A self adjusting multirate algorithm based on the TR-BDF2 method

Abstract

We propose a self adjusting multirate method based on the TR-BDF2 solver. The potential advantages of using TR-BDF2 as the key component of a multirate framework are highlighted. A linear stability analysis of the resulting approach is presented and the stability features of the resulting algorithm are analysed. The analysis framework is completely general and allows to study along the same lines the stability of self adjusting multirate methods based on a generic one step solver. A number of numerical experiments demonstrate the efficiency and accuracy of the resulting approach also the time discretization of hyperbolic partial differential equations.

Implicit multirate GARK methods

“…In [12], a multirate θ-method is presented and analyzed. Recently, multirate methods based on TR-BDF2 were proposed in [5,3]. In [21,18], new strategies for creating implicit multirate infinitesimal methods were introduced.…”