PMCHWT Solver Accelerated by Adaptive Cross Approximation for Efficient Computation of Scattering from Metal Nanoparticles

An accelerated algorithm that can efficiently calculate the light scattering of a single metal nanoparticle was proposed. According to the equivalent principle, the method of moment (MoM) transforms the Poggio–Miller–Chang–Harrington–Wu–Tsai (PMCHWT) integral equations into linear algebraic equations, which are solved by the flexible generalized minimal residual solver (FGMRES). Each element of near field MoM impedance matrix was described by Rao–Wilton–Glisson (RWG) basis functions and calculated by double surface integrals. Due to the low-rank property, the adaptive cross approximation (ACA) algorithm based on the octree data structure was applied to compress the MoM impedance matrix of far field action leading to the significant reduction of solution time and memory. Numerical results demonstrated that the proposed method is both accurate and efficient. Compared with the traditional MoM, the ACA algorithm can significantly reduce the impedance matrix filling time and accelerate the scattering field’s computation from actual metal nanoparticles using PMCHWT integral equations.