Efficient charge assignment and back interpolation in multigrid methods for molecular dynamics

The assignment of atomic charges to a regular computational grid and the interpolation of forces from the grid back to the original atomic positions are crucial steps in a multigrid approach to the calculation of molecular forces. For purposes of grid assignment, atomic charges are modeled as truncated Gaussian distributions. The charge assignment and back interpolation methods are currently bottlenecks, and take up to one-third the execution time of the multigrid method each. Here, we propose alternative approaches to both charge assignment and back interpolation where convolution is used both to map Gaussian representations of atomic charges onto the grid and to map the forces computed at grid points back to atomic positions. These approaches achieve the same force accuracy with reduced run time. The proposed charge assignment and back interpolation methods scale better than baseline multigrid computations with both problem size and number of processors.