Roberts, Steven | Search NASA

DOE OSTI2022

A Fast Time-Stepping Strategy for Dynamical Systems Equipped with a Surrogate Model

Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge--Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. Here, we provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration.

Surrogate models↗

DOE OSTI2021

A unified formulation of splitting-based implicit time integration schemes

Splitting-based time integration approaches such as fractional step, alternating direction implicit, operator splitting, and locally one dimensional methods partition the system of interest into components, and solve individual components implicitly in a cost-effective way. Here this work proposes a unified formulation of splitting time integration schemes in the framework of general-structure additive Runge–Kutta (GARK) methods. Specifically, we develop implicit-implicit (IMIM) GARK schemes, provide the order conditions for this class, and explain their application to partitioned systems of ordinary differential equations. We show that classical splitting methods belong to the IMIM GARK family, and therefore can be studied in this unified framework. New IMIM-GARK splitting methods are developed and tested using parabolic systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2017

CHOMPTT (CubeSat Handling of Multisystem Precision Timing Transfer): From Concept to Launch Pad

Here we present the evolution of a student satellite mission: CHOMPTT (CubeSat Handling of Multisystem Precision Time Transfer), from its original concept as a candidate for the University NanoSatellite Program 8 (UNP8), to a spacecraft ready for launch in Fall of 2017 on ELaNa XIX (Educational Launch of Nanosatellites). The 3U CubeSat houses a 1 kg, 1U OPTI (Optical Precision Timing Instrument) payload, designed and built at the University of Florida, and a 1.5U EDSNNODeS-derived bus from NASA Ames Research Center. The OPTI payload comprises of: 1) a supervisor board that handles payload data, power regulation, and mode settings, 2) an optics assembly of six 1 cm retroreflectors and four laser beacon diodes for ground-tracking; and 3) two fully redundant timing channels, each consisting of: a chip-scale atomic clock, a microprocessor with clock counter, a picosecond event timer, and an avalanche photodetector (APD) with band-pass filter. Several iterations of OPTI have been developed, tested, and designed to achieve its current functionality and design a laboratory breadboard design, a 1.5U high altitude balloon design, engineering unit design, and its current flight unit design. In-lab testing of the current OPTI design indicates a short-term precision of 100 ps, equivalent to a range accuracy of 3 cm necessary to achieve our primary objective of 200 ps time transfer error, and a long-term timing accuracy of 20 ns over one orbit (1.5 hours). After the spacecraft reaches its nominal 500 km orbit at a 85 degree inclination, an experimental laser ranging facility at Kennedy Space Center in Florida, will track and emit 1064 nm nanosecond optical pulses at the CHOMPTT spacecraft. The laser pulses will then reflect off the retroreflector array mounted on the nadir face of CHOMPTT, and return the pulse to the laser ranging facility where the laser ranging facility will record the round-trip duration of the laser pulses. At the same time the pulse arrives at the spacecraft and is reflected by the array, an APD will record the arrival time of the pulses at the nanosatellite. By comparing the arrival of the pulse at the CubeSat and the duration of the round-trip of the laser pulse, the clock discrepancy between the ground and CubeSat atomic clocks can be determined, in addition to the CubeSats range from the facility. The design and verification of the flight version of CHOMPTT will be reviewed and an overview of the lifetime development and progression of CHOMPTT from the inception to launch pad will be presented.

CHOMPTT↗