论文标题
关于非线性麦克斯韦方程的更高级被动保存方案
On higher order passivity preserving schemes for nonlinear Maxwell's equations
论文作者
论文摘要
我们提出了两种策略设计的策略，以保留非线性KERR型媒体中Maxwell方程的高阶离散化方法。两种方法均基于空间和时间上的变异近似方案。这允许严格证明能源保护或耗散，从而在完全离散的级别上进行消极。对于线性介质，提出的方法与混合有限元和隐式runge-kutta方案的某些组合一致。在数值测试中的非线性问题也可以观察到最佳的最佳收敛速率，因此可以预期线性问题。
We present two strategies for designing passivity preserving higher order discretization methods for Maxwell's equations in nonlinear Kerr-type media. Both approaches are based on variational approximation schemes in space and time. This allows to rigorously prove energy conservation or dissipation, and thus passivity, on the fully discrete level. For linear media, the proposed methods coincide with certain combinations of mixed finite element and implicit Runge-Kutta schemes. The order optimal convergence rates, which can thus be expected for linear problems, are also observed for nonlinear problems in the numerical tests.
