Search NASA⌕ Search

SEARCH · Search NASA

Results for “PDES”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Hybrid PDES Simulation of HPC Networks Using Zombie Packets

Although high-fidelity network simulations have proven to be reliable and cost-effective tools to peer into architectural questions for high-performance computing (HPC) networks, they incur a high resource cost. The time spent in simulating a single millisecond of network traffic in the highest detail can take hours, even for static, well-behaved traffic patterns such as uniform random. Surrogate models offer a significant reduction in runtime, yet they cannot serve as complete replacements and should only be used when appropriate. Thus, there is a need for hybrid modeling, where high-fidelity simulation and surrogates run side-by-side. Here, we present a surrogate model for HPC networks in which: packets bypass the network, while the network state is left untouched, i.e., suspended. To bypass the network, we use historical data to estimate the arrival time at which every packet should be scheduled at; to suspend the network, all in-flight packets are scheduled to arrive at their destinations, and are kept in the system to awaken as zombies when switching back to high-fidelity. Speedup for a hybrid model is relative to the proportion of surrogate to high-fidelity. This light-weight surrogate obtained up to 76× speedup. Keeping the zombies in the network showed an increase in the accuracy of the high-fidelity simulation on restart when compared to restarting the network from an empty state.

HPC networks↗
DOE OSTI2022

Asynchronous domain decomposition methods for nonlinear PDEs

One- and two-level parallel asynchronous methods for the numerical solution of nonlinear systems of equations, especially those arising from (nonlinear) partial differential equations, are studied. The proposed methods are based on domain decomposition techniques. Local convergence theorems are presented in several cases, with appropriate hypotheses. Computational results on a shared memory multiprocessor machine for various problems exhibiting nonlinearities are reported, illustrating the potential of these asynchronous methods, especially for heterogeneous clusters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Error Estimates of Residual Minimization Using Neural Networks for Linear PDES

We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates for both continuous and discrete formulations of residual minimization in strong and weak forms. The formulations cover recently developed physicsinformed neural networks based on strong and variational formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

FINAL REPORT: Multigrid for Systems and Time-Dependent PDEs

This report has two sections. The first section is the motivation for looking at differing discretizations on coarse grids for solving a parabolic equation using multigrid in time. The second section contains selected numerical results from the many experiments conducted. The most interesting result is that for explicit fine grid discretizations, the best coarse discretization (i.e. smallest convergence rates) is a weighting between implicit and explicit methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Computer Science Research Needs for Parallel Discrete Event Simulation (PDES)

Historically, scientific computing efforts have demonstrated the clear need for, and effective use of, supercomputing with traditional time-stepped simulations. Nevertheless, there are several areas in the mission spaces of the U.S. Department of Energy and other agencies waiting to tap advanced computing research using a different, discrete event style of modeling, simulation, and analysis. These span a wide spectrum of applications including energy grid resilience, urban planning and policy, transportation science, building technologies, emergency response and planning, environmental impact analysis, computational epidemiology, Internet communications, cyber security, and cyber-physical systems, to name only a few. Even within traditional scientific applications, the role of discrete event modes of execution is increasing in the form of new event-based mathematical solvers such as quantized state integration methods and discrete-continuous hybrid system solvers. Co-design of advanced supercomputing hardware systems is another area that exploits discrete event simulation at its core for effective analyses. Complex systems, entity behaviors and interconnections play a significant role in all these applications, which are mapped to large-scale models with discrete event formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Georgia Tech Accelerated, Compressed, and Regularized Compute of Kinetic-based PDEs (Final Report)

This report summarizes the collaborative effort between Lawrence Livermore National Laboratory and Georgia Tech to enhance the BoBa library for tensor train computation in PDE solvers, with a target on kinetic equations and their continuum limits. We aimed to reduce computational cost and memory usage by replacing traditional array-based computations with tensor trains. We examined the compressibility of time-evolving solutions to the Euler equations with discontinuities. We also explored using the first invsicid and linear regularization of the compressible flow equations via the information geometric regularization (IGR). We explored this in a tensor train formulation. To identify that inverse terms in the IGR equations pose problems for tensor train formulations and investigate efficient methods for batched inversion of tensor trains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Asynchronous numerical solution of PDEs on parallel computers

Asynchronous and partially-synchronous finite difference schemes are investigated for the one-dimensional steady-state and nonsteady-state heat equation, respectively. It is shown experimentally that the asynchronous scheme runs twice as fast as the parallel synchronous scheme. For relatively small values of time levels, however, the asynchronous scheme produces the least accurate results, while the partially-asynchronous scheme is almost as accurate as its synchronous counterpart.

Amitai, Dganit↗