A Crank-Nicolson Finite Element Method and the Optimal Error Estimates for the modified Time-dependent Maxwell-Schrödinger Equations
Provides a stable numerical method with rigorous error bounds for simulating quantum semiconductor devices coupled with electromagnetic fields.
The paper develops a Crank-Nicolson finite element method for the time-dependent Maxwell-Schrödinger equations and proves optimal energy-norm error estimates without time-step restrictions, validated by numerical tests.
In this paper we consider the initial-boundary value problem for the time-dependent Maxwell-Schrödinger equations, which arises in the interaction between the matter and the electromagnetic field for the semiconductor quantum devices. A Crank-Nicolson finite element method for solving the problem is presented. The optimal energy-norm error estimates for the numerical algorithm without any time-step restrictions are derived. Numerical tests are then carried out to confirm the theoretical results.