Novel boundary element based solvers for light scattering from complex ice crystals

英国气象局的业务全球模式及其配置超过和低于预测多云短波辐射效应约30 Wm-2至- 40 Wm-2时，与最新的观测结果相比。作为英国气象局和航天局在理解和减少这些误差方面持续进行的重大投资的一部分，需要准确理解冰晶的散射和吸收特性。在非常大的粒子的限制下，在太阳波长下，光线追踪已成功地用于模拟冰晶的光散射。然而，在实际上非常重要的中型和小型冰范围内，射线追踪是不适用的，需要直接模拟方法来求解基本的麦克斯韦方程。在这里，标准的T矩阵技术是大气研究界的流行工具，它仅限于相当简单的均匀形状。另一种方法是边界元法（BEM），这是一种直接求解技术，不受标准T矩阵方法的几何限制。然而，由于其显着更高的实施复杂性，这些迄今为止很少在气候研究界使用。自2011年以来，UCL一直在开发一种新的开源BEM代码（BEM++，www.bempp.org），由EPSRC赠款EP/I 030042/1和EP/K 03829 X/1。BEM++先前用于模拟复杂冰晶配置的光散射的第一个可行性研究，这些冰晶配置超出了目前公开可用的T矩阵方法（具有不同内部空气腔和子弹头的冰晶）的范围。我们计划在这个非常有前途的初步研究的基础上，开发一个强大的框架，用于模拟冰晶的光散射，包括：麦克斯韦的快速高频求解器。近年来，麦克斯韦边界元法中出现的振荡核的快速方向FMM方法已经发展成相对于波数几乎最佳地缩放。连同运营商预处理的麦克斯韦方程，这些导致快速求解器在很宽的频率范围。这种方法在BEM++中的实施正在进行中，我们将与CASE学生一起应用并研究这些方法在中高频复杂冰晶配置的可扩展性。这将弥合几何光学和电磁学之间的差距。[Time：1年]模拟具有内部不均匀性的冰晶的电磁散射。我们将该方法应用于频谱的微波和亚毫米波区域，以利用英国气象局开发的新仪器。在与这些入射频率相关的较大颗粒尺寸下，颗粒体积可能由冰、水和空气的混合物组成。为了模拟冰晶中的随机不均匀性，我们将耦合有限元法（FEM）与边界元法的外部散射问题。[Time：1.5年]复杂的多次散射配置。我们计划将基于边界元法的解决方案扩展到具有随机取向的冰晶阵列。在Ganesh、Hesthaven和Stamm的工作中，提出了一种缩减基方法，其中使用电磁粒子的个体散射计算来加速粒子阵列的散射场的计算。基于BEM++求解器的能力，我们将建立在这种方法，并将其应用到冰晶阵列。[Time：1.5年]

The Met Office operational global model and its its configurations over and under predict the cloudy short-wave radiative effect by ~30 Wm-2 to - 40 Wm-2 when compared against the latest observations. As part of ongoing significant investments by the Met Office and space agencies in understanding and reducing these errors an accurate understanding of the scattering and absorption properties of ice crystals is required. In the limit of very large particles, at solar wavelengths, ray tracing has been successfully used for simulating light-scattering from ice crystals. However, in the practically very important mid-size and small ice range, ray tracing is not applicable and direct simulation methods are required that solve the underlying Maxwell equation. Here, standard T-Matrix techniques are popular tools in the athmospheric research community, which are restricted to rather simple homogeneous shapes. An alternative are boundary element methods (BEM), a type of direct solution techniques that do not suffer from the geometric restrictions of standard T-Matrix approaches. However, due to their significant higher implementational complexity these have been so far little used in the climate research community. Since 2011, a novel open-source BEM code (BEM++, www.bempp.org) has been in development at UCL, funded by EPSRC grants EP/I030042/1 and EP/K03829X/1. BEM++ was previously used for a first feasibility study for the simulation of light-scattering from complex ice crystal configurations that are out of reach of currently publicly available T-Matrix methods (ice crystals with varying internal air cavities and bullet-rosettes). We are planning to build on this very promising initial study to develop a powerful framework for the simulation of light-scattering from ice crystals, including: Fast High-Frequency solvers for Maxwell. In recent years, fast directional FMM methods for the oscillatory kernels arising in Maxwell BEM have been developed that scale almost optimally with respect to the wavenumber. Together with operator preconditioning for the Maxwell equations these lead to fast solvers across a wide range of frequencies. Implementation of such methods in BEM++ is ongoing and together with the CASE Student we will apply and investigate the scalability of these methods for complex ice crystal configurations at medium to high frequencies. This will bridge the gap between geometric optics and electromagnetism.[Time: 1 year] Simulation of electromagnetic scattering from ice crystals with internal inhomogeneities. We apply the method to the microwave and submillimetre regions of the spectrum to take advantage of new instrumentation developed by the Met Office. At the larger particle sizes of relevance to these incident frequencies, the particle volume is likely to consist of mixtures of ice, water and air. To simulate random inhomogeneities in ice crystals we will couple finite element methods (FEM) with a BEM for the exterior scattering problem. [Time: 1.5 year] Complex multiple scattering configurations. We plan to extend the BEM based solution capabilities to arrays of ice crystals with random orientation. In work by Ganesh, Hesthaven and Stamm a reduced basis approach was proposed in which individual scattering computations of electromagnetic particles are used to accelerate the computation of the scattered field of an array of particles. Based on the BEM++ solver capabilities we will build on this approach and apply it to arrays of ice crystals. [Time: 1.5 years]