Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations

Abstract

We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p, q) = square root of ap(expn 2) + bq(expn 2) - 2cpq, c(expn 2) < ab. We combine our Godunov numerical fluxes with simple Gauss-Seidel-type iterations for solving the corresponding Hamilton Jacobi (HJ) equations. The resulting algorithm is fast since it does not require a sorting strategy as found, e.g., in the fast marching method. In addition, it provides a way to compute solutions to a class of HJ equations for which the conventional fast marching method is not applicable. Our experiments indicate convergence after a few iterations, even in rather difficult cases.

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Document Details

Document Type
Technical Report
Publication Date
May 06, 2003
Accession Number
ADA636928

Entities

People

  • Hong-kai Zhao
  • Li-tien Cheng
  • Stanley Osher
  • Yen-hsi R. Tsai

Organizations

  • Princeton University

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Algorithms
  • Anisotropy
  • Applied Mathematics
  • Boundaries
  • Coefficients
  • Computations
  • Computer Vision
  • Convergence
  • Coordinate Systems
  • Equations
  • Equations Of State
  • Grids
  • Iterations
  • Mathematics
  • Quadratic Equations
  • Steady State
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research