A massively parallel GPU‐accelerated model for analysis of fully nonlinear free surface waves

Abstract

SUMMARYWe implement and evaluate a massively parallel and scalable algorithm based on a multigrid preconditioned Defect Correction method for the simulation of fully nonlinear free surface flows. The simulations are based on a potential model that describes wave propagation over uneven bottoms in three space dimensions and is useful for fast analysis and prediction purposes in coastal and offshore engineering. A dedicated numerical model based on the proposed algorithm is executed in parallel by utilizing affordable modern special purpose graphics processing unit (GPU). The model is based on a low-storage flexible-order accurate finite difference method that is known to be efficient and scalable on a CPU core (single thread). To achieve parallel performance of the relatively complex numerical model, we investigate a new trend in high-performance computing where many-core GPUs are utilized as high-throughput co-processors to the CPU. We describe and demonstrate how this approach makes it possible to do fast desktop computations for large nonlinear wave problems in numerical wave tanks (NWTs) with close to 50/100 million total grid points in double/single precision with 4 GB global device memory available. A new code base has been developed in C++ and compute unified device architecture C and is found to improve the runtime more than an order in magnitude in double precision arithmetic for the same accuracy over an existing CPU (single thread) Fortran 90 code when executed on a single modern GPU. These significant improvements are achieved by carefully implementing the algorithm to minimize data-transfer and take advantage of the massive multi-threading capability of the GPU device.

A Fast GPU-Accelerated Mixed-Precision Strategy for Fully Nonlinear Water Wave Computations

“…1 from [8]. This is not surprisingly since the 3D finite difference operations in [8] are more expensive than the 2D operations in the present work. Still, we would expect an extension to 3D of the present solver to give results in the same range as the dedicated 3D solver.…”

“…The potential flow equations describing fully nonlinear water waves have been efficiently solved and improved from previous work [8]. A highly generic GPU-based library has been developed, not only to solve the present equations, but also a broader range of PDEs that can be well discretized in a finite difference manner.…”

“…The tool was referred to as OceanWave3D. In a recent proof-of-concept study the algorithmic strategy for the OceanWave3D model was first improved and then a massively parallel implementation was carried out and tested on a single GPU [8] with significant performance improvements. The flexible-order finite difference operators was implemented as matrix-free compact stencil operators, in order to further minimize the memory overhead of storing identical entries and avoiding the extra index tables required by traditional sparse matrix formats.…”

“…Fig. 1 is replicated from [8] and illustrates linear scalability of absolute timings as the problem size increases along with speedups relative to optimized single-threaded CPU code. Recently, a library for high-performance PDE solver proto-typing has been established and the OceanWave3D strategy was again transferred to this new library.…”

“…In recent work [8], we have demonstrated that it is now possible to significantly reduce the barriers for practical use of full potential flow theory as the modeling basis for efficient solution of coastal and offshore engineering problems. Our strategy was to do proof-of-concept by utilizing modern Graphics Processing Units (GPUs) for massively parallel computations using a heterogeneous CPU-GPU hardware setup.…”