Correction-Factor Method

For a boundary-element matrix $A$, the package approximates the far field by an FMM-backed map $A_{\mathrm{FMM}}$. Near interactions are evaluated with the boundary-element quadrature and corrected for the interactions already represented by the FMM:

\[\boldsymbol{A}\boldsymbol{x} \approx \boldsymbol{A}_{\mathrm{FMM}}\boldsymbol{x} + \left(\boldsymbol{A}_{\mathrm{near}} - \boldsymbol{A}_{\mathrm{FMM,near}}\right)\boldsymbol{x}.\]

The sparse correction blocks are selected from an H2Trees.BlockTree. Matrix-vector products evaluate the FMM map first and then add the sparse near correction. Transpose and adjoint products follow the corresponding LinearMaps.jl interfaces.