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Preconditioning techniques for iterative solvers in the Discrete Sources Method |
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| Authors: | Vladimir Schmidt Roman Schuh |
| Institution: | a Universität Bremen, Badgasteiner Str. 3, 28359 Bremen, Germany b Institut für Werkstofftechnik, Badgasteiner Str. 3, 28359 Bremen, Germany c Faculty of Applied Mathematics and Computer Science, Lomonosov State University, Lenin's Hills, 119992 Moscow, Russia |
| Abstract: | Different preconditioning techniques for the iterative method MinRes as solver for the Discrete Sources Method (DSM) are presented. This semi-analytical method is used for light scattering computations by particles in the Mie scattering regime. Its numerical schema includes a linear least-squares problem commonly solved using the QR decomposition method. This could be the subject of numerical difficulties and instabilities for very large particles or particles with extreme geometry. In these cases, we showed that iterative methods with preconditioning techniques can provide a satisfying solution.In our previous paper, we studied four different iterative solvers (RGMRES, BiCGStab, BiCGStab(l), and MinRes) considering the performance and the accuracy of a solution. Here, we study several preconditioning techniques for the MinRes method for a variety of oblate and prolate spheroidal particles of different size and geometrical aspect ratio. Using preconditioning techniques we highly accelerated the iterative process especially for particles with a higher aspect ratio. |
| Keywords: | Electromagnetic scattering Discrete source method Krylov subspace iterative solvers Least-squares problem Preconditioning technique |
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