An Efficient Interpolation Based FMM for Dislocation Dynamics Simulations

Although the framework of Dislocation Dynamics (DD) provides powerful tools to model crystal plasticity, their efficient implementation is crucial in order to simulate very large ensembles of dislocations. Among all the steps involved in DD simulations, the computation of the internal elastic forces and energy are the most resource consuming. However, since they are long-ranged interactions, they can be efficiently evaluated using the Fast Multipole Method (FMM). We propose a new FMM formulation based on polynomial interpolations, that is optimized to reduce the memory footprint and the number of flops using fast Fourier transforms. These optimizations are necessary because of the tensorial nature of the kernel and the unusual memory requirements of this application. Regarding parallelism, our code benefits from a hybrid OpenMP/MPI paradigm and a cache-aware data structure. Numerical results will be presented to show the accuracy of this new approach and its parallel scalability.