AN ANALYSIS OF HIGHER ORDER BOUNDARY CONDITIONS FOR THE WAVE EQUATION

Julien Diaz (1) , Patrick Joly (1)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

Thanks to the use of the Cagniard–De Hoop method, we derive an analytic solution in the time domain for the half-space problem associated with the wave equation with Engquist– Majda higher order boundary conditions. This permits us to derive new convergence results when the order of the boundary condition tends to infinity, as well as error estimates. The theory is illustrated by numerical results.

Mots clés: Cagniard--De Hoop method; absorbing boundary conditions; wave equation; error estimates; convergence; Green's function

Domaines: Equations aux dérivées partielles [math.AP]

Julien Diaz, Patrick Joly. AN ANALYSIS OF HIGHER ORDER BOUNDARY CONDITIONS FOR THE WAVE EQUATION. SIAM Journal on Applied Mathematics, 2005, 65 (5), pp.1547-1575. ⟨10.1137/S0036139903436145⟩. ⟨inria-00409197⟩