Trust-region methods for nonlinear elliptic equations with radial basis functions

Francisco Bernal

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We consider the numerical solution of nonlinear elliptic boundary value problems with Kansa's method. We derive analytic formulas for the Jacobian and Hessian of the resulting nonlinear collocation system and exploit them within the framework of the trust-region algorithm. This ansatz is tested on semilinear, quasilinear and fully nonlinear elliptic PDEs (including Plateau's problem, Hele–Shaw flow and the Monge–Ampère equation) with excellent results. The new approach distinctly outperforms previous ones based on linearization or finite-difference Jacobians.
Original languageEnglish (US)
Pages (from-to)1743-1763
Number of pages21
JournalComputers and Mathematics with Applications
Volume72
Issue number7
DOIs
StatePublished - Sep 19 2016
Externally publishedYes

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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