Regularized Wulff Flows, Nonconvex Energies and Backwards Parabolic Equations
نویسندگان
چکیده
In this paper we propose a method of regularizing the backwards parabolic partial differential equations that arise from using gradient descent to minimize surface energy integrals within a level set framework in 2 and 3 dimensions. The proposed regularization energy is a functional of the mean curvature of the surface. Our method uses a local level set technique to evolve the resulting fourth order PDEs in time. Numerical results are shown, indicating stability and convergence to the asymptotic Wulff shape.
منابع مشابه
A Variational Principle for Gradient Flows of Nonconvex Energies
We present a variational approach to gradient flows of energies of the form E = φ1−φ2 where φ1, φ2 are convex functionals on a Hilbert space. A global parameter-dependent functional over trajectories is proved to admit minimizers. These minimizers converge up to subsequences to gradient-flow trajectories as the parameter tends to zero. These results apply in particular to the case of non λ-conv...
متن کاملSolving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method
We present efficient, second-order accurate and adaptive finite-difference methods to solve the regularized, strongly anisotropic Cahn–Hilliard equation in 2D and 3D. When the surface energy anisotropy is sufficiently strong, there are missing orientations in the equilibrium level curves of the diffuse interface solutions, corresponding to those missing from the sharp interface Wulff shape, and...
متن کاملEvans-krylov Estimates for a Nonconvex Monge Ampère Equation
We establish Evans-Krylov estimates for certain nonconvex fully nonlinear elliptic and parabolic equations by exploiting partial Legendre transformations. The equations under consideration arise in part from the study of the “pluriclosed flow” introduced by the first author and Tian [28].
متن کاملA Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).
This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...
متن کاملStability and convergence of fully discrete Galerkin FEMs for the nonlinear thermistor equations in a nonconvex polygon
In this paper, we establish the unconditional stability and optimal error estimates of a linearized backward Euler–Galerkin finite element method (FEM) for the time-dependent nonlinear thermistor equations in a two-dimensional nonconvex polygon. Due to the nonlinearity of the equations and the non-smoothness of the solution in a nonconvex polygon, the analysis is not straightforward, while most...
متن کامل