An adaptive local discrete convolution method for the numerical solution of Maxwell's equations
This work provides a novel numerical method for computational electromagnetics, enabling efficient and accurate simulations on adaptive grids, which is important for applications requiring high resolution in localized regions.
The authors developed an adaptive local discrete convolution method for solving 3D free-space Maxwell's equations on locally refined grids, achieving high accuracy and efficiency. The method uses compact convolution kernels and the method of spherical means, enabling stable time stepping with large Courant numbers.
We present a numerical method for solving the free-space Maxwell's equations in three dimensions using compact convolution kernels on a rectangular grid. We first rewrite Maxwell's Equations as a system of wave equations with auxiliary variables and discretize its solution from the method of spherical means. The algorithm has been extended to be used on a locally-refined nested hierarchy of rectangular grids.