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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Gaussian Mixture Model Solvers for the Boltzmann Equation

This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Support of domain decomposition-based solvers in Chroma

In multilevel integration, the correlation functions are decomposed into factors that depend only on fields localized into lattice subdomains so that they can be independently integrated. Although the standard formulation of the LQCD action is not local in the presence of fermions, past studies have shown approximations of the quark propagator and the fermionic determinant dependent on the gauge fields within specific subdomains can still be effective. We will present our current progress in supporting domain decomposition within Chroma, which is necessary for multilevel integration approaches. The efforts are focused on extending the code base to efficiently manipulate subdomains for lattice fields and operators and performing inversions and eigendecompositions within domains.

Alcalde, Eloy Romero↗
DOE OSTI2024

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Many time-dependent problems and simulations are often modeled using Partial Differential Equations. Traditional modeling approaches that use sequential time-stepping are reaching a bottleneck in optimizing efficiency. The Center of Applied Science and Computing at Lawrence Livermore National Laboratory extensively works on parallelizing these algorithms to leverage the increasing computational power from the growing number of processors in computer hardware. In particular, they aim to design non-intrusive algorithms that can generalize to a variety of problems and sizes without requiring additional information from or modifications on the original problems. Multigrid Reduction in Time (MGRIT) is a parallel-in-time algorithm that is designed to be non-intrusive. This project focuses on increasing the efficiency of MGRIT by approximating the coarse-grid operator using machine learning approaches as a means to find the most non-intrusive, or general, solution.

97 MATHEMATICS AND COMPUTING↗