Accelerating the discrete dipole approximation by initializing with a scalar solution and using a circulant preconditioning

The discrete dipole approximation (DDA) is a method of choice for simulating the electromagnetic scat-tering by objects of arbitrary shape and permittivity. To recover the field inside the object, it requires the iterative solving of a dense linear system which can be time consuming. To ease this task, we propose to start the inversion with the solution of the recently introduced scalar approximation [Chaumet et al. J. Opt. Soc. Am. A, 39 , 1462 (2022)]. This initial guess allows a reduction of the time required for the solving of the linear system up to 50%. In addition, we study the interest of preconditioning the system to accelerate convergence. We show that the gain can be up to a factor of 5, especially for homogeneous objects on a plane substrate.(c) 2023 Elsevier Ltd. All rights reserved.