The phase field theory describing the evolution of a dual phase boundary is extended to
multiphase problems: Each phase is identified with an individual phase field and the …

We introduce a new relaxation scheme for structural topology optimization problems with
local stress constraints based on a phase-field method. In the basic formulation we have a …

The majority of advanced engineering materials contain multiphase and/or multidomain
structures. Their physical and mechanical properties depend strongly on the number of …

In the continuum, close connections exist between mean curvature flow, the Allen-Cahn
(AC) partial differential equation, and the Merriman-Bence-Osher (MBO) threshold dynamics …

We coupled the lattice Boltzmann method with enhanced collisions for hydrodynamics with a
model for the anisotropic liquid/solid phase transition. The model is based on a simple …

The phase field model in two dimensions is used to calculate numerically the operating
states (tip velocity v and tip radius ρ) of dendrites grown from pure melts. At large …

A phase-field model for non-isothermal solidification in multicomponent systems [SIAM J.
Appl. Math. 64 (3)(2004) 775–799] consistent with the formalism of classic irreversible …

We propose and analyze a fully discrete finite element scheme for the phase field model
describing the solidification process in materials science. The primary goal of this paper is to …

During morphogenesis, the shape of living species results from growth, stress relaxation,
and remodeling. When the growth does not generate any stress, the body shape only …

A moving mesh method is developed for the numerical solution of one-dimensional phase-
change problems modelled by the phase-field equations. The computational mesh is …