A computationally efficient phase-field model is developed for two-phase systems with
anisotropic interfacial energy. The approach allows for anisotropies sufficiently high that the …

Semiconductor heteroepitaxy involves a wealth of qualitatively different, competing
phenomena. Examples include three-dimensional island formation, injection of dislocations …

We propose a structure-preserving parametric finite element method (SP-PFEM) for
discretizing the surface diffusion of a closed curve in two dimensions (2D) or a surface in …

We extend the symmetrized parametric finite method for the evolution of a closed curve
under anisotropic surface diffusion in two dimensions, recently proposed by us [W. Bao, W …

We consider surface finite elements and a semi-implicit time step** scheme to simulate
fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier …

In this paper, we present a meshless radial basis function method to solve conservative
Allen–Cahn equation on smooth compact surfaces embedded in R 3, which can inherits the …

Geometrical evolution laws are widely used in continuum modeling of surface and interface
motion in materials science. In this article, we first give a brief review of various kinds of …

We propose a parametric finite element method (PFEM) for efficiently solving the
morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three …

We propose and analyze a unified structure-preserving parametric finite element method
(SP-PFEM) for the anisotropic surface diffusion of curves in two dimensions $(d= 2) $ and …

We proposed ways to implement meshless collocation methods extrinsically for solving
elliptic PDEs on smooth, closed, connected, and complete Riemannian manifolds with …