FastMultipole

type ::Element

Instances of ::Element contain the following properties:

• position: a vector of length 3 describing the Cartesian coordinates of the element position
• strength: a vector of length 4 whose first index describes the source potential, and whose final 3 indices represent the vector source
• potential: a vector of length 4 whose first index is the scalar potential, and whose final 3 indices represent a vector potential
• velocity: a vector of length 3 describing the induced velocity, obtained as the negative gradient of the scalar potential plus curl of the vector potential
• jacobian: a 3x4 matrix containing the concatenated spatial Jacobians of the scalar and vector potentials
• hessian: a 3x3x3 array containing the spatial Hessian of the vector potential

bodies[indexlist] is the same sort operation as performed by the tree sortedbodies[inverseindexlist] undoes the sort operation performed by the tree

drk/dxidx_j

direct!(elements)

Direct calculation of induced potential (no FMM acceleration).

drj/dxi

fmm!(target_systems, source_systems; kwargs...)

Apply all interactions of source_systems acting on target_systems using the fast multipole method. Assumes compatibility functions have been overloaded for both source and target systems.

Arguments

• target_systems: either

  • a system object for which compatibility functions have been overloaded, or
  • a tuple of system objects for which compatibility functions have been overloaded

• source_systems: either

  • a system object for which compatibility functions have been overloaded, or
  • a tuple of system objects for which compatibility functions have been overloaded

Optional Arguments

• expansion_order::Int: the expansion order to be used
• n_per_branch_source::Int: maximum number of bodies from source_systems allowed in a leaf-level branch
• n_per_branch_target::Int: maximum number of bodies from target_systems allowed in a leaf-level branch
• multipole_acceptance_criterion::Float64: number between 0 and 1 (often denoted theta in [0,1]) controls the accuracy by determining the non-dimensional distance after which multipoles are used; 0 means an infinite distance (no error, high cost), and 1 means barely convergent (high error, low cost)

Undoes the sort operation performed by the tree.