Open this publication in new window or tab >>2024 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 98, no 1, article id 30Article in journal (Refereed) Published
Abstract [en]
Radial basis function methods are powerful tools in numerical analysis and have demonstrated good properties in many different simulations. However, for time-dependent partial differential equations, only a few stability results are known. In particular, if boundary conditions are included, stability issues frequently occur. The question we address in this paper is how provable stability for RBF methods can be obtained. We develop a stability theory for global radial basis function methods using the general framework of summation-by-parts operators often used in the Finite Difference and Finite Element communities. Although we address their practical construction, we restrict the discussion to basic numerical simulations and focus on providing a proof of concept.
Place, publisher, year, edition, pages
SPRINGER/PLENUM PUBLISHERS, 2024
Keywords
Global radial basis functions; Time-dependent partial differential equations; Energy stability; Summation-by-part operators
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-199892 (URN)10.1007/s10915-023-02427-8 (DOI)001137638500001 ()
Note
Funding agencies; Open Access funding enabled and organized by Projekt DEAL. JG was supported by AFOSR #F9550-18-1-0316 and ONR MURI #N00014-20-1-2595. JN was supported by Vetenskapsrådet, Sweden grant 2018-05084 VR and 2021-05484 VR, and the University of Johannesburg. PÖ was supported by the Gutenberg Research College, JGU Mainz.
2024-01-032024-01-032024-01-24