Optimization Techniques for Explicit Methods for GPU-Accelerated Solution of Initial Value Problems of Ordinary Differential Equations (OTEGO)

图形处理单元（GPU）越来越多地用于加速计算密集型应用，例如，在科学计算领域，通过利用大规模并行。该项目旨在研究常微分方程组初值问题（IVP）的显式求解方法在GPU上的并行实现。在该项目的第一阶段，开发了一个系统的一般方法的优化和自适应的ODE方法，这是基于数据流图表示的方法，适用于任意显式ODE方法。自适应的目标是在给定的GPU硬件上达到给定IVP的最佳运行时间，从而达到性能的可移植性。单GPU以及同构多GPU集群被视为目标平台。在第一阶段结果的基础上，第二阶段研究新的优化技术，提高求解器的自适应能力。这包括自动生成与方法系数和ODE系统的访问距离相适应的专用实现变体。特别是对于访问距离有限的ODE系统，研究了在一个时间步和几个时间步的阶段上扩展的时间和空间平铺策略。目标平台的范围扩展到异构多GPU集群，包括可用的CPU内核。

Graphics Processing Units (GPUs) are used increasingly to accelerate compute intensive applications, e.g., in the domain of scientific computing, by exploiting massive parallelism. The project proposed investigates parallel implementations of explicit solution methods for initial value problems (IVPs) of systems of ordinary differential equations (ODEs) on GPUs. In the first phase of the project, a systematic general approach for the optimization and self-adaptation of ODE methods was developed, which is based on a representation of the methods by data flow graphs and which is applicable to arbitrary explicit ODE methods. The goal of the self-adaptation is to reach the best possible runtime for the given IVP to be solved on the given GPU hardware and, thus, to reach portability of performance. Single GPUs as well as homogeneous multi-GPU clusters were considered as target platforms. Building on the results of the first phase, the second phase investigates new optimization techniques and improves the self-adaptation capabilities of the solvers. This includes the automatic generation of specialized implementation variants which are adapted to the method coefficients and the access distance of the ODE system. In particular for ODE systems with limited access distance, temporal and spatial tiling strategies which extend over the stages of a time step and over several time steps are investigated. The range of target platforms is extended to heterogeneous multi-GPU clusters, including the available CPU cores.