A block elimination algorithm for multiple scattering of multilayered concentric nanoparticle aggregates

An efficient block elimination method is developed for the calculation of the multiscattering of electromagnetic waves by multilayered concentric nanoparticle aggregates. Instead of applying the LU decomposition or Gaussian elimination method as commonly used for the solution of global translation matrix, the present method partitions the matrix into blocks based on the number of particles in the aggregate and performs the elimination process block by block. A key advantage of this method is that the pivot block needs to be inverted only once, thereby reducing the computational time. This, in combination with a progressive algorithm for a multilayer concentric particle, provides a very efficient numerical procedure for the solution of scattering coefficients for a multilayered concentric nanoparticle cluster. Moreover, the computational efficiency is further improved by parallelization of the block-by-block elimination method. The algorithm only requires updating a portion of the matrix during each elimination stage. Numerical testing shows that the computational time is reduced considerably with the proposed parallel block-by-block elimination method. Computed cases are presented, illustrating that the proposed algorithm is effective for the design of multilayered nanoparticle aggregates with various optical phenomena, including maximum forward or backward scattering features. It is worth noting that the presented methodology is not restricted to nanosized particles; it is applicable to particles with larger size parameters.