[Dune] Non Linear Solver in DUNE

[Carsten Gräser]

Am 06.12.2011 19:04, schrieb Alex Evanovic:
> Hi,
> 
> I am relatively new to the functionalities of DUNE.
> 
> I want to solve a non-linear multidimensional problem. How I do it is, I
> approximate it as a quadratic & compute the hessian. Then, I do Newton
> iterations to solve it.
> 
> So, I approximate my non-linear problem as:
> 
> L (x + del (x) ) = 0.5*del(x)(transpose)* A * del(x) + b * del(x) + c
> 
> where A is the hessian.
> 
> Then I solve, A * del (x) = - b
> 
> & update x = x + del (x) for the next Newton Iteration.
> 
> *I want to know if there is a non-linear solver in DUNE, which can do
> everything for me, if I input the hessian matrix?*
There is no Newton method in the core modules
but there is one in dune-pdelab.

However it seems that you want to solve a minimization
problem and the damping strategy in the pdelab solver
looks like it is intended to minimize the defect.
This is in general not the best choice for a minimization
problem. Perhaps one of the pdelab developers can comment
if this is customizable.

Best,
Carsten