  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.
