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

TL;DR

This paper introduces a fast, multiscale algorithm for simulating the time-dependent behavior of resonant tunneling diodes, improving computational efficiency by decomposing wave functions and interpolating non-resonant parts.

Contribution

It extends and refines a previous stationary algorithm to handle time-dependent evolution, significantly reducing simulation times through a novel wave function decomposition and interpolation approach.

Findings

Simulation times are significantly reduced.

The algorithm accurately captures resonant states.

Improved efficiency over previous methods.

Abstract

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.