A p-variable higher-order finite volume time domain method for electromagnetic scattering problems

TL;DR

This paper introduces a p-variable finite volume time domain method that adaptively employs lower or higher order spatial operators in electromagnetic scattering simulations, reducing computational cost while maintaining overall accuracy.

Contribution

It presents a novel adaptive method that dynamically varies the spatial operator order locally in space and time during electromagnetic scattering simulations.

Findings

Achieves higher-order accuracy with reduced computational cost.

Demonstrates effectiveness on 2D electromagnetic scattering problems.

Maintains overall solution accuracy despite local use of lower-order operators.

Abstract

Higher-order accurate solution to electromagnetic scattering problems are obtained at reduced computational cost in a {\it p}-variable finite volume time domain method. Spatial operators of lower, including first-order accuracy, are employed locally in substantial parts of the computational domain during the solution process. The use of computationally cheaper lower order spatial operators does not affect the overall higher-order accuracy of the solution. The order of the spatial operator at a candidate cell during numerical simulation can vary in space and time and is dynamically chosen based on an order of magnitude comparison of scattered and incident fields at the cell center. Numerical results are presented for electromagnetic scattering from perfectly conducting two-dimensional scatterers subject to transverse magnetic and transverse electric illumination.