GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
On the numerical solution of a hypersingular integral equation in scattering theory
Journal of Computational and Applied Mathematics
A front-tracking method for dendritic solidification
Journal of Computational Physics
Microstructural evolution in inhomogeneous elastic media
Journal of Computational Physics
Hybrid Gauss-Trapezoidal Quadrature Rules
SIAM Journal on Scientific Computing
A level set method for thin film epitaxial growth
Journal of Computational Physics
An efficient numerical method for studying interfacial motion in two-dimensional creeping flows
Journal of Computational Physics
Finite element method for epitaxial growth with attachment-detachment kinetics
Journal of Computational Physics
Finite Element Method for Epitaxial Growth with Thermodynamic Boundary Conditions
SIAM Journal on Scientific Computing
An adaptive fast solver for the modified Helmholtz equation in two dimensions
Journal of Computational Physics
An integral equation method for epitaxial step-flow growth simulations
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Dynamics of multicomponent vesicles in a viscous fluid
Journal of Computational Physics
Removing the stiffness from interfacial flows with surface tension
Journal of Computational Physics
Fast integral equation methods for the modified Helmholtz equation
Journal of Computational Physics
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In this paper, we present a boundary integral method for computing the quasi-steady evolution of an epitaxial island. The problem consists of an adatom diffusion equation (with desorption) on terrace and a kinetic boundary condition at the step (island boundary). The normal velocity for step motion is determined by a two-sided flux. The integral formulation of the problem involves both double- and single-layer potentials due to the kinetic boundary condition. Numerical tests on a growing/shrinking circular or a slightly perturbed circular island are in excellent agreement with the linear analysis, demonstrating that the method is stable, efficient, and spectrally accurate in space. Nonlinear simulations for the growth of perturbed circular islands show that sharp tips and flat edges will form during growth instead of the usual dense branching morphology seen throughout physical and biological systems driven out of equilibrium. In particular, Bales-Zangwill instability is manifested in the form of wave-like fronts (meandering instability) around the tip regions. The numerical techniques presented here can be applied generally to a class of free/moving boundary problems in physical and biological science.