Convergence Acceleration for Time Dependent Parametric Multifidelity Models
For researchers in scientific computing and simulation, this work provides a practical convergence acceleration technique for multifidelity models, though it is incremental as it builds on existing multifidelity and extrapolation methods.
The paper introduces a numerical method to accelerate convergence in multifidelity models for parameterized ODEs, using a three-step algorithm combining multifidelity surrogates, splines, and Richardson extrapolation to achieve superior error with reduced computational cost.
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.