非均质纳米器件 Maxwell-Schrödinger 方程组多尺度方法研究

Numerical calculations for the Maxwell-Schrödinger equations in heterogeneous nanodevices are of great significance to predict the electromagnetic performance of nanodevices and develop new nanodevices. However, it is challenging to carry out the numerical anaylsis and algorithms design for the Maxwell-Schrödinger equations in heterogeneous nanodevices. This project will discuss the electromagnetic problems of nanodevices and focus on the nonlinear Maxwell-Schrödinger coupled equations deeply and systematically. The research contents mainly involve multiscale analysis, multiscale algorithms, multiscale numerical simulations of the Maxwell-Schrödinger equations in heterogeneous nanodevices. The research objectives include: (1) the multiscale asymptotic methods for the nonlinear Maxwell-Schrödinger coupled equations will be presented and the convergence results will be derived, (2) the high-efficency multiscale numerical algorithms for solving the nonlinear Maxwell-Schrödinger coupled equations will be advanced and the convergence will be proved, (3) the multiscale numerical simulations for the nonlinear Maxwell-Schrödinger coupled equations will be realized based on the multiscale methods presented in this project.

非均质纳米器件 Maxwell-Schrödinger 方程组的数值计算对于纳米器件电磁性能预测和新型纳米器件设计具有重要意义，但其数值分析与算法设计非常具有挑战性。本项目拟研究非均质纳米器件中的电磁问题，针对非线性 Maxwell-Schrödinger 耦合方程组开展系统、深入的研究。研究内容主要涉及非均质纳米器件 Maxwell-Schrödinger 方程组的多尺度分析、多尺度算法和多尺度数值模拟。研究目标包括：（1）对非线性 Maxwell-Schrödinger 耦合方程组，提出多尺度渐近方法, 并给出收敛性结果；（2）对非线性 Maxwell-Schrödinger 耦合方程组的求解，发展高效的多尺度数值算法，并给出算法的收敛性证明；（3）基于本项目提出的多尺度方法，实现非线性 Maxwell-Schrödinger 耦合方程组的多尺度数值模拟。