Crystal growth and dendritic solidification
Journal of Computational Physics
Computation of dendrites using a phase field model
Proceedings of the twelfth annual international conference of the Center for Nonlinear Studies on Nonlinearity in Materials Science
Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
Absorbing boundary conditions for diffusion equations
Numerische Mathematik
Algorithms for phase field computation of the dendritic operating state at large supercoolings
Journal of Computational Physics
Artificial boundary conditions for diffusion equations: numerical study
Journal of Computational and Applied Mathematics
A simple level set method for solving Stefan problems
Journal of Computational Physics
RKC: an explicit solver for parabolic PDEs
Journal of Computational and Applied Mathematics
Adaptive mesh refinement computation of solidification microstructures using dynamic data structures
Journal of Computational Physics
Multiscale finite-difference-diffusion-Monte-Carlo method for simulating dendritic solidification
Journal of Computational Physics
Short Note: The type 3 nonuniform FFT and its applications
Journal of Computational Physics
Journal of Computational Physics
On the numerical solution of the heat equation I: Fast solvers in free space
Journal of Computational Physics
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
Hi-index | 31.45 |
We solve the phase-field equations in two dimensions to simulate crystal growth in the low undercooling regime. The novelty is the use of a fast solver for the free space heat equation to compute the thermal field. This solver is based on the efficient direct evaluation of the integral representation of the solution to the constant coefficient, free space heat equation with a smooth source term. The computational cost and memory requirements of the new solver are reasonable and no artificial boundary conditions are needed. This allows one to solve for the thermal field in a computational domain whose size depends only on the size of the growing crystal and not on the extent of the thermal field, which can result in significant computational savings in the low undercooling regime.