Summary: We introduce a new method for approximating the Biot-Savart integral for elliptic Gaussian functions using high-order interpolation and compare it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coefficients by interpolating precomputed values from look-up tables over a wide range of aspect ratios.
When implemented in a full nonlinear vortex method, we find that the new technique is almost three times faster and, unlike the asymptotic method, provides uniform accuracy over the full range of aspect ratios. As a proof-of-concept for large scale computations, we use the new technique to calculate inviscid axisymmetrization and filamentation of a two-dimensional elliptic fluid vortex. We compare our results with those from a pseudo-spectral computation and from electron vortex experiments, and find good agreement among the three approaches.