2 spheres collapsing

The initial front is made of a plane of equation spheres with a radius r₀ = 1 and the speed is defined by c(x,t) = 1 -t. The final time is T=3 and the time stride is Δt = 0.1. As long as the speed is positive the circles will propagate forward. At t=1, the speed changes of sign and the circles start propagating backward.

Plane rotation

This example computed with the Generalized Fast Marching Method in a 3 dimensional mesh. The initial condition is a plane defined by u₀(x) = x₂ + x₁ - 1, and the velocity function by c(x,t) = x₁. The final time is T = 1.

Van Der Pol oscillator

We compute the minimum time function to reach the target

C = {(x1,x2), x21 + x22 ≤ 0.22},r0 > 0

With α ∈ [-1,1], the dynamic is given by :

( x ) f(x1,x2,α) = - x + x (12- x2)+ α 1 2 1