A self adjusting multirate algorithm based on the TR-BDF2 method
For researchers in numerical methods for PDEs, this work offers a new multirate approach with stability analysis, though it is an incremental contribution.
The paper proposes a self-adjusting multirate method using the TR-BDF2 solver, demonstrating its efficiency and accuracy through numerical experiments on hyperbolic PDEs.
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.