Accelerating the discrete dipole approximation by initializing with a scalar solution and using a circulant preconditioning
Résumé
The discrete dipole approximation (DDA) is a method of choice for simulating the electromagnetic scattering 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.
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