On the nonlinear Dirichlet-Neumann method and preconditioner for Newton's method

by   Faycal Chaouqui, et al.

The Dirichlet-Neumann (DN) method has been extensively studied for linear partial differential equations, while little attention has been devoted to the nonlinear case. In this paper, we analyze the DN method both as a nonlinear iterative method and as a preconditioner for Newton's method. We discuss the nilpotent property and prove that under special conditions, there exists a relaxation parameter such that the DN method converges quadratically. We further prove that the convergence of Newton's method preconditioned by the DN method is independent of the relaxation parameter. Our numerical experiments further illustrate the mesh independent convergence of the DN method and compare it with other standard nonlinear preconditioners.


page 1

page 2

page 3

page 4


Global monotone convergence of Newton-like iteration for a nonlinear eigen-problem

The nonlinear eigen-problem Ax+F(x)=λ x is studied where A is an n× n ir...

A full approximation scheme multilevel method for nonlinear variational inequalities

We present the full approximation scheme constraint decomposition (FASCD...

A randomized Newton's method for solving differential equations based on the neural network discretization

We develop a randomized Newton's method for solving differential equatio...

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

Substructured domain decomposition (DD) methods have been extensively st...

Algorithm MGB to solve highly nonlinear elliptic PDEs in Õ(n) FLOPS

We introduce Algorithm MGB (Multi Grid Barrier) for solving highly nonli...

The q-Levenberg-Marquardt method for unconstrained nonlinear optimization

A q-Levenberg-Marquardt method is an iterative procedure that blends a q...

Please sign up or login with your details

Forgot password? Click here to reset