Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations

Osher, Stanley; Sethian, James A.

New numerical algorithms are devised (PSC algorithms) for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front can also be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand-sides, by using techniques from the hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be used also for more general Hamilton-Jacobi-type problems. The algorithms are demonstrated by computing the solution to a variety of surface motion problems.

Document ID

19880001113

Acquisition Source

Legacy CDMS

Document Type

Preprint (Draft being sent to journal)

Authors

Date Acquired

September 5, 2013

Publication Date

September 1, 1987

Subject Category

Report/Patent Number

Accession Number

88N10495

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Distribution Limits

Public

Work of the US Gov. Public Use Permitted.

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