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

离散源法是一种计算复杂形状粒子光散射的有效方法。利用广义点匹配，散射场近似为离散源的线性组合。这意味着通过求解超定线性系统来找到离散源的系数。通常使用直接求解器。对于大型线性系统，直接求解器不再适用。相反，必须使用迭代求解器来加速求解过程。该项目的目标是研究不同的迭代方法和预处理器对各种颗粒形状的适用性。此外，研究发现，对于大颗粒和高纵横比颗粒，一些离散源的重新定位有助于获得正确的解，而通常使用的位置不可能获得正确的解。因此，该项目的第二个目标是研究根据颗粒形状确定离散源的最佳位置的方法。作为一个例子，现实世界的应用散射红细胞将进行调查。在一个合作项目中，需要有效的散射算法来从扫描流式细胞仪获得的光散射数据中对红细胞进行分类。

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 For large linear systems direct solvers are no longer applicable.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.