high performance computing on graphics processing units: hgpu.org

In this chapter, we present details of a heterogenous and massively parallel GPU library implementation in CUDA C/C++ of a nonlinear free surface water wave model [15]. We describe how flexible-order finite difference approximations to the partial differential equations of the model can be proto- typed using library components provided in an in-house library. In this library hardware-specific implementation details are hidden via template-based com- ponents, as described in chapter 1. We provide details of the modelling basis and important unique numerical properties which has been made tuneable to create a powerful tool that can be tailored for specific purposes in engineer- ing analysis. The model is based on unified potential flow theory, and can be applied in scientific applications related to maritime engineering. It can be applied for cost-efficient estimation of wave propagation and transforma- tion of irregular multidirectional waves over variable depth, kinematics and structural wave loads over large areas and scales.
A main motivation of this work is to deliver exceptional performance to minimize calculation times, using modern parallel hardware technologies in combination with a proper choice of discretization methods and data-local al- gorithms. Data-local algorithms with optimal complexity, such that work and memory requirements grow (scale) linearly with problem size on any hardware system. For the wave model this is achieved by explicit time integration and iterative solution of a large non-symmetric and sparse linear σ-transformed Laplace problem. For the latter, we use an iterative Preconditioned Defect Correction (PDC) method, accelerated using a geometric multigrid precondi- tioning strategy. We use modern programming paradigms in the form of MPI and CUDA for development of a novel massively parallel wave modelling tool, executable on modern heterogenous many-core hardware.
One purpose of the developed numerical model is to perform hydrodynamic calculations in computationally intensive interactive real-time simulations. Re- alistic simulations are, with present technology and available computational resources, a tremendous challenge in this setting. Yet, our aim is to take a first step in this direction, and compute first-order accurate hydrodynamics for near-realistic simulations of unsteady ship-wave dynamics in a large ship simulator, used for training purposes in seakeeping operations. For this type of application, a mandatory ingredient for real-time and interactive simulation is a truly high-performance parallel implementation to ensure data process- ing in time for interactive visualization and responses. Details of the model properties, implementation, and promising novel combinations of techniques and algorithms for acceleration of performance are presented. Numerical experiments and benchmarks are provided to demonstrate the accuracy and efficiency of the model across recent generations of many-core CUDA-enabled hardware.