A Parallel 3D Dendritic Growth Simulator Using the Phase-Field Method

We describe an implementation of a parallel finite-difference algorithm for the simulation of alloy solidification in three dimensions using the phase-field model. We also describe the visualization of the output from this simulator. Although this type of simulation has been accomplished before in two dimensions, extending this to three dimensions presents scaling problems for both the computations and the subsequent rendering of the results for visualization. This is due to the O(n4) execution time of the simulation algorithm as well as the O(n3) space requirements for holding the required three-dimensional arrays of field parameters. Additionally, rendering the output of the three-dimensional simulation stresses the available software and hardware when the simulations extend over computational grids of size 500×500×500. Parallel computing libraries and hardware-supported rendering combine to help make this simulator simple to implement, portable, and efficient even when run in heterogeneous environments. This has all been accomplished using simple static uniform grids and finite differencing.