  We demonstrate that the efficiency of the boundary element whispering gallery
microcavity analysis can be improved by orders of magnitude with the inclusion
of Fresnel approximation. Using this formulation, simulation of a microdisk
with wave-number-radius product as large as $kR\approx8,000$ was demonstrated
in contrast to a previous record of $kR\approx100$. In addition to its high
accuracy on computing the modal field distribution and resonance wavelength,
this method yields a relative error of $10%$ in calculating the quality factor
as high as $10^{11}$ through a direct root searching method where the
conventional boundary element method failed to achieve. Finally, quadrupole
shaped cavities and double disks as large as $100 {\mu}m$ in diameter were
modeled by employing as few as $512$ boundary elements whilst the simulation of
such large cavities using conventional boundary element method were not
reported previously.
