Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4967718 | Journal of Computational Physics | 2017 | 20 Pages |
Abstract
In this paper, we present a fast time adaptive numerical method for interface tracking. The method uses an explicit multiresolution description of the interface, which is represented by wavelet vectors that correspond to the details of the interface on different scale levels. The complexity of standard numerical methods for interface tracking, where the interface is described by N marker points, is O(N/Ît), when a time step Ît is used. The methods that we propose in this paper have O(TOLâ1/plogâ¡N+Nlogâ¡N) computational cost, at least for uniformly smooth problems, where tol is some given tolerance and p is the order of the time stepping method that is used for time advection of the interface. The adaptive method is robust in the sense that it can handle problems with both smooth and piecewise smooth interfaces (e.g. interfaces with corners) while keeping a low computational cost. We show numerical examples that verify these properties.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Jelena Popovic, Olof Runborg,