Invariant Sets for Nonlinear Elliptic and Parabolic Systems

1980 ◽  
Vol 11 (6) ◽  
pp. 1075-1103 ◽  
Author(s):  
Hendrik J. Kuiper
Keyword(s):  
Parabolic Systems ◽  
Invariant Sets ◽  
Nonlinear Elliptic ◽  
Elliptic And Parabolic Systems

scholarly journals Quadratic convergence of Levenberg-Marquardt method for elliptic and parabolic inverse robin problems

2018 ◽  
Vol 52 (3) ◽  
pp. 1085-1107 ◽  
Author(s):  
Daijun Jiang ◽  
Hui Feng ◽  
Jun Zou
Keyword(s):  
Quadratic Convergence ◽  
Parabolic Systems ◽  
Adaptive Strategy ◽  
Nonlinear Elliptic ◽  
Highly Nonlinear ◽  
Regularization Parameters ◽  
Levenberg Marquardt ◽  
Ill Posed ◽  
First Time ◽  
Elliptic And Parabolic Systems

We study the Levenberg-Marquardt (L-M) method for solving the highly nonlinear and ill-posed inverse problem of identifying the Robin coefficients in elliptic and parabolic systems. The L-M method transforms the Tikhonov regularized nonlinear non-convex minimizations into convex minimizations. And the quadratic convergence of the L-M method is rigorously established for the nonlinear elliptic and parabolic inverse problems for the first time, under a simple novel adaptive strategy for selecting regularization parameters during the L-M iteration. Then the surrogate functional approach is adopted to solve the strongly ill-conditioned convex minimizations, resulting in an explicit solution of the minimisation at each L-M iteration for both the elliptic and parabolic cases. Numerical experiments are provided to demonstrate the accuracy, efficiency and quadratic convergence of the methods.

Simultaneous directions parallel methods for elliptic and parabolic systems

2004 ◽  
Vol 339 (2) ◽  
pp. 145-150 ◽  
Author(s):  
José R. Galo ◽  
Isidoro I. Albarreal ◽  
M. Carmen Calzada ◽  
José Luis Cruz ◽  
Enrique Fernández-Cara ◽  
...  
Keyword(s):  
Parabolic Systems ◽  
Parallel Methods ◽  
Elliptic And Parabolic Systems
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