Signal processing approach to mesh refinement in simulations of axisymmetric droplet dynamics

We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients principal curvature as function arclength through natural change variables. The trapezoidal rule applied those Fourier-type integrals and resulting formula fits in framework non-uniform fast transform. This observation enables efficiently use an envelope analysis smoothing filter generate guidelines two singularity formation scenarios. Applications also include non-iterative construction uniform parametrization important class plane curves, which used convergence study time-stepping procedure implemented previous work by Nitsche Steen [J. Comput. Phys. 200 (2004) 299].