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 language | English (US) |
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Pages (from-to) | 1743-1763 |
Number of pages | 21 |
Journal | Computers and Mathematics with Applications |
Volume | 72 |
Issue number | 7 |
DOIs | |
State | Published - Sep 19 2016 |
Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2022-06-08Acknowledgements: Portuguese FCT funding under grant SFRH/BPD/79986/2011 and a KAUST Visiting Scholarship at OCCAM in the University of Oxford are acknowledged.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics