MultilevelSummation.jl

A Julia package implementing the Multilevel Summation Method (MSM) of Hardy, Wu, Phillips, Stone, Skeel & Schulten (J. Chem. Theory Comput. 11, 766–779, 2015) for fast evaluation of long-range pair interactions.

Highly experimental — API not yet stable. Current status:

• Pure Julia, multi-threaded CPU via OhMyThreads.jl; GPU port via KernelAbstractions.jl is planned. For best performance launch Julia with julia -t auto.
• Dimensions $d \in \{1,2,3\}$.
• Per-axis boundary conditions: :open / :periodic (mixed BC works).
• Pluggable kernels (InversePower{N}, RationalDecay{N}), splittings (HardyC2Cubic for Coulomb only so far) and interpolation bases (CubicC1).
• AtomsBase + AtomsCalculators interface.

The design contract — repository layout, API surface, duck-typed interfaces — lives in PLAN.md. The live task list with priorities is in PRIORITIES.md.

Installation

using Pkg
Pkg.develop(path = "path/to/MultilevelSummation.jl")

Quick start

A typical workflow at the low-level (unit-free) API:

using MultilevelSummation
using StaticArrays

# 5 random charges in a 4×4×4 box
positions = [SVector{3,Float64}(rand(3) .* 4) for _ in 1:5]
charges   = randn(5)
charges  .-= sum(charges) / 5         # neutralise

# Cell + periodicity
cell     = SMatrix{3,3,Float64}(4 * one(SMatrix{3,3,Float64}))
periodic = (true, true, true)

# MSM hyperparameters
calc = MSMCalculator(
    HardyC2Cubic(2.0, 4),             # cutoff a = 2, L = 4 levels
    CubicC1(),                        # cubic C¹ basis
    0.5,                              # finest grid spacing h = 0.5
)

U      = msm_energy(positions, charges, cell, periodic, calc)
U, F   = msm_energy_forces(positions, charges, cell, periodic, calc)

And the AtomsBase / AtomsCalculators API:

using AtomsBase, AtomsCalculators, Unitful

L = 4.0u"Å"
cell_vec = (SVector(L, 0u"Å", 0u"Å"),
            SVector(0u"Å", L, 0u"Å"),
            SVector(0u"Å", 0u"Å", L))
sys = periodic_system([
    Atom(:Na, SVector(1.0u"Å", 2.0u"Å", 0.5u"Å"); charge = +1.0),
    Atom(:Cl, SVector(2.5u"Å", 1.5u"Å", 3.0u"Å"); charge = -1.0),
], cell_vec)

U = AtomsCalculators.potential_energy(sys, calc)
F = AtomsCalculators.forces(sys, calc)

Units are stripped at the AtomsBase boundary; the numerical core is unit-free.

What MSM does, in one paragraph

The Coulomb (or other translation-invariant) pair kernel K(r) is split into a short-range piece K_0 with compact support |r| ≤ a, plus a sequence of slowly varying pieces K_1, …, K_L interpolated on a nested hierarchy of grids with spacings h, 2h, 4h, …, 2^{L−1} h. Particle charges are scattered to the finest grid (anterpolation), restricted to coarser grids, convolved with each level's K_l stencil, prolonged back down, and gathered at the particles (interpolation). The result is the long-range part of the potential. The short-range piece is summed directly. The total energy is then assembled with a small self-correction to remove the spurious self-interaction picked up by the long-range pathway. See Algorithm for a more detailed walk-through.

What's in the package