Wave-heat coupling in one-dimensional unbounded domains: artificial boundary conditions and an optimized Schwarz method

This paper deals with the coupling between one-dimensional heat and wave equations in unbounded subdomains, as a simplified prototype of fluid-structure interaction problems. First we apply appropriate artificial boundary conditions that yield an equivalent problem, but bounded carry out stability analysis for this coupled problem truncated domains. Then devise optimized Schwarz-in-time (or Schwarz Waveform Relaxation) method numerical solving equations. Particular emphasis is made on design transmission conditions. Notably, setting, optimal can be expressed analytically very simple manner. result illustrated by some experiments.