arXiv subjects

Christian Rasch

Publications and source records attributed to Christian Rasch.

2 recordsLinked to original sources

arXiv2007

Remarks on the O(N) Implementation of the Fast Marching Method

The fast marching algorithm computes an approximate solution to the eikonal equation in O(N log N) time, where the factor log N is due to the administration of a priority queue. Recently, Yatziv, Bartesaghi and Sapiro have suggested to use an untidy priority queue, reducing the overall complexity to O(N) at the price of a small error in the computed solution. In this paper, we give an explicit estimate of the error introduced, which is based on a discrete comparison principle. This estimates implies in particular that the choice of an accuracy level that is independent of the speed function F results in the complexity bound O(Fmax /Fmin N). A numerical experiment illustrates this robustness problem for large ratios Fmax /Fmin .

math.NA↗

arXiv2004

Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.

math.NA↗