Towards efficient interface conditions for a Schwarz domain decomposition algorithm for an advection equation with biharmonic diffusion

This paper addresses the problem of deriving efficient interface conditions for solving biharmonic diffusion–advection equations using a Schwarz global-in-time domain decomposition algorithm. General interface conditions are proposed, which lead to well-posed problems on each subdomain. The equation is then studied in the simplified 1D case. Exact non-local absorbing boundary conditions are derived, and are approximated by optimized local interface conditions, the efficiency of which is illustrated by numerical experiments.