Computation of the exact discrete transparent boundary condition for 1D linear equations

Sonia Fliss (1) , Sébastien Imperiale (2) , Antoine Tonnoir (3)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 M3DISIM - Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine
3 LMI - Laboratoire de Mathématiques de l'INSA de Rouen Normandie

In this work, we are interested in the construction of the exact transparent boundary conditions for a semi-discretized and fully discretized 1D linear PDE. The proposed method is quite general and is based on the computation of a family of canonical functions. Several examples and numerical results to illustrate the method are presented.

Mots clés: Unbounded domain; Discrete transparent boundary conditions; periodic media

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Sonia Fliss, Sébastien Imperiale, Antoine Tonnoir. Computation of the exact discrete transparent boundary condition for 1D linear equations. 2020. ⟨hal-02995046⟩