Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
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.
- Research Organization:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC04-94AL85000; AC04-94-AL85000
- OSTI ID:
- 1184503
- Alternate ID(s):
- OSTI ID: 1250080
- Report Number(s):
- SAND-2014-19077J; 540696
- Journal Information:
- Computer Methods in Applied Mechanics and Engineering, Vol. 289, Issue C; ISSN 0045-7825
- Country of Publication:
- United States
- Language:
- English
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