Implementation of a scalable, performance portable shallow water equation solver using radial basis function-generated finite difference methods

Abstract

In this article, we describe and analyze the computational performance of a parallel shallow water equation (SWE) solver for atmospheric simulation using radial basis function-finite difference (RBF-FD) methods. The inherent "meshless" nature of RBF-FD methods provides significant numerical benefits over standard pseudospectral and traditional FD methods, but there are many challenges in terms of their performance and parallel implementation, due to RBF-FDs use of relatively large halos and unstructured indexing. With the use of reverse Cuthill-McKee node ordering and tiled transposition of the state variable matrices and RBF-FD differentiation matrices, these challenges were overcome. The RBF-FD solver was implemented for the SWE on the rotating sphere using message passing interface plus OpenMP/OpenACC to demonstrate scalability and performance portability on the three currently dominant high performance computing (HPC) architectures, namely, Intel Xeon multicore, Intel Xeon Phi manycore, and NVIDIA graphics processing unit systems.

Micro-combustion modelling with RBF-FD: A high-order meshfree method for reactive flows in complex geometries

“…Over the last decades, RBF-FD methods have been successfully applied to a wide range of problems in science and engineering. Some of the application areas include the geosciences [16,17,18], combustion modelling [19,20], PDEs on surfaces [21,22,23], interface [24,25] and contact [26] problems, as well as scalable high-performance implementations [27,28,29]. For a complete list of references see monograph [14].…”

An adaptive Particle-In-Cell method for liquid simulation using RBF-FD

“…Such a scheme would avoid computing the weights of already mapped stencils, thus increasing the overall performance of the method. Moreover, recent studies have shown promising solutions for solving RBF-FD stencils in parallel by using point indexing (ELLIOTT et al, 2019), which would be another alternative to be investigated for our framework.…”