Parallel Algorithm and MPI Implementation of Numerical Study of Phase Transition in the 3D Thermal Spike Model

We present an algorithm and parallel computer code for numerical investigation of the thermal processes and phase transitions in materials irradiated by the high energy heavy ion beams. We employ the modified thermal spike model based on the coupled heat conductivity equations for the electron gas and the ion lattice subsystems in the target sample. This system of equations is numerically solved in the cylindrical coordinate system in axially non-symmetric (3D) case. We utilize an expansion of the source function in spherical harmonics, a finite difference approximation and semi-explicit numerical scheme. The dynamics of phase transitions is implemented on the basis of the enthalpy approach. The mathematical formulation of the problem is given; a numerical scheme is described; a parallel algorithm is presented on the basis of the MPI technique (Message Passing Interface). The test calculations on the K100 multi-processor cluster (KIAM RAS, Moscow) with various dimension of the finite-difference mesh and with different number of parallel processors demonstrate efficiency of the C++/MPI code.

modeling, numerical methods, phase transitions, thermal spike model, parallel algorithm