Adaptive Wavelet Collocation Method for Simulation of Time Dependent Maxwell's Equations

TL;DR

This paper presents an adaptive wavelet collocation method for efficiently simulating time-dependent Maxwell's equations by dynamically adjusting the computational grid based on field localization, reducing computational costs.

Contribution

It introduces a novel adaptive wavelet collocation approach that dynamically refines the grid during simulation, improving efficiency for electromagnetic problems.

Findings

High compression rate reduces computational cost.

Effective for simulating guided-wave optical devices.

Dynamic grid adaptation enhances accuracy in localized regions.

Abstract

This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of the field at that time instant. In the regions where the fields are highly localized, the method assigns more grid points; and in the regions where the fields are sparse, there will be less grid points. On the adapted grid, update schemes with high spatial order and explicit time stepping are formulated. The method has high compression rate, which substantially reduces the computational cost allowing efficient use of computational resources. This adaptive wavelet collocation method is especially suitable for simulation of guided-wave optical devices.