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

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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.