BEM++ - A high performance boundary element library

许多现代应用，如声学噪声计算、医学成像或雷达，都需要在具有均匀材料特性的域上求解复杂的数学模型。以飞机上的雷达散射为例。电磁波从平面上散射的方式只取决于平面表面的形状和材料，而不取决于周围的均匀介质（空气）。因此，我们可以将模拟平面周围电磁波的三维模型简化为平面二维表面（边界）上的计算。计算这类边界问题的解是边界元法（BEM）的任务。如果计算模型可以被重新表述为边界问题，边界元法可以显著降低计算复杂度，因为只需要对其边界进行离散，而不是对整个域进行离散。但是底层所谓的边界积分方程的性质使得这些方法比域离散化方法更复杂，并且必须仔细设计实现以比基于域的方法更有效。虽然有许多强大的开源软件库可用于基于领域的方法，例如有限元，但很少有软件可用于边界元素，其中大多数是商业的，并为专门的应用领域量身定制。通过这个项目，我们的目标是通过创建一个强大的、免费的、通用的边界元素库来改变这种情况，这个库可以被研究人员用于复杂的模拟，也可以被公司作为他们自己的应用程序的基础。图书馆的设计特别强调对现代计算基础设施的支持。近年来，在多核处理器的出现和用于科学模拟的强大游戏图形卡（gpu）的使用的推动下，计算能力出现了爆炸式增长。最新一代的GPU处理板在所谓的单精度浮点运算方面的峰值性能超过1万亿次浮点运算，在双精度方面仍然超过500千兆次浮点运算。相比之下，在一台台式计算机上安装两个这样的显卡所能达到的性能，在10年前还能跻身世界顶级超级计算机之列。但是，软件库必须经过专门设计，才能充分利用这种巨大的计算能力。在这个项目中，我们将从一开始就优化库，以便在现代多核和混合CPU/GPU计算环境下提供最佳性能。在项目期间，我们特别关注医学成像的两个具有挑战性的应用。第一种是漫射光学层析成像（DOT）。在DOT检查中，乳房或脑部的肿瘤是通过其周围组织不同的光吸收和散射特性来检测的。DOT的某些方面可以建模为边界问题，该库将成为伦敦大学学院医学成像计算中心DOT计算的核心组件。在颅磁刺激中，大脑的某些部分受到外部磁场的影响。这可以用于研究大脑功能，但也有可能有助于治疗抑郁症等疾病。了解经颅磁刺激及其对大脑的影响是一个重要的研究领域，新图书馆将成为雷丁大学综合神经科学和神经动力学中心进行经颅磁刺激数值模拟的重要组成部分。该库不仅对医学成像应用很有趣，而且可以用于不同的领域，如声学噪声设计或电磁应用。我们将在项目结束时组织一次外展活动，向广泛的英国工程公司展示该图书馆，并支持他们在自己的应用程序中采用新的软件包。

Many modern applications, such as in acoustic noise computations, medical imaging or radar require the solution of complex mathematical models over domains with homogeneous material properties. Consider for example radar scattering from an airplane. The way in which electromagnetic waves are scattered off a plane is only determined by the shape and material of the surface of the plane and not by the surrounding homogeneous medium (the air). Hence, we can reduce the three dimensional model of simulating the electromagnetic waves in the surrounding of a plane to a computation over the two dimensional surface (the boundary) of the plane.Computing solutions of such boundary problems is the task of a boundary element method (BEM). If a computational model can be reformulated as a boundary problem BEM can lead to a significant reduction of the computational complexity since instead of the whole domain only its boundary needs to be discretised. But the nature of the underlying so called boundary integral equations makes these methods more complicated to implement than domain discretisation methods, and implementations have to be carefully designed to be more efficient than domain based methods.While there are many powerful open source software libraries available for domain based methods, such as finite elements, very little software is available for boundary elements, most of which is commercial and tailored for specialised application areas. With this project we are aiming to change this situation by creating a powerful freely available and versatile boundary element library that can be used by researchers for complex simulations, but also by companies as basis for their own applications.A particular emphasis in the design of the library is being put on the support of modern computing infrastructures. In recent years there has been an explosion in computing power, driven by the advent of multicore processors and the use of powerful gaming graphics cards (GPUs) for scientific simulations. The newest generations of GPU processing boards have a peak performance of over one Teraflops for so called single precision floating point operations and still more than 500 Gigaflops in double precision. As a comparison, two of such cards in a single desktop computer allow a performance, which would have been among the top supercomputers of the world only 10 years ago. But software libraries will have to be specifically designed to take advantage of this enormous computing power. In this project we will optimize right from the start the library to give optimal performance on modern multicore and hybrid CPU/GPU computing environments.During the project we specifically focus on two challenging applications from medical imaging. The first one is Diffuse Optical Tomography (DOT). In DOT tumors such as in the breast or brain are detected by their different light absorption and scattering properties from the surrounding tissue. Certain aspects of DOT can be modeled as boundary problems and the library is going to become a core component for DOT computations at the Centre for Medical Imaging Computing at UCL. In TMS parts of the brain are influenced by an external magnetic field. This can be used to study brain functionality but also has the potential to be helpful in treating conditions such as depression. Understanding TMS and its effect on the brain is an important research area and the new library will be an essential component of the numerical simulations of TMS at the Centre for Integrative Neurosciences and Neurodynamics at Reading.The library is not only interesting for medical imaging applications, but can be used in diverse areas, such as acoustic noise design, or electromagnetic applications. We will organise an outreach event at the end of the project to present the library to a wide range of UK engineering companies and to support them in adopting the new software packages into their own applications.