A second‐order accurate method for solving the eikonal equation | Zendy

Schwartz Peter | Zendy; Colella Phil | Zendy

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A second‐order accurate method for solving the eikonal equation

Author(s) -

Schwartz Peter,

Colella Phil

Publication year - 2007

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.200701032

Subject(s) - eikonal equation , discretization , piecewise , mathematics , mathematical analysis , fast marching method , order (exchange) , function (biology) , point (geometry) , algorithm , geometry , finance , evolutionary biology , economics , biology

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 and a hybrid discretization of first‐ and second‐order discretizations of the eikonal 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 computes the correct entropy solution in the presence of kinks in the initial surface. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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