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On accuracy and efficiency of constrained reinitialization
Author(s) -
Hartmann D.,
Meinke M.,
Schröder W.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2135
Subject(s) - set (abstract data type) , smoothing , level set method , mathematical optimization , level set (data structures) , displacement (psychology) , function (biology) , computer science , algorithm , mathematics , artificial intelligence , image (mathematics) , psychology , evolutionary biology , psychotherapist , image segmentation , computer vision , biology , programming language
The reinitialization, which is required to regularize the level set function, can be computationally expensive and hence is a determining factor for the overall efficiency of a level set method. However, it often has a significantly adverse impact on the accuracy of the level set solution. This short note is meant to shed light on the efficiency and accuracy issues of the reinitialization process. Using just one clearly defined level set propagation test case with an analytical solution the solutions obtained using a recently proposed efficient lower‐order constrained reinitialization (CR) scheme and standard low‐ and high‐order reinitialization schemes are juxtaposed to evidence the superiority of the novel CR formulation. It is shown that maintaining the location of the zero level set during the reinitialization is crucial for the accuracy and that the displacement caused by standard high‐order reinitialization schemes clearly outweighs the benefit of the high‐order smoothing of the level set function. Finally, results of a three‐dimensional problem are concisely reported to demonstrate the general applicability of the CR scheme. Copyright © 2009 John Wiley & Sons, Ltd.