A double scale fast algorithm for the transient evolution of a resonant tunneling diode

Naoufel Ben Abdallah (1) , Ali Faraj (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ESISAR

The simulation of the time-dependent evolution of the resonant tunneling diode is done by a multiscale algorithm exploiting the existence of resonant states. After revisiting and improving the algorithm developed in [N. Ben Abdallah, O. Pinaud, J. Comp. Phys. 213 (2006) 288-310] for the stationary case, the time-dependent problem is dealt with. The wave function is decomposed into a non resonant part and a resonant one. The projection method to compute the resonant part leads to an accurate algorithm thanks to a suitable interpolation of the non resonant one. The simulation times are largely reduced.

Mots clés: nonlinear Schrödinger equation; time dependent; resonant states; numerical scheme; resonant tunneling diode

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

Naoufel Ben Abdallah, Ali Faraj. A double scale fast algorithm for the transient evolution of a resonant tunneling diode. 2015. ⟨hal-00479989v3⟩