Mixed precision techniques in numerical simulations

离散元方法（DEM）模拟了大量刚性、不可压缩物体之间的相互作用。主流的DEM代码侧重于分析形状（球体，椭球，…），以简化物体之间接触的识别。然而，这一步继续主导着模拟时间。我们研究混合精度、异构编程和数据结构工程技术来解决这些性能热点，并使模拟能够使用非分析的，即三角形状。我们研究如何将数据存储和交换格式从计算格式中分离出来，从而减少检查冲突时需要访问的内存。接下来，我们将研究异构计算的潜力，通过将计算密集型操作卸载到gpu来加速模拟，同时试图隐藏/避免在主机和设备内存之间移动数据的数据传输开销。除了异构计算方面的工作外，还将研究时间步进和集成方案，以补充现代异构系统的通信能力。所有这些步骤都以不同的精度格式实现，并且针对不同的子步骤结合了不同的精度和精度算法。最后，我们将探讨编程语言的扩展是什么样子的，使程序员能够更容易地利用我们开发的任何混合精度的好处，也就是说，我们试图概括我们的想法，使它们对更多的应用领域有益。

Discrete Element Methods (DEM) simulate the interaction of large numbers of rigid, incompressible objects with each other. Mainstream DEM codes focus on analytical shapes (spheres, ellipsoids, ...) to streamline the identification of contacts between objects. This step nevertheless continues to dominate the simulation time. We study mixed precision, heterogeneous programming and data structure engineering techniques to tackle these performance hotspots plus to enable simulations to use nonanalytical, i.e. triangulated shapes.We study how we can separate data storage and exchange formats from compute formats such that we reduce the memory that needs to be accessed to check collisions. Next we investigate the potential for heterogeneous computing to accelerate simulations by offloading compute intense operations to GPUs while trying to hide/avoid the data transfer overheads of moving data between host and device memory. Alongside the work on heterogeneous compute there will be investigations into time stepping and integration schemes that complement the communication capabilities of modern heterogeneous systems. All of these steps are realised with different precision formats and combine different precisions and precision algorithms for different substeps. Lastly, we will explore what a programming language extension looks like to enable programmers to more easily take advantage of any mixed precision benefits we develop, i.e. we try to generalise our ideas to make them beneficial for more application areas.