Simplex Free Adaptive Tree Fast Sweeping and Evolution Methods for Solving Level Set Equations in Arbitrary Dimension

Abstract

We introduce simplex free adaptive tree numerical methods for solv- ing static and time dependent Hamilton-Jacobi equations arising in level set problems in arbitrary dimension. The data structure upon which our method is built is a generalized n-dimensional binary tree, but it does not require the complicated splitting of cubes into simplices (aka gen- eralized n-dimensional triangles or hypertetrahedrons) that current tree based methods require. It has enough simplicity that minor variants of standard numerical Hamiltonians developed for uniform grids can be ap- plied, yielding consistent, monotone, convergent schemes. Combined with the fast sweeping strategy, the resulting tree based methods are highly e cient and accurate. Thus, without changing more than a few lines of code when changing dimension, we have obtained results for calculations in up to n = 7 dimensions.

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Document Details

Document Type
Technical Report
Publication Date
May 06, 2005
Accession Number
ADA438295

Entities

People

  • Jianming Qian
  • S. J. Osher
  • T. C. Cecil

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Computational Complexity
  • Computer Science
  • Computers
  • Convergence
  • Curvature
  • Data Storage Systems
  • Equations
  • Errors
  • Grids
  • Materials
  • Materials Science
  • Mathematics
  • Personal Information Managers
  • Surface Tension
  • Trees (Data Structures)

Fields of Study

  • Mathematics

Readers

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