Fast numerical techniques for the Discrete Sources Method for light scattering computation

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To compute light scattering by complex shaped particles, which are of interest in optical particle characterization, the Discrete Sources Method (DSM) is a suitable and efficient method. Using generalized point matching the scattered field is approximated by a linear combination of discrete sources. This means that the coefficients of the discrete sources are found by solving an overdetermined linear system. Direct solvers are commonly applied. For large linear systems direct solvers are no longer applicable. Instead, iterative solvers have to be used to accelerate the solution process. The goal of the project is to investigate the suitability of different iterative methods and preconditioners for a wide variety of particle shapes.Additionally it was found that with large particles and particles of high aspect ratio some repositioning of the discrete sources helps to obtain a correct solution where no solution was possible with the positions normally used. Therefore the second goal of the project is to investigate methods to determine the optimal position of the discrete sources depending on the particle shape. As an example real-world application scattering by erythrocytes will be investigated. Efficient scattering algorithms will be needed to classify erythrocytes from light scattering data gained by a Scanning Flow Cytometer within a collaborative project.