performance of MinEX to that of METIS, a popular multilevel family of partitioners, using simulated heterogeneous grid configurations. A solver for the classical N-body problem is implemented to provide a framework for the comparisons. Experimental results show that MinEX provides superior quality partitions while being competitive to METIS in speed of execution.

Harvey, Daniel J.↗

Tractable minor-free generalization of planar zero-field Ising models

In this work, we present a new family of zero-field Ising models over N binary variables/spins obtained by consecutive 'gluing' of planar and O(1)-sized components and subsets of at most three vertices into a tree. The polynomial time algorithm of the dynamic programming type for solving exact inference (computing partition function) and exact sampling (generating i.i.d. samples) consists of sequential application of an efficient (for planar) or brute-force (for O(1)-sized) inference and sampling to the components as a black box. To illustrate the utility of the new family of tractable graphical models, we first build a polynomial algorithm for inference and sampling of zero-field Ising models over K 33 -minor-free topologies and over K 5 -minor-free topologies—both of which are extensions of the planar zero-field Ising models—which are neither genus- nor treewidth-bounded. Second, we empirically demonstrate an improvement in the approximation quality of the NP-hard problem of inference over the square-grid Ising model in a node-dependent nonzero 'magnetic' field.

97 MATHEMATICS AND COMPUTING↗

Wave climate and energy resources in the Mariana Islands from a 42-year high-resolution hindcast

We report a high-resolution wave hindcast from 1979 to 2020 was developed for Guam and the Commonwealth of the Northern Mariana Islands, which are influenced by mesoscale and synoptic weather systems from the western Pacific Rim to the Central Pacific. The spectral wave modeling utilized structured global and unstructured regional grids with improved resolution in nearshore waters, where wave resources development is most feasible. The hindcast demonstrates its capability in capturing multi-modal seas through reproduction of bulk and partitioned wave parameters derived from altimetry and buoy measurements. The local wave climate is influenced by the year-round trade winds and tropical cyclones as well as seasonal monsoons, frontal systems, and mid-latitude high- and low-pressure systems. The strong intra-annual variation of the significant wave height and power flux reflects transitions between local and distant weather systems, which account for the diverse wave conditions comprised of short-period wind waves, intermediate-period seas, and long-period swells around the islands. Among the Pacific island regions, spectral partitioning is particularly important for describing the dominant wave components by period and direction with pertinent information conducive to energy resources characterization and coastal zone management in the Mariana Islands.

16 TIDAL AND WAVE POWER↗

A Framework for Parallel Unstructured Grid Generation for Complex Aerodynamic Simulations

A framework for parallel unstructured grid generation targeting both shared memory multi-processors and distributed memory architectures is presented. The two fundamental building-blocks of the framework consist of: (1) the Advancing-Partition (AP) method used for domain decomposition and (2) the Advancing Front (AF) method used for mesh generation. Starting from the surface mesh of the computational domain, the AP method is applied recursively to generate a set of sub-domains. Next, the sub-domains are meshed in parallel using the AF method. The recursive nature of domain decomposition naturally maps to a divide-and-conquer algorithm which exhibits inherent parallelism. For the parallel implementation, the Master/Worker pattern is employed to dynamically balance the varying workloads of each task on the set of available CPUs. Performance results by this approach are presented and discussed in detail as well as future work and improvements.

Zagaris, George↗

Algorithms for the automatic generation of 2-D structured multi-block grids

Two different approaches to the fully automatic generation of structured multi-block grids in two dimensions are presented. The work aims to simplify the user interactivity necessary for the definition of a multiple block grid topology. The first approach is based on an advancing front method commonly used for the generation of unstructured grids. The original algorithm has been modified toward the generation of large quadrilateral elements. The second method is based on the divide-and-conquer paradigm with the global domain recursively partitioned into sub-domains. For either method each of the resulting blocks is then meshed using transfinite interpolation and elliptic smoothing. The applicability of these methods to practical problems is demonstrated for typical geometries of fluid dynamics.

Schoenfeld, Thilo↗

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required a fine initial mesh. Results indicate that our parallel load balancing strategy will remain viable on large numbers of processors.

Oliker, Leonid↗

WIND Toolkit Offshore Summary Dataset

This dataset contains summary statistics for offshore wind resources for the continental United States derived from the Wind Integration National Datatset (WIND) Toolkit. These data are available in two formats: GDB - Compressed geodatabases containing statistical summaries aligned with lease blocks (aliquots) stored in a GIS format. These data are partitioned into Pacific, Atlantic, and Gulf resource regions. HDF5 - Statistical summaries of all points in the offshore Pacific, Atlantic, and Gulf offshore regions. These data are located on the original WIND Toolkit grid and have not been reassigned or downsampled to lease blocks. These data were developed under contract by NREL for the Bureau of Oceanic Energy Management (BOEM).

