Adaptive finite difference schemes based on interpolating wavelets for solving 2D Maxwell’s equations

This paper describes a 2D application of interpolating wavelets and recursive interpolation schemes with thresholding, aiming the representation of the electric and magnetic fields in nonuniform, adaptive grids. Applied to Maxwell´s equations, the method leads to sparse grids that adapt in space to the local smoothness of the fields, and at the same time track the evolution of the fields over time. In general, the number of points in the grid, N_s, is below the maximum number of points, N. It is possible to control N_s, by trading off representation accuracy and data compression, and therefore speed. A numerical example is presented showing the propagation of a Gaussian pulse within a 2D horn.