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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Optimizing a Multiple Right-Hand Side Dslash Kernel for Intel Knights Corner

Lattice Quantum Chromo-dynamics (LQCD) stands unique as the only computationally tractable, non-perturbative, and model-independent quantum field theory of the strong nuclear force. LQCD achieves tractability by discretizing our familiar 4-dimensional space-time onto a hypercubic lattice. The core component of the linear solver used in LQCD is the Wilson-Dirac operator whose finite difference component is called the Dslash operator. Dslash is a nearest neighbor stencil operator summing matrix-vector multiplications over lattice points. The arithmetic intensity of a regular Dslash operator acting on a single vector in single precision is between 0.88-2.29 (depending on the tricks employed) making it memory bandwidth bound on most current architectures, including Xeon Phi. Maximizing the performance of Dslash on Xeon Phi requires deliberate exploitation of its architectural features. One key feature of Xeon Phi is its powerful vector processing unit with lengthy vector registers. There is a class of LQCD computations which aims to solve the Dirac equation for the same lattice gauge fields multiple times. In this case one can gain additional reuse of the gauge field, and potentially simplified vectorization, through applying Dslash to several vectors at the same time; often referred to as Multiple Right Hand Side (MRHS) Dslash. Previous work in this area focused on applying this approach to the Highly Improved Staggered operator, and in cases to the multi-Grid algorithm for Wilson clover fermions. Here, we present two approaches to MRHS Dslash: a vector register blocking approach and one using the software package QPhiX with a custom Code Generator for low-level intrinsics. We explore the Knights Corner instruction set, memory hierarchy, and threading capabilities. For standard lattice sizes used in testing, we observed significant speedups, with sustained performance of over 700 GFLOPS (single precision) in one instance. We achieved up to 27% of theoretical peak performance compared to a maximum of 12% obtained by the previous single RHS method in QPhiX.

Joó, Bálint↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Numerical and Experimental Study of an Aircraft Igniter Plasma Jet Discharge

The spark discharge of an aircraft plasma jet igniter is studied using high-fidelity numerical simulations and X-ray radiography measurements. The target problem here features the thermal expansion of hot gas introduced by the electric spark within a confined igniter cavity, which eventually evolves into a pulsed jet of a high-temperature kernel. A comprehensive set of models adapted from existing strategies for internal combustion engine spark plug discharge is extended to the target problem, including the modeling of energy deposition, plasma reactions, thermodynamic properties, and heat losses. A series of validation and parameter studies are performed and presented. The kernel size is found to be sensitive to heat losses arising from radiation and hot gas remained within the discharge cavity, rather than heat conduction to the wall in the discharge cavity. Depending on the enforced shape of the post-breakdown electric arc, the spark kernel can be off-centered, tilted, and considerably asymmetric. These features have been previously not considered when studying such igniter configurations and may have a first-order impact on the ignition process. Provided a proper setup of the heat loss models and electric arc shape, the numerical results are quantitatively comparable to the experimental results in terms of the kernel size, shape, and velocity throughout different stages after the spark discharge.

Tang, Yihao↗