Ordered upwind methods for static Hamilton–Jacobi equations

DOI10.1073/pnas.201222998zbMath1002.65112OpenAlexW2094668823WikidataQ33944251 ScholiaQ33944251MaRDI QIDQ4547681

Alexander Vladimirsky, James A. Sethian

Publication date: 11 September 2002

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: http://www.pnas.org/content/vol98/issue20/#APPLIED_MATHEMATICS

zbMATH Keywords

optimal controlfinite difference methodeikonal equationseismologycharacteristicsstatic Hamilton-Jacobi equationsordered upwind methodspaths on surfaces

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Finite difference methods for boundary value problems involving PDEs (65N06) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25) Boundary value problems for nonlinear first-order PDEs (35F30)

Related Items

Noise-induced transition in the Zeldovich–Semenov model with local and global bifurcations, Transport and diffusion of material quantities on propagating interfaces via level set methods., A paraxial formulation for the viscosity solution of quasi-P eikonal equations, Legendre-transform-based fast sweeping methods for static Hamilton-Jacobi equations on triangulated meshes, An efficient jet marcher for computing the quasipotential for 2D SDEs. Enhancing accuracy and efficiency of quasipotential solvers, Neighbor-gradient single-pass method for solving anisotropic eikonal equation, Fast-phase space computation of multiple arrivals, A Fast-marching Algorithm for Nonmonotonically Evolving Fronts, A level set-based Eulerian approach for anisotropic wave propagation, Convergence rate for the ordered upwind method, A fast sweeping method for static convex Hamilton-Jacobi equations, Ordered line integral methods for computing the quasi-potential, High order fast sweeping methods for static Hamilton-Jacobi equations, A uniformly second order fast sweeping method for eikonal equations, Estimation of reactive fluxes in gradient stochastic systems using an analogy with electric circuits, Fast sweeping methods for hyperbolic systems of conservation laws at steady state, A low complexity algorithm for non-monotonically evolving fronts, Numerical simulation of pedestrian flow past a circular obstruction, Computing the quasipotential for nongradient SDEs in 3D, Lax-Friedrichs sweeping scheme for static Hamilton-Jacobi equations, Finding the quasipotential for nongradient SDEs, A linear finite-difference scheme for approximating randers distances on cartesian grids, Impact of heterogeneity upon the accuracy of the eikonal solution using the fast marching method, Numerical geometric acoustics: an eikonal-based approach for modeling sound propagation in 3D environments, Numerical solution to optimal feedback control by dynamic programming approach: a local approximation algorithm, A fast single-pass method for solving the generalized eikonal equation in a moving medium, A Model for Optimal Human Navigation with Stochastic Effects, A Hamilton-Jacobi framework for modeling folds in structural geology, Alternating evolution methods for static Hamilton-Jacobi equations, From Bellman to Dijkstra: Set-Oriented Construction of Globally Optimal Controllers, PDE-Based Multidimensional Extrapolation of Scalar Fields over Interfaces with Kinks and High Curvatures, A second order discontinuous Galerkin fast sweeping method for eikonal equations, Single pass computation of first seismic wave travel time in three dimensional heterogeneous media with general anisotropy, A numerical framework for modeling folds in structural geology, Convergence analysis of the fast sweeping method for static convex Hamilton-Jacobi equations, Transient drainage volume characterization and flow simulation in reservoir models using the fast marching method, Information-seeking control under visibility-based uncertainty, An ordered line integral method for computing the quasi-potential in the case of variable anisotropic diffusion, Hybrid fast sweeping methods for anisotropic eikonal equation in two-dimensional tilted transversely isotropic media, Modeling wildland fire propagation with level set methods, An efficient algorithm for Hamilton-Jacobi equations in high dimension, An ordered upwind method with precomputed stencil and monotone node acceptance for solving static convex Hamilton-Jacobi equations, A rotating-grid upwind fast sweeping scheme for a class of Hamilton-Jacobi equations, Optimal paths for variants of the 2D and 3D Reeds-Shepp car with applications in image analysis, Computing the quasipotential for highly dissipative and chaotic SDEs an application to stochastic Lorenz'63, Minimal Stencils for Discretizations of Anisotropic PDEs Preserving Causality or the Maximum Principle, A set oriented approach to global optimal control, A Fast Eulerian Approach for Computation of Global Isochrons in High Dimensions, Modeling Environmental Crime in Protected Areas Using the Level Set Method, Corner cases, singularities, and dynamic factoring, Riemannian Fast-Marching on Cartesian Grids, Using Voronoi's First Reduction of Quadratic Forms, An immersed boundary method for geometrical shock dynamics, Optimal Control with Budget Constraints and Resets, A third order fast sweeping method with linear computational complexity for eikonal equations

Cites Work

• A note on two problems in connexion with graphs
• On Deterministic Control Problems: An Approximation Procedure for the Optimal Cost I. The Stationary Problem
• Computing geodesic paths on manifolds
• A Viscosity Solutions Approach to Shape-From-Shading
• Level Sets of Viscosity Solutions: some Applications to Fronts and Rendez-vous Problems
• Fast methods for the Eikonal and related Hamilton– Jacobi equations on unstructured meshes
• An O(N log N) algorithm for shape modeling.
• Efficient algorithms for globally optimal trajectories
• A fast marching level set method for monotonically advancing fronts.