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A second-order
accurate method for solving the signed distance function
equation
Peter Schwartz and Phillip Colella |
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Vol. 5 (2010), No. 1, 81–97
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 65-02
Secondary: 76-02
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Milestones
Received: 5 February 2008
Revised: 9 July 2009
Accepted: 27 December 2009
Published: 3 February 2010
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Authors |
| Peter Schwartz | |
| Lawrence Berkeley National
Laboratory 1 Cyclotron Road, MS 50A-1148MS 50A-1148 Berkeley CA 94720 United States |
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| 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 |
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