The original formulation of the firefighter problem defines a discrete-time process where fire starts at designated subset vertices graph G. At each subsequent discrete time unit, propagates from burnt vertex to all its neighbors unless they are defended by that can move between any pair in single unit. Once is or defended, it remains state, and terminates when no longer spread. In this work, w...

In this paper, a monolithic arbitrary Lagrangian–Eulerian (ALE)-finite element method (FEM) is developed based upon novel ALE mapping for type of parabolic/mixed parabolic moving interface problem with jump coefficients. A stable Stokes-pair mixed FEM within specific stabilization technique and time-difference scheme are to discretize in both semi- fully discrete fashion, which the stability er...

Recent research developments in the area of spacetime metamaterial structures and systems have raised new questions as to how physics fundamental phenomena is altered presence modulation. In this context, we present a generalized comparative description phenomenon total internal reflection (TIR) at different dynamic interfaces. Such interfaces include, beyond classical corresponding boundaries ...

In this paper, we present a time and space rescaling scheme for the computation of moving interface problems. The idea is to map time–space such that the interfaces can evolve exponentially fast in the new time scale while the area/volume enclosed by the interface remains unchanged. The rescaling scheme significantly reduces the computation time (especially for slow growth), and enables one to ...

We deal with some parallel algorithms for the numerical approximation of the front propagation problem. The model describe an interface moving in the normal direction with velocity c(x) > 0.