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At least 775 records · Page 43

Towards improved speed and accuracy of laser powder bed fusion simulations via representation of multiple time scales

Here, we report the result of investigations into alternative representations of the temporal evolution of the laser powder bed fusion (LPBF) process. In order to provide the reader with sufficient context for the following discussion, the modeling challenge and its underlying cause, as well as current attempts to provide a satisfactory solution, will be discussed. Next, the author will describe two numerical methods (multirate time integration and parallel-in-time) to better represent the temporal scales of the problem. Finally, the results of applying these methods to a two-dimensional version of the heat transfer portion of the LPBF problem will be presented, reporting on both convergence and performance behavior, which indicate the possibility of significant speedup of solution calculations (40–100 times), along with well-characterized effects on solution accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Path-accelerated stochastic molecular dynamics: Parallel-in-time integration using path integrals

Massively parallel computer architectures create new opportunities for the performance of long-time scale molecular dynamics (MD) simulations. Here, we introduce the path-accelerated molecular dynamics method that takes advantage of distributed computing to reduce the wall-clock time of MD simulation via parallelization with respect to stochastic MD time steps. The marginal distribution for the time evolution of a system is expressed in terms of a path integral, enabling the use of path sampling techniques to numerically integrate MD trajectories. By parallelizing the evaluation of the path action with respect to time and by initializing the path configurations from a nonequilibrium distribution, the algorithm enables significant speedups in terms of the length of MD trajectories that can be integrated in a given amount of wall-clock time. The method is demonstrated for Brownian dynamics, although it is generalizable to other stochastic equations of motion including open systems. We apply the method to two simple systems, a harmonic oscillator and a Lennard-Jones liquid, and we show that in comparison to the conventional Euler integration scheme for Brownian dynamics, the new method can reduce the wall-clock time for integrating trajectories of a given length by more than three orders of magnitude in the former system and more than two in the latter. This new method for parallelizing MD in the dimension of time can be trivially combined with algorithms for parallelizing the MD force evaluation to achieve further speedup.

Rosa-Raíces, Jorge L.↗

Aerodynamic Shape Optimization Using Hybridized Differential Evolution

An aerodynamic shape optimization method that uses an evolutionary algorithm known at Differential Evolution (DE) in conjunction with various hybridization strategies is described. DE is a simple and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems. Various hybridization strategies for DE are explored, including the use of neural networks as well as traditional local search methods. A Navier-Stokes solver is used to evaluate the various intermediate designs and provide inputs to the hybrid DE optimizer. The method is implemented on distributed parallel computers so that new designs can be obtained within reasonable turnaround times. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. (The final paper will include at least one other aerodynamic design application). The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated.

Madavan, Nateri K.↗

Automated Algorithms for Quantum-Level Accuracy in Atomistic Simulations: LDRD Final Report.

This report summarizes the result of LDRD project 12-0395, titled "Automated Algorithms for Quantum-level Accuracy in Atomistic Simulations." During the course of this LDRD, we have developed an interatomic potential for solids and liquids called Spectral Neighbor Analysis Poten- tial (SNAP). The SNAP potential has a very general form and uses machine-learning techniques to reproduce the energies, forces, and stress tensors of a large set of small configurations of atoms, which are obtained using high-accuracy quantum electronic structure (QM) calculations. The local environment of each atom is characterized by a set of bispectrum components of the local neighbor density projected on to a basis of hyperspherical harmonics in four dimensions. The SNAP coef- ficients are determined using weighted least-squares linear regression against the full QM training set. This allows the SNAP potential to be fit in a robust, automated manner to large QM data sets using many bispectrum components. The calculation of the bispectrum components and the SNAP potential are implemented in the LAMMPS parallel molecular dynamics code. Global optimization methods in the DAKOTA software package are used to seek out good choices of hyperparameters that define the overall structure of the SNAP potential. FitSnap.py, a Python-based software pack- age interfacing to both LAMMPS and DAKOTA is used to formulate the linear regression problem, solve it, and analyze the accuracy of the resultant SNAP potential. We describe a SNAP potential for tantalum that accurately reproduces a variety of solid and liquid properties. Most significantly, in contrast to existing tantalum potentials, SNAP correctly predicts the Peierls barrier for screw dislocation motion. We also present results from SNAP potentials generated for indium phosphide (InP) and silica (SiO 2 ). We describe efficient algorithms for calculating SNAP forces and energies in molecular dynamics simulations using massively parallel computers and advanced processor ar- chitectures. Finally, we briefly describe the MSM method for efficient calculation of electrostatic interactions on massively parallel computers.

