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Title: Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equations at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.
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  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0045-7825; 540696
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 289; Journal Issue: C; Journal ID: ISSN 0045-7825
Research Org:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories, Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING nonlinear model reduction; Gappy POD; temporal correlation; forecasting; initial guess