Tim Barth's World:

Path Planning Examples Using Viscosity Solutions of Hamilton-Jacobi Equations Path Planning Examples Using Viscosity Solutions of Hamilton-Jacobi Equations:

[Mars Eikonal Solution]

Mars Terrain Navigation
Optimal Transit Time Paths Assuming
A Vehicle That Moves With Terrain
Slope Dependent Speed (click on image) 		.....
[Eikonal Solution]
Optimal Mountain Trek
Eikonal Solution Using P_2 (Quadratic) Approximation
(click on image) 		.....
[Eikonal Obstacle Solution] Obstacle Navigation
Eikonal Solution Using P_2 (Quadratic) Approximation
(click on image)




First Arrival Incident and Reflected Phase


Obstacle Problem

Short MPEG Movie Clips From Numerical Computations: Short MPEG Movie Clips From Numerical Computations:


[Minimal Surface]
Minimal Surface Evolution
Via Hamilton-Jacobi Equations 		[M=3 Step Flow]
Inviscid M=3 Step Flow

[Navier-Stokes Solution]
Numerical Navier-Stokes Solution
On Triangulated Domain (Mach Contours)


Some Recent Papers and Lecture Notes:

  • Numerical Methods for Conservation Laws on Unstructured Meshes Barth, T.J. , "Numerical Methods and Error Estimation for Conservation Laws on Structured and Unstructured Meshes", Von Karman Institute, LS04-2003, 2003, pp 1-65.
    • Error Estimation and Adaptive Discretization Methods in CFD

  • From Springer-Verlag Publishing.
    • "Error Estimation and Adaptive Discretization Methods in CFD", Lecture Notes on Computational Science and Engineering , T.J. Barth, H. Deconinck (Eds.), Vol. 25, 2003, 344 pages, hardcover.     		[Link: Springer LNCSE]


  • A-Posteriori Error Estimation for Higher Order Godunov Finite Volume Methods on Unstructured Meshes Barth, T.J. and Larson, M.G. , "A-Posteriori Error Estimation for Higher Order Godunov Finite Volume Methods on Unstructured Meshes", Finite Volumes for Complex Applications III, R. Herbin and D. Kroner (Eds), HERMES Science Publishing Ltd, London, June 2002, pp. 41-63.


  • A-Posteriori Error Estimation for Higher Order Godunov Finite Volume Methods on Unstructured Meshes Barth, T.J. and Larson, M.G. , "A-Posteriori Error Estimation for Higher Order Godunov Finite Volume Methods on Unstructured Meshes", Finite Volumes for Complex Applications III, R. Herbin and D. Kroner (Eds), HERMES Science Publishing Ltd, London, June 2002, pp. 41-63.


  • Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature Abgrall, R. and Barth, T.J. , "Residual Distribution Schemes for Conservation Laws Via Adaptive Quadrature", SIAM J. Sci. Comput., Vol. 24, No. 3, 2002, pp. 732--769.


  • Energy Stable Discontinuous Galerkin Discretization of First-Order Nonlinear Conservation Laws Barth, T.J., "Energy Stable Flux Formulas for the Discontinuous Galerkin Discretization of First-Order Nonlinear Conservation Laws", Proceedings ICFD NMFD 2001.


  • Energy Stable Flux Formulas for the Discontinuous Galerkin Discretization of First-Order Nonlinear Conservation Laws Barth, T.J. and Charrier, P. , "Energy Stable Flux Formulas for the Discontinuous Galerkin Discretization of First-Order Nonlinear Conservation Laws", NASA Ames Research Center Report #NAS-01-001, February 2001


  • Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension Barth, T.J. , "Simplified Discontinuous Galerkin Methods for Systems of Conservation Laws with Convex Extension", 1st International Conference on DG Methods, May 24-26, 1999, NASA Report NAS-99-009, also appears in Lecture Notes in Computational Science and Engineering , Springer-Verlag Pub., Vol. 11, 2000.


  • A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems Barth, T.J. and M.G. Larson, " A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems", 1st International Conference on DG Methods, May 24-26, 1999, NASA Report NAS-99-010, also appears in Lecture Notes in Computational Science and Engineering , Springer-Verlag Pub., Vol. 11, 2000.


    • Numerical Schemes for the Hamilton-Jacobi and LevelSet Equations on Triangulated Domains
  • Barth, T.J. and Sethian J.A., "Numerical Schemes for the Hamilton-Jacobi and LevelSet Equations on Triangulated Domains", J. Comp. Phys. , Vol. 145, No. 1, 1998, pp. 1--40.


    • A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Flow on Triangulated Domains Schur Complement Parallel Preconditioning
  • Barth, T.J., Chan, T.F. and Tang, W.-P., "A Parallel Non-Overlapping Domain-Decomposition Algorithm for Compressible Flow on Triangulated Domains", AMS Contemp. Math. , Vol. 218, 1998, pp. 23--41.


    • Symmetrization, Convex Entropies, Hyperbolics, Conservation Laws, etc.
  • Barth, T.J. , "Numerical Methods for Gasdynamic Systems on Unstructure Meshes", Lecture Notes in Computational Science and Engineering , Springer-Verlag Pub., Vol. 5, 1998, pp. 195--285.


    • Some Requested Papers From the Past:

  • T.J. Barth and D.C. Jespersen, AIAA 89-0366, The Design and Application of Upwind Schemes on Unstructured Meshes

  • T.J. Barth and P.O. Frederickson, AIAA 90-0013, Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction

  • Barth, T.J. Lecture Notes from VKI Lecture Series in CFD Course (4/94).

  • VKI Lecture Notes: Part 1 [.9Mb gzipped]

  • VKI Lecture Notes: Part 2 [1.1Mb gzipped]

  • VKI Lecture Notes: Part 3 [1.6Mb gzipped]

  • VKI Lecture Notes: Part 4 [2.3Mb gzipped]


    • NASA Code-IN Grants in Parallel Algorithm Research:


    Scalable Numerical Algorithms: J. Xu
  • NAG2-1236, Penn. State (J. Xu, Dept. of Mathematics) , "Scalable Numerical Algorithms on Nonhetrogeneous Computing Environments..."


    • Scalable Numerical Algorithms: T. Chan
  • NAG2-1238, U.C. Los Angeles (T.F. Chan, Dept. of Mathematics) , "Scalable Numerical Algorithms on Nonhetrogeneous Computing Environments..."



    • Items of Interest:

    Multiscale and Multiresolution Algorithms
  • You missed it!!! YES2000, The Yosemite Symposium on Advanced Multiscale and Multiresolution Methods. Oct 29 - Nov 1, 2000. Check the live Yosemite webcam.

  • You missed this too!! NATO/NASA/VKI Lecture Series, "Error Estimation and Solution Adaptive Methods for Computational Fluid Dynamics", To be held at the NASA Ames Research Center, September 10-14, 2001. More information

    Multiscale and Multiresolution Methods

  • From Springer-Verlag Publishing.
    • "Multiscale and Multiresolution Methods", Lecture Notes on Computational Science and Engineering , T.J. Barth, T. Chan, and R. Haimes (Eds.), Vol. 20, Nov. 2001, 384 pages, softcover. See the Table of Contents     		[Link: Springer LNCSE]











    $Created by: Timothy Barth, Last Modified: Dec. 3, 2002 8:15:57 by barth@nas.nasa.gov$