Energy-stable global radial basis function methods on summation-by-parts form

2022/04/07 by Jan Glaubitz, Jan Nordström, Glaubitz, Jan +3 · 2 citations
Engineering · #65D12 #65D25 #65N12 #65N35 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2204.03291

openalex publication_date 2022/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 and construct energy-stable radial basis function methods using the general framework of summation-by-parts operators often used in the Finite Difference and Finite Element communities.

Cited by

• Two-step Generalized RBF-Generated Finite Difference Method on Manifolds
• Towards provable energy-stable overset grid methods using sub-cell summation-by-parts operators

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