TY  - JOUR
AU  - Kohnke, Bartosz
AU  - Kutzner, Carsten
AU  - Beckmann, Andreas
AU  - Lube, Gert
AU  - Kabadshow, Ivo
AU  - Dachsel, Holger
AU  - Grubmüller, Helmut
TI  - A CUDA fast multipole method with highly efficient M2L far field evaluation
JO  - The international journal of high performance computing applications
VL  - 35
IS  - 1
SN  - 1741-2846
CY  - Thousand Oaks, Calif.
PB  - Sage Science Press
M1  - FZJ-2021-00076
SP  - 97 - 117
PY  - 2021
AB  - Solving an N-body problem, electrostatic or gravitational, is a crucial task and the main computational bottleneck in many scientific applications. Its direct solution is an ubiquitous showcase example for the compute power of graphics processing units (GPUs). However, the naïve pairwise summation has 𝒪(𝑁2) computational complexity. The fast multipole method (FMM) can reduce runtime and complexity to 𝒪(𝑁) for any specified precision. Here, we present a CUDA-accelerated, C++ FMM implementation for multi particle systems with 𝑟−1 potential that are found, e.g. in biomolecular simulations. The algorithm involves several operators to exchange information in an octree data structure. We focus on the Multipole-to-Local (M2L) operator, as its runtime is limiting for the overall performance. We propose, implement and benchmark three different M2L parallelization approaches. Approach (1) utilizes Unified Memory to minimize programming and porting efforts. It achieves decent speedups for only little implementation work. Approach (2) employs CUDA Dynamic Parallelism to significantly improve performance for high approximation accuracies. The presorted list-based approach (3) fits periodic boundary conditions particularly well. It exploits FMM operator symmetries to minimize both memory access and the number of complex multiplications. The result is a compute-bound implementation, i.e. performance is limited by arithmetic operations rather than by memory accesses. The complete CUDA parallelized FMM is incorporated within the GROMACS molecular dynamics package as an alternative Coulomb solver.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000578560700001
DO  - DOI:10.1177/1094342020964857
UR  - https://juser.fz-juelich.de/record/889151
ER  -