Parallel domain discretization algorithm for RBF-FD and other meshless numerical methods for solving PDEs
Matjavz Depolli,J. Slak,Gregor Kosec +2 more
- Vol. abs/2202.01457, pp 106773-106773
TLDR
In this article , a parallel dimension-independent node positioning algorithm based on Poisson disc sampling is presented for use on shared-memory computers, such as the modern workstations with multi-core processors.Abstract:
In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on Poisson disc sampling is parallelized for use on shared-memory computers, such as the modern workstations with multi-core processors. The parallel algorithm uses a global spatial indexing method with its data divided into two levels, which allows for an efficient multi-threaded implementation. The addition of bootstrapping enables the algorithm to use any number of parallel threads while remaining as general as its sequential variant. We demonstrate the algorithm performance on six complex 2- and 3-dimensional domains, which are either of non rectangular shape or have varying nodal spacing or both. We perform a run-time analysis of the algorithm, to demonstrate its ability to reach high speedups regardless of the domain and to show how well it scales on the experimental hardware with 16 processor cores. We also analyse the algorithm in terms of the effects of domain shape, quality of point placement, and various parallelization overheads. read more
Citations
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Journal Article
Refined RBF-FD analysis of non-Newtonian natural convection
Miha Rot,Gregor Kosec +1 more
TL;DR: In this paper , a refined RBF-FD solution for a non-Newtonian fluid in a closed differentially heated cavity is presented, which is governed by three coupled nonlinear partial differential equations, namely heat transport, momentum transport and mass continuity.
Proceedings ArticleDOI
Stability analysis of RBF-FD and WLS based local strong form meshless methods on scattered nodes
Mitja Jančič,Gregor Kosec +1 more
TL;DR: In this paper , the radial basis function generated finite differences (RBF-FD) and weighted least squares (WLS) algorithms are compared on a two-and three-dimensional domain.
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A meshless multiscale method for simulating hemodynamics
TL;DR: In this article , a localized Radial Basis Function (RBF) collocation meshless flow solver is developed and tightly coupled to a 0D Lumped-Parameter Model (LPM) for solution of the peripheral circulation.
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Volume and Mass Conservation in Lagrangian Meshfree Methods
TL;DR: In this article , the authors introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in mesh-free collocation methods, and introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation.
Proceedings ArticleDOI
A hybrid RBF-FD and WLS mesh-free strong-form approximation method
TL;DR: In this article , a local mesh-free strong-form method that combines the stability of RBF-FD with the computational effectiveness of Diffuse Approximation Method (DAM), forming a so-called hybrid method was proposed.
References
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