Application Examples

This section contains end-to-end examples for each supported kernel.

The FMM uses 64-bit arithmetic when the inputs are Float64 or ComplexF64. If all coordinates, charges, and kernel values are provided as Float32 or ComplexF32, it uses the 32-bit library. Mixing 32-bit and 64-bit inputs is rejected.

Laplace FMM

using MKL # or another BLAS/LAPACK backend configured for your Julia session
using ExaFMMt

# 64 bit representation
nsources = 10000
ntargets = 8000
sources = rand(Float64, nsources, 3)
targets = rand(Float64, ntargets, 3)
charges = rand(Float64, nsources)

A = setup(sources, targets, LaplaceFMMOptions())
y = A * charges

# 32 bit representation
sources = rand(Float32, nsources, 3)
targets = rand(Float32, ntargets, 3)
charges = rand(Float32, nsources)

A = setup(sources, targets, LaplaceFMMOptions())
y = A * charges
y[1:5]

5-element Vector{Float32}:
 605.8342
 799.66956
 737.7829
 785.0377
 794.9795

Helmholtz FMM

using MKL # or another BLAS/LAPACK backend configured for your Julia session
using ExaFMMt

# 64 bit representation
nsources = 10000
ntargets = 8000
sources = rand(Float64, nsources, 3)
targets = rand(Float64, ntargets, 3)
charges = rand(ComplexF64, nsources)
wavek = ComplexF64.(1.0 + 1.0*im)

A = setup(sources, targets, HelmholtzFMMOptions(wavek))
y = A * charges

# 32 bit representation
sources = rand(Float32, nsources, 3)
targets = rand(Float32, ntargets, 3)
charges = rand(ComplexF32, nsources)
wavek = ComplexF32.(1.0 + 1.0*im)

A = setup(sources, targets, HelmholtzFMMOptions(wavek))
y = A * charges
y[1:5]

5-element Vector{ComplexF32}:
  256.1479f0 + 687.96265f0im
 233.13249f0 + 647.94324f0im
 272.63608f0 + 702.6121f0im
 265.07922f0 + 692.14404f0im
 313.40564f0 + 766.0445f0im

Modified-Helmholtz FMM

using MKL # or another BLAS/LAPACK backend configured for your Julia session
using ExaFMMt

# 64 bit representation
nsources = 10000
ntargets = 8000
sources = rand(Float64, nsources, 3)
targets = rand(Float64, ntargets, 3)
charges = rand(Float64, nsources)
wavek = Float64(1.0)

A = setup(sources, targets, ModifiedHelmholtzFMMOptions(wavek))
y = A * charges

# 32 bit representation
sources = rand(Float32, nsources, 3)
targets = rand(Float32, ntargets, 3)
charges = rand(Float32, nsources)
wavek = Float32(1.0)

A = setup(sources, targets, ModifiedHelmholtzFMMOptions(wavek))
y = A * charges
y[1:5]

5-element Vector{Float32}:
 423.99603
 590.29504
 393.5976
 316.07837
 384.0625