Lacunae-Based Artificial Boundary Conditions for the Numerical Simulation of Unsteady Waves Governed by Vector Models

Abstract

Artificial boundary conditions (ABCs) are constructed for the computation of unsteady acoustic and electromagnetic waves. The waves propagate from a source or a scatterer toward infinity, and are simulated numerically on a truncated domain, while the ABCs provide the required closure at the external artificial boundary. They guarantee the complete transparency of this boundary for all the outgoing waves. They are non-local in both space and time but can be implemented efficiently because their temporal non-locality is fixed and limited. The restriction of temporal nonlocality of the proposed ABCs does not come as a result of any model simplification or approximation, but rather as a consequence of a fundamental property of the solutions — the presence of lacunae, or in other words, sharp aft fronts of the waves, in odd-dimension spaces.