Analysis of high order fast interface tracking methods

Runborg, Olof

doi:10.1007/s00211-014-0613-5

Cited by 4 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is to be noted that in order to control the resolution of wavefronts, we can also adapt and include other front tracking methods, such as the grid-based particle method [35] and the fast interface tracking method [36,37], in the algorithm. The main contributions of this paper include the second step of the algorithm in part 1, i.e.…”

Section: Introductionmentioning

confidence: 99%

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

Motamed

Runborg

2015

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

a b s t r a c tWe present a novel wavefront method based on Gaussian beams for computing high frequency wave propagation problems. Unlike standard geometrical optics, Gaussian beams compute the correct solution of the wave field also at caustics. The method tracks a front of two canonical beams with two particular initial values for width and curvature. In a fast post-processing step, from the canonical solutions we recreate any other Gaussian beam with arbitrary initial data on the initial front. This provides a simple mechanism to include a variety of optimization processes, including error minimization and beam width minimization, for a posteriori selection of optimal beam initial parameters. The performance of the method is illustrated with two numerical examples.Published by Elsevier Ltd.

show abstract

Section: Introductionmentioning

confidence: 99%

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

Motamed

Runborg

2015

Computers & Mathematics with Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…Its meshsize is bounded below by a predetermined parameter h, and its vertices provide a discrete sampling of M. Given t ∈ (0, T ), the front C t can be recovered using interpolation. Methods with a similar flavour have been explored in [24] which presents a high order fast interface tracking method, and [17] where the authors formulate n 'quasilinear PDEs satisfied by the manifold's local parametrization' and 'solve that system locally in an Eulerian framework'.…”

mentioning

confidence: 99%

A Fast-marching Algorithm for Nonmonotonically Evolving Fronts

Tcheng¹,

Nave²

2016

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. The non-monotonic propagation of fronts is considered. When the speed function F : R n × [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-set M of the solution φ : R n × [0, T ] → R is the graph of ψ : R n → 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 using a discretization of such a Dirichlet problem, with no restrictions on the sign of F . The output is a directed graph whose vertices evenly sample M. The convergence, consistency and stability of the scheme are addressed. Bounds on the computational complexity are estimated, and experimentally shown to be on par with the Fast Marching Method. Examples are presented where the algorithm is shown to be globally first-order accurate. The complexities and accuracies observed are independent of the monotonicity of the evolution.

show abstract

Adaptive fast interface tracking methods

Popovic¹,

Runborg

2017

Journal of Computational Physics

View full text Add to dashboard Cite

Analysis of high order fast interface tracking methods

Cited by 4 publications

References 25 publications

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

A wavefront-based Gaussian beam method for computing high frequency wave propagation problems

A Fast-marching Algorithm for Nonmonotonically Evolving Fronts

Adaptive fast interface tracking methods

Contact Info

Product

Resources

About