The Eulerian method

• Discussion on Theory
• Status Report

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Reproduction of Sethian and Osher's work on Propagating Fronts

These are curves moving under their own curvature as determined by the speed function, F(K), where K is the mean curvature.

• 1-D Cosine Front Propagation: psi=cos(6*pi*x) with speed function F(K) = 1-e*K
  • Numerical Method
  • e=0.025, psi=1
  • e=0.100, psi=1
• 1-D Cosine Front Propagation: psi=cos(2*pi*x) with F(K) = -K
  • Numerical Method
  • most recent plot, psi=1
• Two Dimensions: 7-point star propagation, F(K)=1
  • Numerical Method
  • Initial Data contour plot
  • Time Evolved Data contour plot
• Two Dimensions: 7-point star propagation, F(K)=-K
  • Initial Data contpur plot
  • Time Evolved Data contour plot

Application to curved space

Same cosine propagation with added curved space (external damping factor exp[-t^2/s^2]) showing the dependence of the shape of the front on the curved spacetime.

• e=0.100, psi=cos(x*pi)