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A second-order accurate method for solving the signed distance function equation. (English) Zbl 1190.65162

Summary: 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 S. Kim [SIAM J. Sci. Comput. 22, No. 6, 2178–2193 (2001; Zbl 0994.76080)] 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.

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
35F21 Hamilton-Jacobi equations

Citations:

Zbl 0994.76080
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