17 WIND ENERGY↗

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↗

Mapping to Irregular Torus Topologies and Other Techniques for Petascale Biomolecular Simulation, In: SC '14: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis

Currently deployed petascale supercomputers typically use toroidal network topologies in three or more dimensions. While these networks perform well for topology-agnostic codes on a few thousand nodes, leadership machines with 20,000 nodes require topology awareness to avoid network contention for communication-intensive codes. Topology adaptation is complicated by irregular node allocation shapes and holes due to dedicated input/output nodes or hardware failure. In the context of the popular molecular dynamics program NAMD, we present methods for mapping a periodic 3-D grid of fixed-size spatial decomposition domains to 3-D Cray Gemini and 5-D IBM Blue Gene/Q toroidal networks to enable hundred-million atom full machine simulations, and to similarly partition node allocations into compact domains for smaller simulations using multiple copy algorithms. Additional enabling techniques are discussed and performance is reported for NCSA Blue Waters, ORNL Titan, ANL Mira, TACC Stampede, and NERSC Edison.

Computer Science↗

Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC

In this work, we present an efficient implementation of polynomial filtering methods in PARSEC, a real-space pseudopotential based Kohn–Sham density functional theory solver. The implementation described here improves upon a Chebyshev-filtered subspace iteration algorithm used in the previous version of PARSEC. We present a hybrid polynomial filtering scheme that combines Chebyshev-filtered subspace iteration and a spectrum slicing method that partitions the spectrum into several spectral slices and uses bandpass-filtered subspace iteration to compute approximate eigenpairs within each interior slice simultaneously. We describe a procedure to partition a spectrum and construct polynomial filters. We also discuss a number of practical issues such as the use of appropriate data layouts for carrying out the computation on a two-dimensional process grid and how to achieve good load balance by allocating an appropriate number of process groups to each spectral slice. Numerical examples are presented to demonstrate the effectiveness of the hybrid polynomial filtering method as well as the superior parallel scalability of spectrum slicing in comparison to that of Chebyshev-filtered subspace iteration.

97 MATHEMATICS AND COMPUTING↗

Observed Scaling in Clouds and Precipitation and Scale Incognizance in Regional to Global Atmospheric Models

We use observations of robust scaling behavior in clouds and precipitation to derive constraints on how partitioning of precipitation should change with model resolution. Our analysis indicates that 90-99% of stratiform precipitation should occur in clouds that are resolvable by contemporary climate models (e.g., with 200 km or finer grid spacing). Furthermore, this resolved fraction of stratiform precipitation should increase sharply with resolution, such that effectively all stratiform precipitation should be resolvable above scales of ~50 km. We show that the Community Atmosphere Model (CAM) and the Weather Research and Forecasting (WRF) model also exhibit the robust cloud and precipitation scaling behavior that is present in observations, yet the resolved fraction of stratiform precipitation actually decreases with increasing model resolution. A suite of experiments with multiple dynamical cores provides strong evidence that this `scale-incognizant' behavior originates in one of the CAM4 parameterizations. An additional set of sensitivity experiments rules out both convection parameterizations, and by a process of elimination these results implicate the stratiform cloud and precipitation parameterization. Tests with the CAM5 physics package show improvements in the resolution-dependence of resolved cloud fraction and resolved stratiform precipitation fraction.

atmospheric↗

Assimilation of Gridded Terrestrial Water Storage Observations from GRACE into a Land Surface Model

Observations of terrestrial water storage (TWS) from the Gravity Recovery and Climate Experiment (GRACE) satellite mission have a coarse resolution in time (monthly) and space (roughly 150,000 km(sup 2) at midlatitudes) and vertically integrate all water storage components over land, including soil moisture and groundwater. Data assimilation can be used to horizontally downscale and vertically partition GRACE-TWS observations. This work proposes a variant of existing ensemble-based GRACE-TWS data assimilation schemes. The new algorithm differs in how the analysis increments are computed and applied. Existing schemes correlate the uncertainty in the modeled monthly TWS estimates with errors in the soil moisture profile state variables at a single instant in the month and then apply the increment either at the end of the month or gradually throughout the month. The proposed new scheme first computes increments for each day of the month and then applies the average of those increments at the beginning of the month. The new scheme therefore better reflects submonthly variations in TWS errors. The new and existing schemes are investigated here using gridded GRACE-TWS observations. The assimilation results are validated at the monthly time scale, using in situ measurements of groundwater depth and soil moisture across the U.S. The new assimilation scheme yields improved (although not in a statistically significant sense) skill metrics for groundwater compared to the open-loop (no assimilation) simulations and compared to the existing assimilation schemes. A smaller impact is seen for surface and root-zone soil moisture, which have a shorter memory and receive smaller increments from TWS assimilation than groundwater. These results motivate future efforts to combine GRACE-TWS observations with observations that are more sensitive to surface soil moisture, such as L-band brightness temperature observations from Soil Moisture Ocean Salinity (SMOS) or Soil Moisture Active Passive (SMAP). Finally, we demonstrate that the scaling parameters that are applied to the GRACE observations prior to assimilation should be consistent with the land surface model that is used within the assimilation system.

