Analysis of high order fast interface tracking methods (Q466052)

The paper is devoted to the construction and analysis of fast high-order methods for tracking a front in a given velocity field. The methods begin with a high-order subdivision of the interface on which a multiresolution decomposition is based. Then it is shown that the associated wavelet vectors can be identified with the solutions to certain ordinary differential equations (ODEs). When numerically solving these ODEs, an important observation is that the step sizes of the solvers may be chosen in a way that depends on the wavelet scales. This allows to use computationally cheap methods for a large part of the work, and so the overall complexity is much smaller than in a straightforward approach. The author proves sufficient conditions on the stability properties of the ODE solver in order for the complete algorithm to be rapdily convergent. It turns out that, e.g., all explicit Runge-Kutta methods are admissible for properly chosen subdivision schemes.