Vol. 5, No. 1, 2010

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ISSN: 2157-5452 (e-only)
ISSN: 1559-3940 (print)
A second-order accurate method for solving the signed distance function equation

Peter Schwartz and Phillip Colella

Vol. 5 (2010), No. 1, 81–97
Abstract

We present a numerical method for computing the signed distance to a piecewise-smooth surface defined as the zero set of a function. It is based on a marching method by Kim (2001) and a hybrid discretization of first- and second-order discretizations of the signed distance function equation. If the solution is smooth at a point and at all of the points in the domain of dependence of that point, the solution is second-order accurate; otherwise, the method is first-order accurate, and computes the correct entropy solution in the presence of kinks in the initial surface.

Keywords
eikonal, narrow band, Hamilton–Jacobi, signed distance function
Mathematical Subject Classification 2000
Primary: 65-02
Secondary: 76-02
Milestones
Received: 5 February 2008
Revised: 9 July 2009
Accepted: 27 December 2009
Published: 3 February 2010
Authors
Peter Schwartz
Lawrence Berkeley National Laboratory
1 Cyclotron Road, MS 50A-1148MS 50A-1148
Berkeley CA 94720
United States
http://seesar.lbl.gov/ANAG/staff/schwartz/index.html
Phillip Colella
Applied Numerical Algorithms Group
Lawrence Berkeley National Laboratory
1 Cyclotron Road MS 50A-1148
Berkeley CA 94720
United States