Distance function and extension in normal direction for implicitly defined interfaces

Peter  Frolkovič; Karol  Mikula; Jozef  Urbán

doi:10.3934/dcdss.2015.8.871

Article Contents

2015, Volume 8, Issue 5: 871-880. Doi: 10.3934/dcdss.2015.8.871

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Distance function and extension in normal direction for implicitly defined interfaces

1.
Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava

Received: December 31, 2013

Revised: May 31, 2014

Published: October 2015

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Abstract

In this paper we present a novel application of extrapolation procedure for three popular numerical algorithms to compute the distance function for an interface that is given only implicitly. The methods include the fast marching method [8], the fast sweeping method [10] and the linearization method [10]. The extrapolation procedure removes the necessity of a special initialization procedure for the grid nodes next to the interface that is used so far with the methods, thus it represents a natural extension of these methods. The extrapolation procedure can be used also for an extension of a function that is defined only locally on the interface in the direction given by the gradient of distance function [2].

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Mathematics Subject Classification: Primary: 35L50, 76M12; Secondary: 65L20.

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References

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