General info

The spirit of SLDA method is to exploit only the local densities during the computation process. This feature makes the method an excellent candidate for utilization multithreading computing units like GPUs. Instead of iterate over all lattice points (case of CPU implementation), we can create number of lattice points NX x NY x NZ concurrent and independent threads, and assign with each single thread all operations related to one point either in position or momentum space, see Fig. below. Switching between spaces is performed by parallel cuFFT implementation, which is even more than 100 times faster than CPU implementation (like FFTW).

MPI space and GPUs

Time-dependent codes evolve quasiparticle wave functions (qpwfs) which number depends mainly in the lattice size and value of the cut-off energy ec. The number of wave-functions is printed under the name nwf, for example:

# INIT2: nwf=46032 wave-functions to scatter

Quasiparticle wave functions are distributed uniformly among np MPI process. For example if above example is executed on np=32 then each process is responsible for evolving nwfip = 46032/32 = 1438.5. (In practice for this example processes evolve either 1438 or 1439 qpwf). Qpwfs are evolved by GPUs. It requires that for each MPI process a GPU must be assigned. Suppose that the code is executed on 4 nodes, and each node is equipped with 4 GPUs. Consider the following execution command:

mpiexec -ppn 8 -np 32 ./td-wslda-2d input.txt

where:

• ppn: processes per node,
• np: number of processes.