RT Journal Article
T1 Trust-region methods for nonlinear elliptic equations with radial basis functions
A1 Bernal Martínez, Francisco Manuel
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.
PB Elsevier
SN 0898-1221
YR 2016
FD 2016-10
LK https://hdl.handle.net/10016/32113
UL https://hdl.handle.net/10016/32113
LA eng
NO Portuguese FCT funding under grant SFRH/BPD/79986/2011 and a KAUST Visiting Scholarship at OCCAM in the University of Oxford are acknowledged.
DS e-Archivo
RD 1 sept. 2024