Application of Dey–Mittra conformal boundary algorithm to 3D electromagnetic modeling

The Dey–Mittra conformal boundary conditions have been implemented for the finite-difference time-domain (FDTD) electromagnetic solver of the VORPAL plasma simulation framework and studied in the context of three-dimensional, large-scale computations. The maximum stable time step when using these boundary conditions can be arbitrarily small, due to the presence of small fractional cells inside the vacuum region. Use of the Gershgorin Circle theorem allows the determination of a rigorous criterion for exclusion of small cells in order to have numerical stability for particular values of the ratio f DM ≡ Δ t / Δ t CFL of the time step to the Courant–Friedrichs–Lewy value for the infinite system. Application to a spherical cavity shows that these boundary conditions allow computation of frequencies with second-order error for sufficiently small f DM . However, for sufficiently fine resolution, dependent on f DM , the error becomes first order, just like the error for stair-step boundary conditions. Nevertheless, provided one does use a sufficiently small value of f DM , one can obtain third-order accuracy through Richardson extrapolation. Computations for the TESLA superconducting RF cavity design compare favorably with experimental measurements.