Back and Forth Error Compensation and Correction Methods for Removing Errors Induced by Uneven Gradients of the Level Set Function

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Title: Back and Forth Error Compensation and Correction Methods for Removing Errors Induced by Uneven Gradients of the Level Set Function
Author: Dupont, Todd F. ; Liu, Yingjie
Abstract: We propose a method that signi cantly improves the accuracy of the level set method and could be of fundamental importance for numerical solutions of di fferential equations in general. Level set method uses the level set function, usually an approximate signed distance function Φ to represent the interface as the zero set of Φ. When Φ is advanced to the next time level by an advection equation, its new zero level set will represent the new interface position. But the non zero curvature of the interface will result in uneven gradients of the level set function which induces extra numerical error. Instead of attempting to reduce this error directly, we update the level set function Φ forward in time and then backward to get another copy of the level set function, say Φ[1]. Φ[1] and Φ should have be equal if there were no numerical error. Therefore Φ - Φ[1] provides us the information of error induced by uneven gradients and this information can be used to compensate Φ before updating Φ forward again in time.
Description: AMS subject classifications. 65M60, 65M12
Type: Pre-print
URI: http://hdl.handle.net/1853/29473
Date: 2002
Contributor: Georgia Institute of Technology. School of Mathematics
University of Chicago. Dept. of Computer Science
Relation: CDSNS2002-389
Publisher: Georgia Institute of Technology
Subject: Flux corrected transport
Front tracking
Level set method

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