# A Fast-marching Algorithm for Nonmonotonically Evolving Fronts

@article{Tcheng2016AFA, title={A Fast-marching Algorithm for Nonmonotonically Evolving Fronts}, author={Alexandra Tcheng and Jean-Christophe Nave}, journal={SIAM J. Scientific Computing}, year={2016}, volume={38} }

- Published in SIAM J. Scientific Computing 2016
DOI:10.1137/15M1017302

The non-monotonic propagation of fronts is considered. When the speed function F : Rn × [0, T ]→ R is prescribed, the non-linear advection equation φt + F |∇φ| = 0 is a HamiltonJacobi equation known as the level-set equation. It is argued that a small enough neighbourhood of the zero-level-setM of the solution φ : Rn × [0, T ]→ R is the graph of ψ : Rn → R where ψ solves a Dirichlet problem of the form H(u, ψ(u),∇ψ(u)) = 0. A fast-marching algorithm is presented where each point is computed… CONTINUE READING

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 37 REFERENCES

## Convergence of a Generalized Fast-Marching Method for an Eikonal Equation with a Velocity-Changing Sign

VIEW 15 EXCERPTS

HIGHLY INFLUENTIAL

## Convergent Difference Schemes for Degenerate Elliptic and Parabolic Equations: Hamilton-Jacobi Equations and Free Boundary Problems

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Redistancing by flow of time dependent eikonal equation

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations

VIEW 2 EXCERPTS

HIGHLY INFLUENTIAL

## A fast marching level set method for monotonically advancing fronts.

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Fast marching algorithms for non-monotonically evolving fronts

## Analysis of high order fast interface tracking methods

VIEW 1 EXCERPT