Using MPI (2nd ed.): portable parallel programming with the message-passing interface
Using MPI (2nd ed.): portable parallel programming with the message-passing interface
A continuum model of grain boundaries
Physica D
Multigrid
Journal of Computational Physics
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Numerical Recipes 3rd Edition: The Art of Scientific Computing
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models
Journal of Computational Physics
Hi-index | 31.46 |
An implicit, second-order space and time discretization scheme together with a parallel multigrid method involving a strip grid domain partitioning has been developed to solve fully coupled, nonlinear phase field equations involving solute and heat transport for multiple solidifying dendrites. The computational algorithm has been shown to be stable and monotonously convergent, and allowed time marching steps that were 3-4 orders of magnitude larger than those employed in similar explicit approaches, resulting in an increase of 3-4 orders of magnitude in computing efficiency. Full solute and thermal coupling was achieved for metallic alloys with a realistic, high Lewis number of 10^4. The parallel multigrid computing scheme is shown to provide a scalable methodology that allowed the efficient use of distributed supercomputing resource to simulate the evolution of tens of complex shaped 2D dendrites in a computational domain containing tens or even hundreds of millions of grid points. The simulations have provided insight into the dynamic interplay of many growing dendrites in a more realistic fully coupled thermal-solute condition, capturing for the first time fine scale features such as dendrite splitting.