Energy-Stable Global Radial Basis Function Methods on Summation-By-Parts Form

Jan Glaubitz, Jan Nordström, Philipp Öffner

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number30
JournalJournal of Scientific Computing
Volume98
Issue number1
DOIs
Publication statusPublished - Jan 2024

Keywords

  • Energy stability
  • Global radial basis functions
  • Summation-by-part operators
  • Time-dependent partial differential equations

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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