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

Met Office业务全球模式及其上下配置与最新观测结果相比，预测的多云短波辐射效应约为30Wm-2至-40Wm-2。作为气象局和空间机构正在进行的了解和减少这些误差的重大投资的一部分，需要对冰晶的散射和吸收特性有一个准确的了解。在极大粒子的限制下，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，在实际非常重要的中小冰区，射线追踪是不适用的，需要用直接的模拟方法来求解潜在的麦克斯韦方程。在这里，标准的T矩阵技术是大气研究社区中流行的工具，仅限于相当简单的均匀形状。一种替代方法是边界元方法(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，由于它们的实施复杂性显著较高，到目前为止，这些方法在气候研究界还很少使用。自2011年以来，伦敦大学学院一直在开发一种新的开源BEM程序(BEM++，www.bempp.org)，该程序得到EPSRC赠款EP/I030042/1和EP/K03829X/1的资助。BEM++之前被用于模拟复杂冰晶结构的光散射的第一个可行性研究，这些结构是目前公开可用的T-Matrix方法(具有不同内部气腔和子弹花环的冰晶体)无法实现的。我们计划在这项非常有希望的初步研究的基础上，开发一个强大的框架来模拟冰晶的光散射，包括：Maxwell的快速高频解算器。近年来，针对Maxwell边界元中产生的振荡核的快速定向FMM方法得到了发展，其尺度几乎是关于波数的最优尺度。再加上麦克斯韦方程的算子预条件，这些导致了在广泛的频率范围内的快速求解器。这些方法在BEM++中的实施正在进行中，我们将与案例学生一起应用和研究这些方法在中高频复杂冰晶配置中的可扩展性。这将在几何光学和电磁学之间架起一座桥梁。[时间：1年]内部不均匀冰晶电磁散射的模拟。我们将该方法应用于微波和亚毫米光谱区域，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，我们将有限元方法与外部散射问题的边界元相结合。[时间：1.5年]复杂的多重散射配置。我们计划将基于边界元的解决方案能力扩展到具有随机取向的冰晶阵列。在Ganesh，Hesthaven和Stamm的工作中，提出了一种简化基方法，其中使用电磁粒子的单独散射计算来加速计算粒子阵列的散射场。基于BEM++解算器的功能，我们将在此基础上构建该方法，并将其应用于冰晶阵列。[时间：一年半]

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]