A Parallel 3D Dendritic Growth Simulator using the Phase-Field Method
William L. George, James A. Warren
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 thistype 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 simulationstresses the available software and hardware when the simulations extend over computational grids of size 500 x 500 x500. Parallel computing libaries andhardware supported rendering combine to help make this simulator simple to implement, portable, and efficient even when run in heterogenous environments. This has all been accomplished using simple static uniform grids and finite differencing.