TY - JOUR
T1 - Trust-region methods for nonlinear elliptic equations with radial basis functions
AU - Bernal, Francisco
N1 - KAUST Repository Item: Exported on 2022-06-08
Acknowledgements: 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.
PY - 2016/9/19
Y1 - 2016/9/19
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/678723
UR - https://linkinghub.elsevier.com/retrieve/pii/S0898122116304060
UR - http://www.scopus.com/inward/record.url?scp=84991233364&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2016.07.014
DO - 10.1016/j.camwa.2016.07.014
M3 - Article
SN - 0898-1221
VL - 72
SP - 1743
EP - 1763
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 7
ER -