Abstract
<jats:p>We present a non-iterative domain decomposition framework in which the incident field is decomposed into overlapping spline atoms (dolines) forming a partition of unity. Each lo calized excitation independently illuminates a reduced computational subdomain solved by the Fourier Modal Method (FMM), after which the local solutions are coherently recombined to reconstruct the global electromagnetic field. Beyond the decomposition itself, we show that the reconstructed Poynting flux naturally separates into coherent and incoherent contributions. The incoherent power originates from interaction terms between neighboring localized fields and provides an intrinsic, reference-free measure of the electromagnetic interaction energy not recovered after localization. Numerical validations performed on large-scale metalenses show that increasing the spline order significantly reduces the incoherent power, indicating improved preservation of electromagnetic coupling. The proposed framework provides both an efficient massively parallel strategy for rigorous electromagnetic simulations and a physically meaningful energetic criterion for assessing localized field decompositions.</jats:p>