A non-iterative domain decomposition time integrator for the linear wave equation

In this talk we will motivate, construct and analyze a non-iterative domain decomposition time integrator for the linear wave equation. The central concept involves combining an implicit solution step on spatial subdomains with a cost-effective, yet precise, local, explicit prediction step. In that sense the method is similar to methods from Blum, Lisky and Rannacher or Dawson and Dupont, which have been designed mainly for parabolic problems. While the locality of the prediction combined with the decomposition into subdomains allows for parallelization across space, the scheme progresses sequentially through time. However, unlike similar methods, this time stepping is only performed once, without any iterations involved. We show that the scheme achieves second-order convergence in time and conclude the presentation with some words on its parallel implementation and numerical experiments.

The talk is based on joint work with Marlis Hochbruck. Funded by the Deutsche Forschungs-gemeinschaft (DFG, German Research Foundation) — Project-ID 258734477 — CRC 1173.

Contatti:
gabriele.ciaramella@polimi.it
ilario.mazzieri@polimi.it