Module cluster 

Multiple scattering in clusters of particles: solves of (I - T C) X = T B.

Upstream: treams.TMatrix.cluster and treams.TMatrix.interaction.

T is the block-diagonal matrix of the particles’ own T-matrices, C couples every pair of particles through the singular expansion between their centres, and B holds incident fields, one column each. The scattered fields X follow from one of four solvers:

Solver	Particles	Method	Use it for
particle_cluster, cylindrical_particle_cluster	any T-matrices	dense LU	the full cluster T-matrix and gradients of the particle T-matrices and positions
sphere_cluster	homogeneous nonmagnetic spheres in vacuum	dense LU	the full cluster T-matrix and gradients of radii, permittivities and positions
InteractionFactor	any T-matrices, or the spheres of sphere_cluster_factor	dense LU, kept	many incident fields with one factorization
IterativeSphereCluster	homogeneous nonmagnetic spheres in vacuum	GMRES, no dense matrix	large clusters and few incident fields

The dense solvers store C and its LU factors, n² entries for n modes in total. IterativeSphereCluster stores only the geometry and the Mie coefficients and applies C one particle pair at a time.

treams-rs	treams
particle_cluster	TMatrix.cluster(tmats, positions).interaction.solve()
cylindrical_particle_cluster	TMatrixC.cluster(tmats, positions).interaction.solve()
sphere_cluster	the same with TMatrix.sphere T-matrices
interaction()	TMatrix.interaction.solve()
InteractionFactor, IterativeSphereCluster	none

Modules

interaction 🔒

Dense solves of (I - T C) X = T B through one LU factorization of I - T C.

iterative 🔒

Matrix-free sphere clusters: GMRES solves for requested incident fields that never form the coupling matrix. treams-rs extension.

particles 🔒

Clusters of arbitrary spherical or cylindrical particle T-matrices.

spheres 🔒

Dense clusters of homogeneous nonmagnetic spheres in vacuum, with gradients of the radii, permittivities and positions.

Structs

IlluminateGradient

Gradients of the local T-matrix, the coupling and the incident fields of an IlluminateResidual.

IlluminateResidual

What InteractionFactor::record saves for its pullback: the shared factor and the total incident response B + C X and scattered fields of the requested columns.

InteractionFactor

The LU factorization of I - T C, kept with the local T-matrix T and the coupling C, for any number of incident-field solves.

InteractionGradient

Gradients of the inputs of interaction, in the order of its arguments.

InteractionResidual

What interaction saves for its pullback: the factorization of I - T C and the interacting T-matrix X.

IterativeGradient

Gradients of an IterativeResidual, without a dense coupling matrix or its gradient.

IterativeResidual

What IterativeSphereCluster::record saves for its pullback: the shared cluster, the incident fields, the GMRES options and the solution.

IterativeSolution

Scattered local multipoles for only the requested incident columns.

IterativeSphereCluster

The matrix-free counterpart of sphere_cluster: the same spheres, solved with GMRES for the requested incident columns only.

ParticleClusterGradient

Gradients of the inputs of particle_cluster and cylindrical_particle_cluster, in the order of their arguments: the local matrices, the positions of the basis and the wavenumbers.

ParticleClusterResidual

What particle_cluster and cylindrical_particle_cluster save for their pullback: the interaction solve, with one local block per particle, and the expansion residual of the coupling.

SphereClusterGradient

Gradients of the inputs of sphere_cluster, in the order of its arguments.

SphereClusterResidual

What sphere_cluster saves for its pullback: the Mie residual of each sphere, the translation plan between two spheres, the positions and the interaction solve.

Functions

cylindrical_particle_cluster

Couple the cylindrical T-matrices of different particles with fixed axial mode labels and solve for the interacting T-matrix.

interaction

Solve a multiple-scattering system for the interacting T-matrix X = (I - T C)⁻¹ T, keeping its LU factorization for the pullback.

particle_cluster

Couple the spherical T-matrices of different particles in a common embedding medium and solve for the interacting T-matrix.

sphere_cluster

Solve a finite cluster of homogeneous, nonmagnetic spheres in vacuum.

sphere_cluster_factor

Assemble and factor a sphere cluster for repeated requested illuminations.