Convergence Acceleration for Time Dependent Parametric Multifidelity Models
Abstract
We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time integration scheme. Our first contribution is in novel analysis of the multifidelity procedure, providing a convergence estimate. Our second contribution is development of a three-step algorithm that uses multifidelity surrogates to accelerate convergence: step one uses a multifidelity procedure at three levels to obtain accurate predictions using inexpensive (large timestep) models. Step two uses high-order splines to construct continuous trajectories over time. Finally, step three combines spline predictions at three levels to infer an order of convergence and compute a sequence transformation prediction (in particular we use Richardson extrapolation) that achieves superior error. We demonstrate our procedure on linear and nonlinear systems of parameterized ordinary differential equations.
Cite
@article{arxiv.1808.03379,
title = {Convergence Acceleration for Time Dependent Parametric Multifidelity Models},
author = {Vahid Keshavarzzadeh and Robert M. Kirby and Akil Narayan},
journal= {arXiv preprint arXiv:1808.03379},
year = {2018}
}