Comptes Rendus
Evaluating a distance function
Rémi Abgrall1 
1Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023), pp. 5-15

Computing the distance function to some surface or line is a problem that occurs very frequently. There are several ways of computing a relevant approximation of this function, using for example technique originating from the approximation of Hamilton Jacobi problems, or the fast sweeping method. Here we make a link with some elliptic problem and propose a very fast way to approximate the distance function.

Received:
Revised:
Accepted:
Online First:
Published online:
DOI: 10.5802/crmeca.155
Keywords: Hamilton jacobi equation, distance function, Hopf-Cole transformation, elliptic problem, linear solver

Rémi Abgrall  1

1 Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Rémi Abgrall. Evaluating a distance function. Comptes Rendus. Mécanique, The scientific legacy of Roland Glowinski, Volume 351 (2023), pp. 5-15. doi: 10.5802/crmeca.155
@article{CRMECA_2023__351_S1_5_0,
     author = {R\'emi Abgrall},
     title = {Evaluating a distance function},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {5--15},
     year = {2023},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {351},
     number = {S1},
     doi = {10.5802/crmeca.155},
     language = {en},
}
TY  - JOUR
AU  - Rémi Abgrall
TI  - Evaluating a distance function
JO  - Comptes Rendus. Mécanique
PY  - 2023
SP  - 5
EP  - 15
VL  - 351
IS  - S1
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.155
LA  - en
ID  - CRMECA_2023__351_S1_5_0
ER  - 
%0 Journal Article
%A Rémi Abgrall
%T Evaluating a distance function
%J Comptes Rendus. Mécanique
%D 2023
%P 5-15
%V 351
%N S1
%I Académie des sciences, Paris
%R 10.5802/crmeca.155
%G en
%F CRMECA_2023__351_S1_5_0

[1] Stanley Osher; Chi-Wang Shu High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal., Volume 28 (1991) no. 4, pp. 907-922 | DOI | Zbl | MR

[2] Rémi Abgrall Numerical discretization of the first-order Hamilton–Jacobi equation on triangular meshes, Commun. Pure Appl. Math., Volume 49 (1996) no. 12, pp. 1339-1373 | DOI | Zbl | MR

[3] James A. Sethian Fast marching methods, SIAM Rev., Volume 41 (1999) no. 2, pp. 199-235 | DOI | Zbl | MR

[4] Hiroaki Nishikawa A hyperbolic Poisson solver for wall distance computation on irregular triangular grids, J. Comput. Phys., Volume 445 (2021), 110599 | DOI | MR | Zbl

[5] Christopher Basting; Dmitri Kuzmin A minimization-based finite element formulation for interface-preserving level set reinitialization, Computing, Volume 95 (2013) no. S1, pp. 13-25 | DOI | MR

[6] Thomas Adams; Stefano Giani; William M. Coombs A high-order elliptic PDE based level set reinitialisation method using a discontinuous Galerkin discretisation, J. Comput. Phys., Volume 379 (2019), pp. 373-391 | DOI | Zbl | MR

[7] Guy Barles Solutions de viscosité des équations de Hamilton–Jacobi, Mathématiques & Applications (Berlin), 17, Springer, 1994 | MR | Zbl

[8] Rémi Abgrall Construction of simple, stable, and convergent high order schemes for steady first order Hamilton–Jacobi equations, SIAM J. Sci. Comput., Volume 31 (2009) no. 4, pp. 2419-2446 | MR | DOI | Zbl

[9] Pascal Hénon; Pierre Ramet; Jean Roman PaStiX: A High-Performance Parallel Direct Solver for Sparse Symmetric Definite Systems, Parallel Comput., Volume 28 (2002) no. 2, pp. 301-321 | DOI | Zbl | MR

[10] Christophe Geuzaine; Jean-François Remacle Gmsh: a 3-D finite element mesh generator with built-in pre- and post-processing facilities, Int. J. Numer. Methods Eng., Volume 79 (2009) no. 11, pp. 1309-1331 | DOI | MR | Zbl

[11] Hao Liu; Roland Glowinski; Shingyu Leung; Jianliang Qian A finite element/operator-splitting method for the numerical solution of the three dimensional Monge–Ampère equation, J. Sci. Comput., Volume 81 (2019) no. 3, pp. 2271-2302 | DOI | Zbl

[12] Roland Glowinski; Hao Liu; Shingyu Leung; Jianliang Qian A finite element/operator-splitting method for the numerical solution of the two dimensional elliptic Monge–Ampère equation, J. Sci. Comput., Volume 79 (2019) no. 1, pp. 1-47 | DOI | Zbl

[13] Alexandre Caboussat; Roland Glowinski; Dimitrios Gourzoulidis A least-squares/relaxation method for the numerical solution of the three-dimensional elliptic Monge–Ampère equation, J. Sci. Comput., Volume 77 (2018) no. 1, pp. 53-78 | DOI | Zbl

Cited by Sources:

Comments - Policy