GRACE↗

Dependencies of Simulated Convective Cell and System Growth Biases on Atmospheric Instability and Model Resolution

Abstract This study evaluates convective cell properties and their relationships with convective and stratiform rainfall within a season‐long convection‐permitting weather research and forecasting simulation over central Argentina using radar, satellite, and radiosonde measurements from the RELAMPAGO‐CACTI field campaign. The simulation slightly underestimates radar‐estimated rainfall over the ∼3.5‐month evaluation period but underestimates stratiform rainfall by 46% and overestimates convective rainfall by 43%. As convective available potential energy (CAPE) increases, the convective rainfall overestimation decreases, but the stratiform rainfall underestimation increases such that the contribution of convective to total rainfall remains constantly high biased by ∼26%. Overestimated convective rainfall arises from the simulation generating 2.6 times more precipitating convective cells (14,299) than observed by radar (5,662) despite similar observed and simulated cell growth processes, with relatively wide cells contributing mostly to excessive convective rainfall. Relatively shallow cells, typically reaching heights of 4–7 km, contribute most to the cell number bias. This cell number bias increases as CAPE decreases, potentially because cells and their updrafts become narrower and more under‐resolved as CAPE decreases. The gross overproduction of precipitating shallow cells leads to overly efficient precipitation and inadequate detrainment of ice aloft, thereby diminishing the formation of robust stratiform rainfall regions. Decreasing model horizontal grid spacing from 3 to 1 or 0.333 km for low (<300 J kg −1 ) and high CAPE (>1,000 J kg −1 ) cases results in minimal change to cell number, depth, and convective‐to‐stratiform partitioning biases. This suggests that improving prediction of these convective properties depends on factors beyond solely increasing model resolution.

54 ENVIRONMENTAL SCIENCES↗

Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian

We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗

A cohesive zone treatment for the material point method involving problems of large deformation and damage

A new algorithm is described that permits the use of cohesive zones in the material point method for problems involving large deformation and fracture. In contrast to previous cohesive zone implementations, this method does not utilize massless surface-element particles. Instead, cohesive tractions are computed using the shape function mappings from a reference grid configuration in combination with explicitly defined particle surface normals and surface positions. These normals and relative surface positions are updated each time step according to particle deformation. The tractions are converted to cohesive forces using the nodal areas and mapped back to particles using the same reference shape function mappings. These forces are then remapped by conventional particle-to-grid interpolation as external forces using the current-configuration shape-function mappings. This allows highly compliant cohesive zones to function over jump displacements larger than a grid cell. Upon damage, these interfaces can revert to conventional multi-field contact surfaces. This approach is general and readily applies to two and three dimensions as well as being compatible with damage-field gradient partitioning offering exceptional computational flexibility. The framework for this method enables other capabilities, such as improved contact precision using explicitly defined surface normals and positions, and a method to mitigate spurious material damage at weak discontinuities between stiff brittle materials and soft or compliant materials.

Cohesive zone↗

Short-Term Global Horizontal Irradiance Forecasting Based on Sky Imaging and Pattern Recognition

Accurate short-term forecasting is crucial for solar integration in the power grid. In this paper, a classification forecasting framework based on pattern recognition is developed for 1-hour-ahead global horizontal irradiance (GHI) forecasting. Three sets of models in the forecasting framework are trained by the data partitioned from the preprocessing analysis. The first two sets of models forecast GHI for the first four daylight hours of each day. Then the GHI values in the remaining hours are forecasted by an optimal machine learning model determined based on a weather pattern classification model in the third model set. The weather pattern is determined by a support vector machine (SVM) classifier. The developed framework is validated by the GHI and sky imaging data from the National Renewable Energy Laboratory (NREL). Results show that the developed short-term forecasting framework outperforms the persistence benchmark by 16% in terms of the normalized mean absolute error and 25% in terms of the normalized root mean square error.

14 SOLAR ENERGY↗