A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels

Pankaj K. Mishra*, Gregory E. Fasshauer, Mrinal K. Sen, Leevan LING

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

35 Citations (Scopus)


Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless implementation and is referred to as the radial basis-generated finite difference (RBF-FD) method. In this paper, we propose a stabilized RBF-FD approach with a hybrid kernel, generated through a hybridization of the Gaussian and cubic RBF. This hybrid kernel was found to improve the condition of the system matrix, consequently, the linear system can be solved with direct solvers which leads to a significant reduction in the computational cost as compared to standard RBF-FD methods coupled with present stable algorithms. Unlike other RBF-FD approaches, the eigenvalue spectra of differentiation matrices were found to be stable irrespective of irregularity, and the size of the stencils. As an application, we solve the frequency-domain acoustic wave equation in a 2D half-space. In order to suppress spurious reflections from truncated computational boundaries, absorbing boundary conditions have been effectively implemented.

Original languageEnglish
Pages (from-to)2354-2368
Number of pages15
JournalComputers and Mathematics with Applications
Issue number9
Publication statusPublished - 1 May 2019

Scopus Subject Areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

User-Defined Keywords

  • Ill-conditioning
  • Partial differential equations
  • Radial basis functions
  • RBF-FD


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