Thompson, Aidan Patrick↗

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. By locally refining and coarsening the mesh to capture physical phenomena of interest, such procedures make standard computational methods more cost effective. Unfortunately, an efficient parallel implementation of these adaptive methods is rather difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. This requires significant communication at runtime, leading to idle processors and adversely affecting the total execution time. Nonetheless, it is generally thought that unstructured adaptive- grid techniques will constitute a significant fraction of future high-performance supercomputing. Various dynamic load balancing methods have been reported to date; however, most of them either lack a global view of loads across processors or do not apply their techniques to realistic large-scale applications.

Oliker, Leonid↗

The inviscid incompressible limit of Kelvin–Helmholtz instability for plasmas

The Kelvin–Helmholtz Instability (KHI) is an interface instability that develops between two fluids or plasmas flowing with a common shear layer. KHI occurs in astrophysical jets, solar atmosphere, solar flows, cometary tails, planetary magnetospheres. Two applications of interest, encompassing both space and fusion applications, drive this study: KHI formation at the outer flanks of the Earth’s magnetosphere and KHI growth from non-uniform laser heating in magnetized direct-drive implosion experiments. Here, we study 2D KHI with or without a magnetic field parallel to the flow. We use both the GAMERA code, which solves the compressible Euler equations, and the STRATOSPEC code, which solves the Navier-Stokes equations under the Boussinesq approximation, coupled with the magnetic field dynamics. GAMERA is a global three-dimensional MHD code with high-order reconstruction in arbitrary nonorthogonal curvilinear coordinates, which is developed for a large range of astrophysical applications. STRATOSPEC is a three-dimensional pseudo-spectral code with an accuracy of infinite order (no numerical diffusion). Magnetized KHI is a canonical case for benchmarking hydrocode simulations with extended MHD options. An objective is to assess whether or not, and under which conditions, the incompressibility hypothesis allows to describe a dynamic compressible system. For comparing both codes, we reach the inviscid incompressible regime, by decreasing the Mach number in GAMERA, and viscosity and diffusion in STRATOSPEC. Here, we specifically investigate both single-mode and multi-mode initial perturbations, either with or without magnetic field parallel to the flow. The method relies on comparisons of the density fields, 1D profiles of physical quantities averaged along the flow direction, and scale-by-scale spectral densities. We also address the triggering, formation and damping of filamentary structures under varying Mach number or Atwood number, with or without a parallel magnetic field. Comparisons show very satisfactory results between the two codes. The vortices dynamics is well reproduced, along with the breaking or damping of small-scale structures. We end with the extraction of growth rates of magnetized KHI from the compressible regime to the incompressible limit in the linear regime assessing the effects of compressibility under increasing magnetic field. The observed differences between the two codes are explained either from diffusion or non-Boussinesq effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

97 MATHEMATICS AND COMPUTING↗

A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation

The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world’s largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work.

97 MATHEMATICS AND COMPUTING↗

Wavefront shaping with a Hadamard basis for scattering soil imaging

Here, soil is a scattering medium that inhibits imaging of plant-microbial-mineral interactions that are essential to plant health and soil carbon sequestration. However, optical imaging in the complex medium of soil has been stymied by the seemingly intractable problems of scattering and contrast. Here, we develop a wavefront shaping method based on adaptive stochastic parallel gradient descent optimization with a Hadamard basis to focus light through soil mineral samples. Our approach allows a sparse representation of the wavefront with reduced dimensionality for the optimization. We further divide the used Hadamard basis set into subsets and optimize a certain subset at once. Simulation and experimental optimization results demonstrate our method has an approximately seven times higher convergence rate and overall better performance compared to that with optimizing all pixels at once. The proposed method can benefit other high-dimensional optimization problems in adaptive optics and wavefront shaping.

47 OTHER INSTRUMENTATION↗

Single-shot diffusion measurement in laser-polarized Gas

A single-shot pulsed gradient stimulated echo sequence is introduced to address the challenges of diffusion measurements of laser polarized 3He and 129Xe gas. Laser polarization enhances the NMR sensitivity of these noble gases by >10(3), but creates an unstable, nonthermal polarization that is not readily renewable. A new method is presented which permits parallel acquisition of the several measurements required to determine a diffusive attenuation curve. The NMR characterization of a sample's diffusion behavior can be accomplished in a single measurement, using only a single polarization step. As a demonstration, the diffusion coefficient of a sample of laser-polarized 129Xe gas is measured via this method. Copyright 1999 Academic Press.

