GPU accelerated RBF-FD solution of Poisson's equation
Mitja Jan\v{c}i\v{c}, Jure Slak, Gregor Kosec
TL;DR
This paper presents a GPU-accelerated method for solving Poisson's equation using RBF-FD on scattered nodes in 2D, analyzing how different orders impact computational efficiency.
Contribution
It introduces a GPU implementation of RBF-FD for Poisson's equation and examines the influence of polynomial order on acceleration performance.
Findings
GPU acceleration improves solution speed
Higher orders affect computational efficiency
Method is robust for scattered nodes
Abstract
The Radial Basis Function-generated finite differences became a popular variant of local meshless strong form methods due to its robustness regarding the position of nodes and its controllable order of accuracy. In this paper, we present a GPU accelerated numerical solution of Poisson's equation on scattered nodes in 2D for orders from 2 up to 6. We specifically study the effect of using different orders on GPU acceleration efficiency.
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Taxonomy
TopicsNumerical methods in engineering · Fluid Dynamics Simulations and Interactions · Advanced Numerical Methods in Computational Mathematics