Adaptive Fast Interface Tracking Methods: Part I: Time Adaptivity
(English)Manuscript (preprint) (Other academic)
In this paper, we present a fast adaptive numerical method for interface tracking that uses an explicit multiresolution description of the interface. The interface 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 marker points, is O(N/dt), where N is the number of points on the interface and dt is the time step. The methods that we propose in this paper have O(tol^(-1/p)log N) computational cost, where tol is some given tolerance and p is the order of the numerical method for ordinary differential equations that is used for time advection of the interface. The adaptivity makes methods robust in the sense that they can handle problems with both smooth and non-smooth interfaces (i.e. interfaces with corners) while keeping low computational cost.
interface tracking, time adaptivity, multiresolution representation
IdentifiersURN: urn:nbn:se:kth:diva-105059OAI: oai:DiVA.org:kth-105059DiVA: diva2:568059
QS 20122012-11-152012-11-152012-11-16Bibliographically approved