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Journal of Scientific Computing

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01-04-2021

Monomial Augmentation Guidelines for RBF-FD from Accuracy Versus Computational Time Perspective

Authors: Mitja Jančič, Jure Slak, Gregor Kosec

Published in: Journal of Scientific Computing | Issue 1/2021

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Abstract

Local meshless methods using RBFs augmented with monomials have become increasingly popular, due to the fact that they can be used to solve PDEs on scattered node sets in a dimension-independent way, with the ability to easily control the order of the method, but at a greater cost to execution time. We analyze this ability on a Poisson problem with mixed boundary conditions in 1D, 2D and 3D, and reproduce theoretical convergence orders practically, also in a dimension-independent manner, as demonstrated with a solution of Poisson’s equation in an irregular 4D domain. The results are further combined with theoretical complexity analyses and with conforming execution time measurements, into a study of accuracy versus execution time trade-off for each dimension. Optimal regimes of order for given target accuracy ranges are extracted and presented, along with guidelines for generalization.

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Title: Monomial Augmentation Guidelines for RBF-FD from Accuracy Versus Computational Time Perspective
Authors: Mitja Jančič
Jure Slak
Gregor Kosec
Publication date: 01-04-2021
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2021
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01401-y

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