Asymptotics for the level set equation near a maximum

A Discontinuous Spectral Element Method for the Level Set Equation

Near-Isometric Level Set Tracking

Implicit representations of geometry have found applications in shape modeling, simulation, and other graphics pipelines. These representations, however, do not provide information about the paths of individual points as shapes move and undergo deformation. For this reason, we reconsider the problem of tracking points on level set surfaces, with the goal of designing an algorithm that — unlike ...

Asymptotics for the biharmonic equation near the tip of a crack

A BINARY LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION

This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jac...

Fine Asymptotics near Extinction and Elliptic Harnack Inequalities for the Fast Diffusion Equation

We consider the Fast Diffusion Equation (FDE) ut = ∆u in a bounded smooth domain Ω ⊂ R with homogeneous Dirichlet conditions; the exponent range is ms = (d − 2)+/(d + 2) < m < 1. It is known that bounded positive solutions u(t, x) of such problem extinguish in a finite time T , and also that such solutions approach a separate variable solution u(t, x) ∼ (T − t)1/(1−m)f(x), as t → T−. We show th...