Stability analysis of interface temporal discretization in grid overlapping methods

We investigate the stability of a temporal discretization of interface terms in grid overlapping methods. A matrix stability analysis is performed on a model problem of the one-dimensional diffusion equation on overlapping grids. The scheme stability is first analyzed theoretically, and a proof of the unconditional stability of the first-order interface extrapolation scheme with the firstand second-order time integration for any overlap size is presented. For the higher-order schemes, we obtain explicit estimates of the spectral radius of the corresponding discrete matrix operator and document the values of the stability threshold depending on the number of grid points and the size of overlap. The influence of iterations on stability properties is also investigated. Numerical experiments are then presented relating the obtained stability bounds to the observed numerical values. Semidiscrete analysis confirms the derived scaling for the stability bounds.