US Patent 12073149 Computing interactions of sources embedded in three dimensional layered media

Systems and methods for computing interactions of charge sources embedded in three dimensional (3D) layered media. At least one of the methods includes decomposing the Green's function representing the potential caused by a charge source into a free space component and a plurality of reaction components; generating, for each reaction component of the plurality of reaction components, a multipole expansion (ME) operator and a multipole to local (M2L) translation operator; performing, for each reaction component of the plurality of reaction components, a convergence analysis of an ME of that reaction component; defining, for each reaction component, polarization charge sources based on the convergence analysis and combining the polarization charges sources with the charge sources; and computing, using a fast multipole method (FMM), interactions of the charge sources based on the polarization charge sources, the ME operators, and the M2L translation operators.