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arXiv · 1808.03379

Convergence Acceleration for Time Dependent Parametric Multifidelity Models

Vahid Keshavarzzadeh·Robert M. Kirby·Akil Narayan
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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.

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Vahid Keshavarzzadeh, Robert M. Kirby, Akil Narayan. 2018-08-10. Convergence Acceleration for Time Dependent Parametric Multifidelity Models. https://arxiv.org/abs/1808.03379

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