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DEM代码侧重于解析形状(球体、椭球体等)以简化对象之间接触的识别。然而，这一步继续主导着模拟时间。我们研究了混合精度、异质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解析型，即三角化形状。我们研究了如何将数据存储和交换格式与计算格式分开，从而减少需要访问以检查冲突的内存。接下来，通过将计算密集型操作卸载到GPU，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，我们研究了异质计算加速模拟的潜力。除了关于异质计算的工作外，还将对补充现代异质系统通信能力的时间推进和集成方案进行调查。所有这些步骤都以不同的精度格式实现，并针对不同的子步结合了不同的精度和精度算法。最后，我们将探索编程语言扩展是什么样子，使程序员能够更容易地利用我们开发的任何混合精度优势，即我们试图概括我们的想法，使它们适用于更多的应用领域。

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.