Non-NASA Center↗

CSB-RNN: A Faster-Than-Realtime RNN Acceleration Framework with Compressed Structured Blocks

Recurrent Neural Networks (RNN) is widely applied to temporal sequence analysis, where real-time performance is usually in demand. However, RNN suffers a heavy computational workload as the model comes with a large weight matrix. To alleviate the pain, model compression (pruning) schemes have been proposed for RNN that pruning the redundant (near-zero) weight-values. On the one hand, the non-structured pruning methods achieve a considerable pruning rate while bringing the computational irregularity, which is un-friendly to parallel-hardware. On the other hand, the existing structured pruning methods consider the hardware parallelism; However, they suffer a poor pruning rate due to the restrict constraints on pruning structure. This paper presents CSB-RNN, an optimized full-stack RNN framework with the novel compressed structured block (CSB) technique. The CSB-pruned RNN model comes with both fine-granularity that benefits the pruning rate and regular structure that facilitates the hardware-parallelism. Further, we propose a novel hardware architecture for inferencing the CSB-pruned model. Different from conventional parallel hardware, this architecture solves the block-workload imbalance issue and achieves an over 95% hardware utilization. With the experiments on 10 RNN models in 5 application domains, the CSB-RNN realizes 7×-20× lossless compression and up to 50× acceptable lossy-compression, which is 2×-7× to the prior art. With the addition of the novel hardware, the compressed-RNN inference reaches a super real-time latency of 10-400µs with FPGA implementation.

Shi, Runbin↗

A Shift Selection Strategy for Parallel Shift-Invert Spectrum Slicing in Symmetric Self-Consistent Eigenvalue Computation

The central importance of large scale eigenvalue problems in scientific computation necessitates the development massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing excessive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions which will be explored in future work.

97 MATHEMATICS AND COMPUTING↗

Efficient ICCG on a shared memory multiprocessor

Different approaches are discussed for exploiting parallelism in the ICCG (Incomplete Cholesky Conjugate Gradient) method for solving large sparse symmetric positive definite systems of equations on a shared memory parallel computer. Techniques for efficiently solving triangular systems and computing sparse matrix-vector products are explored. Three methods for scheduling the tasks in solving triangular systems are implemented on the Sequent Balance 21000. Sample problems that are representative of a large class of problems solved using iterative methods are used. We show that a static analysis to determine data dependences in the triangular solve can greatly improve its parallel efficiency. We also show that ignoring symmetry and storing the whole matrix can reduce solution time substantially.

Hammond, Steven W.↗

A parallel algorithm for global routing

A Parallel Hierarchical algorithm for Global Routing (PHIGURE) is presented. The router is based on the work of Burstein and Pelavin, but has many extensions for general global routing and parallel execution. Main features of the algorithm include structured hierarchical decomposition into separate independent tasks which are suitable for parallel execution and adaptive simplex solution for adding feedthroughs and adjusting channel heights for row-based layout. Alternative decomposition methods and the various levels of parallelism available in the algorithm are examined closely. The algorithm is described and results are presented for a shared-memory multiprocessor implementation.

Brouwer, Randall J.↗

Low-synch Gram–Schmidt with delayed reorthogonalization for Krylov solvers

The parallel strong-scaling of iterative methods is often determined by the number of global reductions at each iteration. Low-synch Gram-Schmidt algorithms are applied here to the Arnoldi algorithm to reduce the number of global reductions and therefore to improve the parallel strong-scaling of iterative solvers for nonsymmetric matrices such as the GMRES and the Krylov-Schur iterative methods. In the Arnoldi context, the factorization is "left-looking" and processes one column at a time. Among the methods for generating an orthogonal basis for the Arnoldi algorithm, the classical Gram-Schmidt algorithm, with reorthogonalization (CGS2) requires three global reductions per iteration. A new variant of CGS2 that requires only one reduction per iteration is presented and applied to the Arnoldi algorithm. Delayed CGS2 (DCGS2) employs the minimum number of global reductions per iteration (one) for a one-column at-a-time algorithm. The main idea behind the new algorithm is to group global reductions by rearranging the order of operations. DCGS2 must be carefully integrated into an Arnoldi expansion or a GMRES solver. Numerical stability experiments assess robustness for Krylov-Schur eigenvalue computations. Performance experiments on the ORNL Summit supercomputer then establish the superiority of DCGS2 over CGS2.

97 MATHEMATICS AND COMPUTING↗